scholarly journals Exact generalized partition function of 2D CFTs at large central charge

2019 ◽  
Vol 2019 (5) ◽  
Author(s):  
Anatoly Dymarsky ◽  
Kirill Pavlenko
Keyword(s):  
Partition Function ◽  
Central Charge ◽  
Generalized Partition

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

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.

c = 1 − 6(n − 1)2/n, THEORIES COUPLED TO GRAVITY: A COMMENT ON THEIR POSSIBLE LATTICE MODELS REALIZATIONS

1991 ◽  
Vol 06 (18) ◽  
pp. 1709-1719 ◽  
Author(s):  
HUBERT SALEUR
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Potts Model ◽  
Planar Graphs ◽  
Critical Line ◽  
Central Charge ◽  
Lattice Models ◽  
Genus Zero ◽  
Regular Lattices ◽  
Beraha Numbers

We discuss the recently proposed logarithmic violation of scaling for c = 1 − 6(n − 1)2/n theories in the light of lattice models. We study for this purpose the Q state Potts model in its antiferromagnetic regime eK − 1 = −Q1/2, coupled to gravity. Setting Q1/2 = 2 cos π/t, this model is known to have a generic central charge c = 1 − 6(t − 1)2/t. Summing over all possible planar graphs allows us to make connection with Kostov's solution of IRF models, and to calculate the genus zero properties along the critical line. Except for n = 1, 2 we do not get indications of logarithmic violations. The apparent regularity of the thermodynamic properties (γ str = −(n − 1) = integer ) is explained by a discontinuity of the free energy of the Potts model when Q crosses the Beraha numbers [Formula: see text], n ≥ 3 in the antiferromagnetic region. Such behavior was recently observed for some regular lattices. The logarithmic terms for n = 2, c = −2 appear simply because a derivative with respect to Q has to be taken to define a non-vanishing partition function. Only the n = 1, c = 1 logarithmic terms seem to have a non-trivial origin.

scholarly journals On the spectrum of pure higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Luis F. Alday ◽  
Jin-Beom Bae ◽  
Nathan Benjamin ◽  
Carmen Jorge-Diaz
Keyword(s):  
Black Hole ◽  
Partition Function ◽  
Path Integral ◽  
Higher Spin Gravity ◽  
Central Charge ◽  
Modular Invariance ◽  
Light Spectrum ◽  
Negative Norm ◽  
Deficit Angle ◽  
Higher Spin

Abstract We study the spectrum of pure massless higher spin theories in AdS3. The light spectrum is given by a tower of massless particles of spin s = 2, ⋯ , N and their multi-particles states. Their contribution to the torus partition function organises into the vacuum character of the $$ {\mathcal{W}}_N $$ W N algebra. Modular invariance puts constraints on the heavy spectrum of the theory, and in particular leads to negative norm states, which would be inconsistent with unitarity. This negativity can be cured by including additional light states, below the black hole threshold but whose mass grows with the central charge. We show that these states can be interpreted as conical defects with deficit angle 2π(1 − 1/M). Unitarity allows the inclusion of such defects into the path integral provided M ≥ N.

scholarly journals The topological line of ABJ(M) theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Nicola Gorini ◽  
Luca Griguolo ◽  
Luigi Guerrini ◽  
Silvia Penati ◽  
Domenico Seminara ◽  
...  
Keyword(s):  
Partition Function ◽  
Central Charge ◽  
Exact Representation ◽  
One Dimensional ◽  
Topological Sector ◽  
The Matrix ◽  
The One ◽  
The Masses ◽  
Dimension One ◽  
M Theory

Abstract We construct the one-dimensional topological sector of $$ \mathcal{N} $$ N = 6 ABJ(M) theory and study its relation with the mass-deformed partition function on S3. Supersymmetric localization provides an exact representation of this partition function as a matrix integral, which interpolates between weak and strong coupling regimes. It has been proposed that correlation functions of dimension-one topological operators should be computed through suitable derivatives with respect to the masses, but a precise proof is still lacking. We present non-trivial evidence for this relation by computing the two-point function at two-loop, successfully matching the matrix model expansion at weak coupling and finite ranks. As a by-product we obtain the two-loop explicit expression for the central charge cT of ABJ(M) theory. Three- and four-point functions up to one-loop confirm the relation as well. Our result points towards the possibility to localize the one-dimensional topological sector of ABJ(M) and may also be useful in the bootstrap program for 3d SCFTs.

