scholarly journals One-loop partition function, gauge accessibility and spectra in AdS3 gravity

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Joel Acosta ◽  
Alan Garbarz ◽  
Andrés Goya ◽  
Mauricio Leston
Keyword(s):  
Partition Function ◽  
Essential Spectrum ◽  
Integrability Condition ◽  
Gauge Condition ◽  
Rank 2 ◽  
The One ◽  
Square Integrability ◽  
Isolated Eigenvalues ◽  
Asymptotically Hyperbolic ◽  
Metric Fluctuations

Abstract We continue the study of the one-loop partition function of AdS3 gravity with focus on the square-integrability condition on the fluctuating fields. In a previous work we found that the Brown-Henneaux boundary conditions follow directly from the L2 condition. Here we rederive the partition function as a ratio of Laplacian determinants by performing a suitable decomposition of the metric fluctuations. We pay special attention to the asymptotics of the fields appearing in the partition function. We also show that in the usual computation using ghost fields for the de Donder gauge, such gauge condition is accessible precisely for square-integrable ghost fields. Finally, we compute the spectrum of the relevant Laplacians in thermal AdS3, in particular noticing that there are no isolated eigenvalues, only essential spectrum. This last result supports the analytic continuation approach of David, Gaberdiel and Gopakumar. The purely essential spectra found are consistent with the independent results of Lee and Delay of the essential spectrum of the TT rank-2 tensor Lichnerowickz Laplacian on asymptotically hyperbolic spaces.

scholarly journals Towards the classification of rank-r $$ \mathcal{N} $$ = 2 SCFTs. Part I. Twisted partition function and central charge formulae

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Mario Martone
Keyword(s):  
Partition Function ◽  
Central Charge ◽  
Singular Locus ◽  
Companion Paper ◽  
Coulomb Branch ◽  
Energy Limit ◽  
Superconformal Field Theories ◽  
Rank 2 ◽  
Explicit Formulae

Abstract We derive explicit formulae to compute the a and c central charges of four dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of $$ \mathcal{N} $$ N = 2 SCFTs which culminate with our $$ \mathcal{N} $$ N = 2 UV-IR simple flavor condition. This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d $$ \mathcal{N} $$ N = 2 SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper.This manuscript is dedicated to the memory of Rayshard Brooks, George Floyd, Breonna Taylor and the countless black lives taken by US police forces and still awaiting justice. Our hearts are with our colleagues of color who suffer daily the consequences of this racist world.

scholarly journals Gauge theories on compact toric manifolds

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Francesco Fucito ◽  
Jose Francisco Morales ◽  
Massimiliano Ronzani ◽  
Ekaterina Sysoeva ◽  
...  
Keyword(s):  
Partition Function ◽  
Gauge Theories ◽  
Blow Up ◽  
Gauge Coupling ◽  
Piecewise Constant Function ◽  
Partition Functions ◽  
Piecewise Constant ◽  
Toric Manifolds ◽  
Holomorphic Anomaly ◽  
The One

AbstractWe compute the $$\mathcal{N}=2$$ N = 2 supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the Kähler form with jumps along the walls where the gauge symmetry gets enhanced. The partition function on such manifolds is written as a sum over the residues of a product of partition functions on $$\mathbb {C}^2$$ C 2 . The evaluation of these residues is greatly simplified by using an “abstruse duality” that relates the residues at the poles of the one-loop and instanton parts of the $$\mathbb {C}^2$$ C 2 partition function. As particular cases, our formulae compute the SU(2) and SU(3) equivariant Donaldson invariants of $$\mathbb {P}^2$$ P 2 and $$\mathbb {F}_n$$ F n and in the non-equivariant limit reproduce the results obtained via wall-crossing and blow up methods in the SU(2) case. Finally, we show that the U(1) self-dual connections induce an anomalous dependence on the gauge coupling, which turns out to satisfy a $$\mathcal {N}=2$$ N = 2 analog of the $$\mathcal {N}=4$$ N = 4 holomorphic anomaly equations.

scholarly journals Spectrum of the M5-traveling waves

2020 ◽  
Vol 15 ◽  
pp. 66
Author(s):  
Salvador Cruz-García
Keyword(s):  
Essential Spectrum ◽  
Traveling Waves ◽  
Imaginary Axis ◽  
Weighted Space ◽  
Cell Movement ◽  
Mesenchymal Cell ◽  
Weight Functions ◽  
Dimensional Version ◽  
The One ◽  
Linearized Operator

In this paper, we study the essential spectrum of the operator obtained by linearizing at traveling waves that occur in the one-dimensional version of the M5-model for mesenchymal cell movement inside a directed tissue made up of highly aligned fibers. We show that traveling waves are spectrally unstable in L2(ℝ; ℂ3) as the essential spectrum includes the imaginary axis. Tools in the proof include exponential dichotomies and Fredholm properties. We prove that a weighted space Lw2(ℝ; ℂ3) with the same function for the tree variables of the linearized operator is no suitable to shift the essential spectrum to the left of the imaginary axis. We find a pair of appropriate weight functions whereby on the weighted space Lwα2(ℝ; ℂ2) × Lwε2(ℝ; ℂ) the essential spectrum lies on {Reλ<0}, outside the imaginary axis.

