2019年度のセミナー

Date/Place January 21st (Tue.) 15:30-16:30 / H701
Name Kodai Sakurai (KIT, Karlsruhe)
Title Radiative corrections to Higgs decays in various extended Higgs models
Abstract Current measurements by the LHC experiments have revealed that the discovered Higgs boson possesses SM-like nature. Nevertheless, this does not means that the Higgs sector of the standard model (SM) is verified. Possibilities of the extended Higgs sectors, which often appears in new physics models, still are not excluded. considering no observation of new particles, precise measurements of the discovered Higgs boson can be more and more significant. It requires accurate evaluations of the Higgs boson observables. Therefore, we have calculated radiative corrections to decay rates of the discovered Higgs boson, and the branching ratios in various extended Higgs models, such as the Higgs singlet model, 4 types of two Higgs doublet models and the inert doublet model. all analytical results have been implemented in our computation program for the discovered Higgs boson, H-COUP.
In this talk, I will describe the impact of loop contributions of additional Higgs bosons for the decay branching ratios. Also, I will discuss whether or not above extended Higgs models are discriminated by precise measurements of the branching ratios at future collider experiments. This talk is based on [arXiv:1906.10070].

 

Date/Place January 14th (Tue.) 15:30-16:30 / H601
Name Keisuke Yanagi (U. of Tokyo)
Title Dark Matter Heating vs. Rotochemical Heating in Old Neutron Stars
Abstract WIMP DMs in the Universe accumulate in neutron stars (NSs) through their interactions with nucleons. It has been known that their annihilation inside the NS core causes late-time heating, with which the surface temperature becomes T_s ≃ (2−3)×10^3 K for the NS age t>10^6−10^7 years. Thus the measurement of NS surface temperature can be used as a new probe of WIMP DMs. Because of the strong gravity of NSs, DM heating has several advantages compared to the direct detection experiments on the earth. Despite such advantages, the background on the DM heating is rarely discussed in the particle physics community. In particular, the rotochemical heating, internal heating caused by the out-of-equilibrium beta reactions in a NS, should be considered because it does not assume any exotic physics. In fact, if the rotochemical heating operates in a NS, it may conceal the DM heating effects. In this work, we reevaluate the significance of the DM heating in NSs, including the effect of the rotochemical heating. We show that the signature of DM heating can still be detected in old ordinary pulsars, and discuss what is necessary to confirm the evidence for the DM heating.

 

Date/Place January 10th (Fri.) 13:00-14:00 / H701
Name Takahiro Sagawa (U. of Tokyo)
Title Thermodynamic resource theory of quantum many-body systems and generalized quantum Stein’s lemma
Abstract Resource theory is an information-theoretic framework (or a set of ideas) to quantify “useful resources” and has attracted much attention in light of quantum information theory. Specifically, resource theory of thermodynamics attempts to characterize state convertibility from a quantum state to another one by thermodynamically feasible classes of quantum dynamics such as thermal operations and Gibbs-preserving maps. Thermodynamic resource theory has been extensively studied for small-scale systems, while its relevance to quantum many-body systems has not yet been established.
In this seminar, I will talk about our recent result [1,2] on the existence of a macroscopic thermodynamic potential even in out-of-equilibrium and fully quantum situations. We proved that asymptotic state convertibility by thermal operations is completely characterized a single thermodynamic potential, if the state is translation-invariant and spatially ergodic, and the Hamiltonian is local and translation-invariant. In general, the thermodynamic potential is given by a quantity called the spectral divergence rate, while under the above-mentioned assumptions it reduces to the Kullback-Leibler (KL) divergence rate. A main part of the proof relies on quantum hypothesis testing; we proved a generalization of the quantum Stein’s lemma beyond independent and identically distributed (i.i.d.) situations. Our result provides a mathematically rigorous foundation that a nonequilibrium thermodynamic potential emerges in the macroscopic world.
[1] P. Faist, T. Sagawa, K. Kato, H. Nagaoka, and F. G. S. L. Brandao, Phys. Rev. Lett. 123, 250601 (2019).
[2] T. Sagawa, P. Faist, K. Kato, K. Matsumoto, H. Nagaoka, and F. G. S. L. Brandao, arXiv:1907.05650.