scholarly journals The two-sphere partition function in two-dimensional quantum gravity

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Dionysios Anninos ◽  
Teresa Bautista ◽  
Beatrix Mühlmann
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Path Integral ◽  
Central Charge ◽  
Liouville Theory ◽  
Two Dimensional ◽  
Positive Cosmological Constant ◽  
Gauge Fixing ◽  
Semiclassical Expansion

Abstract We study the Euclidean path integral of two-dimensional quantum gravity with positive cosmological constant coupled to conformal matter with large and positive central charge. The problem is considered in a semiclassical expansion about a round two-sphere saddle. We work in the Weyl gauge whereby the computation reduces to that for a (timelike) Liouville theory. We present results up to two-loops, including a discussion of contributions stemming from the gauge fixing procedure. We exhibit cancelations of ultraviolet divergences and provide a path integral computation of the central charge for timelike Liouville theory. Combining our analysis with insights from the DOZZ formula we are led to a proposal for an all orders result for the two-dimensional gravitational partition function on the two-sphere.

scholarly journals The two-sphere partition function in two-dimensional quantum gravity at fixed area

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Beatrix Mühlmann
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Path Integral ◽  
Central Charge ◽  
Gravity Theory ◽  
Feynman Diagrams ◽  
Two Dimensional ◽  
Loop Order ◽  
Fixed Area

Abstract We discuss two-dimensional quantum gravity coupled to conformal matter and fixed area in a semiclassical large and negative matter central charge limit. In this setup the gravity theory — otherwise highly fluctuating — admits a round two-sphere saddle. We discuss the two-sphere partition function up to two-loop order from the path integral perspective. This amounts to studying Feynman diagrams incorporating the fixed area constraint on the round two-sphere. In particular we find that all ultraviolet divergences cancel to this order. We compare our results with the two-sphere partition function obtained from the DOZZ formula.

GENERALIZED PARTITION FUNCTION FOR BOSE STATISTICS AND THERMODYNAMIC FUNCTIONS

1999 ◽  
Vol 13 (29n30) ◽  
pp. 1055-1062 ◽  
Author(s):  
HONG-YI FAN ◽  
HUI ZOU
Keyword(s):  
Partition Function ◽  
Coherent State ◽  
Thermodynamic Functions ◽  
Nonlinear Medium ◽  
Symmetric Matrix ◽  
State Representation ◽  
Bose Distribution ◽  
Bose Statistics ◽  
Photon Gas ◽  
Generalized Partition

Based on the density operator's coherent state representation [Phys. Lett.A252, 281 (1999)], we extend the well-known Bose distribution's partition function Ξ [Formula: see text] for ideal photon gas [Formula: see text] to that of an assembly of photon gas interacting with nonlinear medium described by the Hamiltonian [Formula: see text], where A=(a1,a2,…,an), Ω is a symmetric matrix, and we report that the corresponding partition function is [Formula: see text] As a result, the generalized Bose distribution and thermodynamic functions are derived.

scholarly journals Monodromy methods for torus conformal blocks and entanglement entropy at large central charge

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Marius Gerbershagen
Keyword(s):  
Partition Function ◽  
Central Charge ◽  
Entanglement Entropy ◽  
Finite Size ◽  
Zero Point ◽  
Two Dimensional ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Replica Trick ◽  
Twist Operators

Abstract We compute the entanglement entropy in a two dimensional conformal field theory at finite size and finite temperature in the large central charge limit via the replica trick. We first generalize the known monodromy method for the calculation of conformal blocks on the plane to the torus. Then, we derive a monodromy method for the zero-point conformal blocks of the replica partition function. We explain the differences between the two monodromy methods before applying them to the calculation of the entanglement entropy. We find that the contribution of the vacuum exchange dominates the entanglement entropy for a large class of CFTs, leading to universal results in agreement with holographic predictions from the RT formula. Moreover, we determine in which regime the replica partition function agrees with a correlation function of local twist operators on the torus.

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