scholarly journals NON-PERTURBATIVE SOLUTION OF THE SUPER-VIRASORO CONSTRAINTS

1993 ◽  
Vol 08 (13) ◽  
pp. 1205-1214 ◽  
Author(s):  
K. BECKER ◽  
M. BECKER
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Scaling Limit ◽  
Virasoro Constraints ◽  
Perturbative Solution ◽  
The One ◽  
Genus Expansion ◽  
Double Scaling Limit

We present the solution of the discrete super-Virasoro constraints to all orders of the genus expansion. Integrating over the fermionic variables we get a representation of the partition function in terms of the one-matrix model. We also obtain the non-perturbative solution of the super-Virasoro constraints in the double scaling limit but do not find agreement between our flows and the known supersymmetric extensions of KdV.

scholarly journals Comments on open string with ‘massive’ boundary term

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190748
Author(s):  
Arkady A. Tseytlin
Keyword(s):  
Scattering Amplitudes ◽  
Partition Function ◽  
Gauge Field ◽  
Path Integral ◽  
Open String ◽  
One Dimensional ◽  
Conformally Invariant ◽  
Additional Constant ◽  
The One ◽  
Definition Of

We discuss possible definition of open string path integral in the presence of additional boundary couplings corresponding to the presence of masses at the ends of the string. These couplings are not conformally invariant implying that as in a non-critical string case one is to integrate over the one-dimensional metric or reparametrizations of the boundary. We compute the partition function on the disc in the presence of an additional constant gauge field background and comment on the structure of the corresponding scattering amplitudes.

scholarly journals Superstatistics of the one-dimensional Klein-Gordon oscillator with energy-dependent potentials

2020 ◽  
Vol 66 (5 Sept-Oct) ◽  
pp. 671
Author(s):  
M. Labidi ◽  
A. Boumali ◽  
A. Ndem Ikot
Keyword(s):  
Thermal Properties ◽  
Partition Function ◽  
Thermodynamic Properties ◽  
Gamma Distribution ◽  
Low Energy ◽  
Tsallis Statistics ◽  
One Dimensional ◽  
Klein Gordon ◽  
The One ◽  
Energy Dependent

AbstractIn this paper, we investigated the influence of energy-dependent potentials on the thermodynamic properties of the Klein-Gordon oscillator(KGO): in this way all thermal properties have been determinate via the well-know Euler-Maclaurin method. After this, we extend our study to the case of superstatistical properties of our problem in question. The probability densityf(β)followsχ2− superstatistics (=Tsallis statistics or Gamma distribution). Under the approximation of the low-energy asymptotics of superstatistics, the partition function, at first, has been calculated. This approximation leads to a universal parameterqfor any superstatistics, not only for Tsallis statistics. By using the desired partition function, all thermal properties have been obtained in terms of the parameterq. Also, the influence of the this type of potentials on these properties, via the parameterγ, are well discussed.

scholarly journals The one-loop partition function of super-Yang–Mills theory on

2005 ◽  
Vol 711 (1-2) ◽  
pp. 199-230 ◽  
Author(s):  
Marcus Spradlin ◽  
Anastasia Volovich
Keyword(s):  
Partition Function ◽  
Yang Mills ◽  
The One ◽  
Super Yang Mills Theory

scholarly journals TWO-FORM GRAVITY AND THE GENERATION OF SPACE-TIME

1996 ◽  
Vol 11 (17) ◽  
pp. 3033-3048
Author(s):  
MIYUKI KATSUKI ◽  
AKIO SUGAMOTO ◽  
SHIN’ICHI NOJIRI
Keyword(s):  
Effective Potential ◽  
Planck Scale ◽  
Conformal Factor ◽  
Einstein Gravity ◽  
Space Time ◽  
Gauge Condition ◽  
Cosmological Term ◽  
Divergent Term ◽  
Temporal Gauge ◽  
The One

In the framework of the two-form gravity, which is classically equivalent to the Einstein gravity, the one-loop effective potential for the conformal factor of metric is calculated in the finite volume and in the finite temperature by choosing a temporal gauge condition. There appears a quartically divergent term which cannot be removed by the renormalization of the cosmological term and we find there is only one nontrivial minimum in the effective potential. If the cutoff scale has a physical meaning, e.g. the Planck scale coming from string theory, this minimum might explain why the space-time is generated, i.e. why the classical metric has a nontrivial value.

GEOMETRIC REGULARIZATION AND GAUGE INVARIANCE IN CHERN–SIMONS THEORIES

1992 ◽  
Vol 07 (02) ◽  
pp. 235-256 ◽  
Author(s):  
MANUEL ASOREY ◽  
FERNANDO FALCETO
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Gauge Condition ◽  
Simons Theory ◽  
Coupling Constant ◽  
Gauge Transformations ◽  
Yang Mills ◽  
The One ◽  
Chern Simons ◽  
Three Dimensional Space

Some perturbative aspects of Chern–Simons theories are analyzed in a geometric-regularization framework. In particular, we show that the independence from the gauge condition of the regularized theory, which insures its global meaning, does impose a new constraint on the parameters of the regularization. The condition turns out to be the one that arises in pure or topologically massive Yang–Mills theories in three-dimensional space–times. One-loop calculations show the existence of nonvanishing finite renormalizations of gauge fields and coupling constant which preserve the topological meaning of Chern–Simons theory. The existence of a (finite) gauge-field renormalization at one-loop level is compensated by the renormalization of gauge transformations in such a way that the one-loop effective action remains gauge-invariant with respect to renormalized gauge transformations. The independence of both renormalizations from the space–time volume indicates the topological nature of the theory.

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