 

Date/Place December 17th (Tue.) 15:30-16:30 / H711
Name Yukinari Sumino (Tohoku U.)
Title A geometric view of loop integral reduction by IBP recurrence relations
Abstract During the last decades, there have been remarkable developments in the technology of analytical calculations for high energy processes in particle physics. I will first review the key ingredients in the technology, which are based on reduction of complicated multiloop integrals to a small set of basis integrals by using a class of recursion relations. Then I will introduce a new idea to re-interpret the reduction procedure by developing a geometric view in terms of a generating function in a multi-dimensional space and a successive dimensional reduction algorithm.

 

Date/Place December 10th (Tue.) 15:30-16:30 / H711
Name Hiromasa Watanabe (U. of Tsukuba)
Title Partial deconfinement in gauge theories (Slides)
Abstract We discuss the existence and its properties of the partial deconfinement which is the phase SU(M) sector in SU(N) deconfines in large-N gauge theories at finite temperature. This implies that the partial deconfinement is relating to Gross-Witten-Wadia transition and the spontaneous breaking of gauge symmetry. We will also discuss the application to real QCD and the holographic-dual gravity theory as well because the concept of partial deconfinement originally proposed to understand a curious black hole.

 

Date/Place December 3rd (Tue.) 15:30-16:30 / H711
Name Atsuyuki Yamada (Nagoya U.)
Title To be, or not to be finite? The Higgs potential in Gauge-Higgs Unification (Slides)
Abstract In this seminar, we investigate the finiteness of the Higgs effective potential in an SU(N) Gauge-Higgs Unification (GHU) model defined on M^4xS^1. We obtain the Higgs effective potential at the two-loop level and find that it is finite. We also discuss that the Higgs effective potential is generically divergent for the three- or higher-loop levels. As an example, we consider an SU(N) gauge theory on M^5xS^1, where the one-loop corrections to the four-Fermi operators are divergent. We find that the Higgs effective potential depends on their counter terms at the three-loop level.

 

Date/Place November 26th (Tue.) 15:30-16:30 / H711
Name Ipsita Saha (IPMU)
Title Alignement limit in multi-Higgs doublet models (Slides)
Abstract The LHC Higgs data are showing a gradual inclination towards the standard model (SM) result, and the realization of an SM-like limit becomes essential for beyond the SM scenarios to survive. Considering the accuracy that can be achieved in future colliders, models beyond the standard model that acquire the 'alignment limit' with an SM-like Higgs boson can surpass others in the long run. In this seminar, I will explain how to realize such limit in multi-Higgs doublet models, exemplifying in particular in two and three Higgs doublet extensions. Using a convenient parametrization, I will demonstrate that the alignment limit for CP-conserving three Higgs-doublet models (3HDM) takes on the same analytic structure as that in the case of two Higgs-doublet models (2HDM). Further, I will explain how such alignment limit can be efficiently implemented in a variety of 3HDM while in 2HDM extensions how such alignment limit can also draw crucial conclusions on the model parameter space with an absolute stable potential.

 

Date/Place November 19th (Tue.) 15:30-16:30 / H711
Name Hikaru Kawai (Kyoto U.)
Title Quantum Gravity and Naturalness (Slides)
Abstract We discuss the possibility that naturalness can be understood as an effect of quantum gravity. In particular, we will consider a mechanism by which the electroweak scale is naturally obtained from the Planck scale.

 

Date/Place November 12th (Tue.) 15:30-16:30 / H711
Name Sumito Yokoo (SOKENDAI)
Title Scale invariance feature extraction of neural network
Abstract Theoretical understanding of why the Deep Neural Network (DNN) works so well is still unclear. One of possible answers to this question is that DNN extract features of the input data hierarchically through a process of coarse-graining. It reminds us of the basic concept of renormalization group (RG) in statistical physics. In order to explore possible relations between DNN and RG, we use the Restricted Boltzmann Machine (RBM) and Auto Encoder applied to Ising model and construct a flow of temperature generated by the RBM and the Auto Encoder. We show that the RBM and Auto Encoder trained by spin configurations at various temperatures generate a flow on which the temperature approaches the critical temperature Tc = 2.27 and how the flow depends on the width and depth of the RBM and the Auto Encoder. We discuss why it flows towards Tc and how the RBM and Auto Encoder contains the information of spin configurations by singular value decomposition of the weight matrices of the trained RBM and Auto Encoder.

 

Date/Place October 29th (Tue.) 15:30-16:30 / H711
Name Yuya Kusuki (YITP)
Title Fusion matrix approach to AdS/CFT
Abstract The conformal bootstrap has provided new insights into the AdS/CFT. For example, we can address the issues, “How can we derive the B-H entropy from CFT?”, “Whether does the pure AdS exist or not?”, etc. by the bootstrap. However, we are stuck with the problem of solving the bootstrap equation because of its difficulty. In this talk, we introduce a new technique to solve the bootstrap equation by utilizing the “fusion matrix”. This gives us new universal formulae other than the Cardy formula in holographic CFT. Besides the bootstrap, we would like to emphasize that there are a number of applications of the fusion matrix approach. If I have enough time, I will take an example of such applications, which addresses an interesting question in the AdS/CFT, “How does information spread in chaotic systems?”.

 

Date/Place October 15th (Tue.) 15:30-16:30 / H711
Name Seiji Terashima (YITP)
Title Classical Limit of Large N Gauge Theories with Conformal Symmetry(Slides)
Abstract We study classical limit of conformal field theories realized by large N gauge theories using the generalized coherent states. For generic large N gauge theories with conformal symmetry, we show that the classical limit of them is described by the classical Einstein gravity. This may be regarded as a kind of derivation of the AdS/CFT correspondence.

 

Date/Place October 8th (Tue.) 15:30-16:30 / H711
Name Kentaroh Yoshida (Kyoto Univ.)
Title Gravitational perturbations as TTbar deformations in the JT gravity
Abstract Recently, TTbar deformations in 2D quantum field theories have been well studied. In particular, as shown by S. Dubovsky et al, when 2D gravity is coupled, gravitational perturbations can be regarded as TTbar deformations of the matter sector and the S-matrix gets a gravitational dressing factor. In this talk, I will show that gravitational perturbations in the Jackiw-Teitelboim (JT) gravity can be seen as TTbar deformations and argue a generalization of Dubovsky et al's work from flat space to AdS_2. This is based on the collaboration 1906.03865 and a work in progress with T. Ishii, S. Okumura and J. Sakamoto.

 

Date/Place October 1st (Tue.) 15:30-16:30 / H711
Name Stefan Heusler (Munster Univ.)
Title Decoding quantum properties form classical physics: On the relation between level repulsion and periodic orbits in quantum chaos theory
Abstract Recently, the intrest in quantum chaos is increasing in various fields of physics. In quantum chaos, level repulsion is one of the fascinating properties of those quantum systems were the classical counterpart is fully chaotic. In my talk I will explain the key ideas relating classical periodic orbit theory with random matrix theory on a non-technical level.
References:
S. Heusler, S. Müller, A. Altland, P. Braun, and F. Haake (2007): „Periodic-Orbit Theory of Level Correlations”, Phys. Rev. Lett. 98, 044103
https://www.researchgate.net/publication/6447996_Periodic-Orbit_Theory_of_Level_Correlations

 

Date/Place July 30th (Tue.) 15:30-16:30 / H711
Name Frank Ferrari (Université Libre de Bruxelles)
Title CFT1, Generalized SYK Models and Holographic Boundary Condition Changing Operators
Abstract Because there is no rotational symmetry in one dimension, two-point functions in CFT1 can be governed by two *distinct* critical exponents when t goes to plus or minus infinity. I will explain how this behaviour is found in natural generalizations of the standard complex SYK model and I will compute the associated critical exponents in this context. I will then introduce a new class of operators in holography, whose effect is to change the boundary conditions of bulk fields at the boundary of AdS, switching between so-called “standard” and “alternate” quantization schemes. In the case of AdS2/CFT1, these operators are local. I will explain how to compute their critical dimensions and argue that their two-point functions are governed in general by two distinct exponents.

 

Date/Place July 23th (Tue.) 15:30-16:30 / H711
Name So Chigusa (U. of Tokyo)
Title Indirect Studies of Electroweakly Interacting Particles at 100 TeV Hadron Colliders (Slides)
Abstract There are many models beyond the standard model which include electroweakly interacting massive particles (EWIMPs), often in the context of the dark matter. We study the indirect search of EWIMPs using a precise measurement of the lepton pair production cross sections at future 100 TeV hadron colliders. It is revealed that this search strategy is suitable in particular for Higgsino and that the Higgsino mass up to about 850 GeV will be covered at 5 sigma level irrespective of the chargino and neutralino mass difference. We also show that the property of the observed signal, in particular its weak charges and mass, can be independently read off by using both the neutral and charged current processes.

 

Date/Place July 16th (Tue.) 15:30-16:30 / H711
Name Kazuyuki Kanaya (Tsukuba U.)
Title QCD Thermodynamics with Gradient Flow (Slides)
Abstract The gradient flow introduced by Narayanan, Neuburger and Luescher has caused various drastic improvements in lattice evaluation of physical observables. Among them, we are applying a method developed by Hiroshi Suzuki in 2013. This is a general method based on the gradient flow to calculate any renormalized observables on the lattice. In particular, the method is applicable also to observables whose base symmetry is broken by the lattice regularization. Suzuki developed the method to calculate the energy-momentum tensor which is based on the Poincare invariance. We apply it to QCD with Wilson-type quarks to cope with the problems associated with the explicit violation of the chiral symmetry. From a study of finite-temperature QCD with 2+1 flavors of improved Wilson quarks, we found that the method works quite well. I report also on the status of our recent effort to calculate thermodynamic quantities just at the physical point.

 

Date/Place July 10th (Wed.) 12:10-13:10 / H711
Name Ya Zhang (Peking U./Osaka U.)
Title Choosing the right SM-EFT operator basis (Slides)
Abstract The Standard Model Effective Field Theory (SM-EFT) is a good framework to describe the new heavy particle degrees, and there are several operator bases commonly used which are believed to be equivalent to each other. However, the interpretation of possible deviations turns out to be basis-dependent, and we use the unitary constraints which are the largest possible deviations theoretically allowed to illustrate this point. The results suggest that one should choose the operator basis consistent with the possible UV scenario one believes in.

 

Date/Place July 9th (Tue.) 15:30-16:30 / \ H711
Name Tomohiro Matsuda (Saitama Inst. Tech.)
Title Non-perturbative baryogenesis and the resurgence (Slides)
Abstract After inflation the inflaton starts to oscillate and reheats the Universe. Non-perturbative particle production caused by the oscillation is called preheating. The non-perturbative particle production uses Bogoliubov transformation, which can be related to the mixing between plus and minus sign asymptotic solutions. Mathematically, such mixing is given by a connection formula of the differential equation. Our focus is the origin of the matter/antimatter asymmetry of the scenario. To analyze the asymmetry, we use the exact WKB analysis and the connection formula of Voros. This shows how to calculate (exact) particle production when interaction is introduced. Our result reveals that singularities of the equation, which is related to time-dependent baryon number violating interaction, is responsible for the asymmetry.

 

Date/Place June 25th (Tue.) 15:30-16:30 / H711
Name Masaaki Tomii (Columbia Univ.)
Title Non-perturbative conversion of Wilson coefficients from four-flavor to three-flavor theories using lattice QCD (Slides)
Abstract The first lattice result for direct CP violation in $K \to \pi\pi$ decay in the Standard Model published by RBC/UKQCD in 2015 is desired to be more precise to see the deviation from the experimental value more clearly. In this talk, I will overview RBC/UKQCD’s calculation of $K \to \pi\pi$ matrix elements mentioning a particular error source: Since RBC/UKQCD calculated the matrix elements with the four-quark operators in the three-flavor theory, we need the corresponding Wilson coefficients in the three-flavor theory, which can be obtained by converting from the four-flavor theory. Since the perturbative conversion needs to be done below the charm threshold, where perturbative calculation is not precise, it can cause a significant uncertainty. In fact, it resulted in one of the biggest systematic uncertainties in the previous work. To resolve this problem, we are trying to do this conversion in a non-perturbative prescription using lattice QCD. I will explain the strategy of the conversion and show some results of an exploratory calculation.

 

Date/Place June 18th (Tue.) 15:30-16:30 / H711
Name Kei Yagyu (Osaka U.)
Title Strong dynamics as an origin of the light Higgs boson and BSM phenomena (Slides)
Abstract The discovered Higgs boson with a mass of 125 GeV could be a pseudo Nambu-Goldstone boson originated from strong dynamics. In this scenario, the so-called composite Higgs scenario, we can naturally explain the smallness of the Higgs boson mass as compared with a typical new physics scale; i.e., O(1-10) TeV. In my talk, first I introduce the minimal composite Higgs model, and explain how the light Higgs boson is induced from strong dynamics. I then discuss composite Higgs models which introduce non-minimal Higgs sectors at the EW scale, and show some properties of Higgs bosons such as a mass spectrum, coupling constants and so on. I will also talk some prospects of my future work about the connection between composite Higgs models and BSM phenomena.

 

Date/Place June 11th (Tue.) 15:30-16:30 / H711
Name Christian Rohrhofer (Osaka U.)
Title Lattice QCD and the High Temperature Phase (Slides)
Abstract After a short introduction to lattice QCD at finite temperature I will discuss some general properties of the chiral phase transition and aspects of confinement. I will present the evolution o\ f symmetries in the hadronic spectrum for two flavor QCD. Chiral and U(1) axial symmetry are found to be restored above the critcal temperature, and an additional SU(2)_CS symmetry is observed wit\ hin a temperature window. This symmetry is absent in vacuum QCD as well as for non-interacting quarks and could help to understand the effective degrees of freedom for high temperature QCD.

 

Date/Place June 11th (Tue.) 13:00-14:00 / H711
Name Yasunori Nomura (UC Berkeley)
Title Quantum Mechanics of an Evaporating Black Hole (Slides)
Abstract A coherent picture of the quantum mechanics of a collapse-formed, evaporating black hole is presented. In a distant frame, semiclassical theory in the zone describes microscopic dynamics of only the "hard modes," the modes that are hard enough to be discriminated in the timescale of Hawking emission. The thermal nature of these modes arises from microcanonical typicality of the full black hole degrees of freedom, mostly composed of the "soft modes," the modes that cannot be discriminated at the semiclassical level. The hard modes are purified by a combined system of the soft modes and early Hawking radiation, but not by either of them separately. This intrinsically tripartite structure of entanglement is general, regardless of the age of the black hole. The interior spacetime emerges only at a coarse-grained level. To describe it, an effective theory can be erected at each time, which applies only to a limited spacetime region determined by the time at which the theory is erected. The entire interior of the black hole can be described only using multiple effective theories erected at different times, realizing the idea of complementarity. We analyze implications of the entanglement structure described here for various phenomena, including Hawking evaporation and general information retrieval. For multiple entangled black holes, it implies that semiclassical objects dropped into different black holes cannot meet in the interior, although each object smoothly enters the horizon of the black hole to which it is falling. We also discuss physics in Rindler space, elucidating how it is obtained as a smooth limit of the black hole physics.

 

Date/Place June 4th (Tue.) 15:30-16:30 / H711
Name Dongmin Gang (KIAS)
Title Magnetically charged AdS4 black hole from M5-branes (Slides)
Abstract In this talk, I consider a magnetically charged AdS4 black hole which is made of N M5-branes wrapped on M3(hyperbolic 3-manifold)*Sigma_g (Riemann surface of genus g). By computing vacuum degeneracy of the system at large N, we give a microscopic derivation of the Bekenstein-Hawking entropy of the black hole. By studying sub-leading corrections to the vacuum degeneracy in 1/N, we present perturbative quantum corrections to the Bekenstein-Hawking entropy.

 

Date/Place May 28th (Tue.) 15:30-16:30 / H711
Name Michal P. Heller (Max Planck Institute for Gravitational Physics (Albert Einstein Institute) / National Centre for Nuclear Research)
Title Path integral optimization as circuit complexity(Slides)
Abstract Early efforts to understand complexity in field theory have primarily employed a geometric approach based on the concept of circuit complexity in quantum information theory. In a parallel vein, it has been proposed that certain deformations of the Euclidean path integral that prepares a given operator or state may provide an alternative definition, whose connection to the standard notion of complexity is less apparent. In this talk, I will bridge the gap between these two proposals in two-dimensional conformal field theories, by explicitly showing how the latter approach from path integral optimization may be given a concrete realization within the standard gate counting framework. In particular, I will show that when the background geometry is deformed by a Weyl rescaling, a judicious gate counting allows one to recover the Liouville action as a particular choice within a more general class of cost functions. Based on 1904.02713.

 

Date/Place May 21st (Tue.) 15:30-16:30 / H711
Name Katsumasa Nakayama (Osaka U.)
Title Lattice field theory for QCD and tensor representation (Slides)
Abstract In this talk I will introduce my recent studies and what I am interested in. For QCD, I apply the lattice formulation to calculate physical values such as the charm quark mass $m_c$ and the strong coupling constant $\alpha_s$. I focus on the perturbative regime such as the short-distance correlators and Dirac eigenvalue density in the high eigenvalue regimes. In order to reduce systematic errors, I use the generalized Domain-wall fermion formulation. For Tensor representation, I would like to show you an aspect of this topic in the context of the lattice field theory. Recently, this topic receives people's attention with the tensor renormalization group method, worm algorithm, and sign-problem. After the brief review of these works, I give you an explanation of my work on Supersymmetric quantum mechanics.

 

Date/Place May 14th (Tue.) 15:30-16:30 / H711
Name C-P Yuan (Michigan State U.)
Title Soft gluon resummation effect for processes with final state jets (Slides)
Abstract I will discuss the effect of multiple soft gluon emission to the differential distributions of di-jet production and various W, Z, top quark and Higgs boson production processes at the LHC, by applying the transverse momentum resummation formalism. I will focus on what the soft gluon resummation is and why the resummation calculation is needed to compare to data.

 

Date/Place May 7th (Tue.) 15:30-16:30 / H711
Name Yoshinori Matsuo (Osaka U.)
Title Vacuum energy and apparent horizon of evaporating black holes (Slides)
Abstract Static spherically symmetric black-hole-like solutions to the semi-classical Einstein equation are studied. We show that there are no divergences around the Schwarzschild radius even for the Boulware vacuum, if the back reaction from the vacuum energy is taken into account. The solutions have no event horizon. Instead, there is a local minimum in the radius, like geometries around the neck of the wormhole. This effect of the vacuum energy plays a crucial role in a small neighborhood of the apparent horizon of evaporating black holes. The local minimum of the radius becomes the apparent horizon when the black hole is evaporating by the Hawking radiation. Information can get away from the apparent horizon since it is time-like because of the negative vacuum energy.

 

Date/Place Apr. 23rd (Tue.) 15:30-16:30 / H711
Name Hiroyuki Ishida (KEK)
Title Sneutrino dark matter in a SUSY inverse seesaw model (Slides)
Abstract In this talk, I will introduce a supersymmetric inverse seesaw model where three kinds of additional super multiplets are introduced into the MSSM. Two of them are usual singlet-like super multiplets to realize inverse seesaw mechanism and the last one is introduced to generate lepton number violation dynamically. All the scales in the model are set around the electroweak scale. Thanks to existing the origin of lepton number violation, sneutrino dark matter can be resonantly annihilate into visible particles and thermal relic abundance can be matched with observation.

 

Date/Place Apr. 16th (Tue.) 15:30-16:30 / H711
Name Natsumi Nagata (U. of Tokyo)
Title Limit on the Axion Decay Constant from the Cooling Neutron Star in Cassiopeia A (Slides)
Abstract The observed rapid cooling of the neutron star (NS) located at the center of the supernova remnant Cassiopeia A (Cas A) can be explained in the minimal NS cooling scenario. This consequence may be changed if there exists an extra cooling source, such as axion emission. In this talk, I will first give a brief review on the standard NS cooling theory. I will then discuss the Cas A NS cooling in the presence of axion emission. It turns out that we can obtain a lower limit on the axion decay constant from the Cas A NS cooling observation, which is as strong as existing limits set by other astrophysical observations such as SN1987A.

 

Date/Place Apr. 9th (Tue.) 15:30-16:30 / H711
Name Yu Nakayama (Rikkyo U.)
Title Realization of impossible anomalies (Slides)
Abstract In this talk, I discuss how (not) to realize impossible anomalies. The Wess-Zumino consistency condition allows more exotic forms of anomalies than those we usually encounter such as CP odd Pontryagin density in four-dimensional Weyl anomaly. These are apparently impossible because they cannot correspond to any (unregularized) conformally invariant correlation functions. I want to argue that this no-go argument may be a red herring. I show that some of these impossible anomalies avoid the no-go argument because they are not primary operators, and the others circumvent it because they are realized as semi-local terms as is the case with the conformally invariant Green-Schwartz mechanism and in the higher dimensional analogue of Liouville or linear dilaton theory.

 

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