scholarly journals Path integral derivation of the Brown-Henneaux central charge

2001 ◽  
Vol 64 (6) ◽  
Author(s):  
Hiroaki Terashima
Keyword(s):  
Path Integral ◽  
Central Charge

CONSTRAINED FERMIONIC MODELS IN NON-TRIVIAL TOPOLOGICAL SECTORS

1992 ◽  
Vol 07 (24) ◽  
pp. 2179-2188 ◽  
Author(s):  
ENRIQUE F. MORENO
Keyword(s):  
Path Integral ◽  
Degrees Of Freedom ◽  
Central Charge ◽  
Coulomb Gas ◽  
Effective Theory ◽  
Fermionic Model ◽  
Topological Sector ◽  
Integral Treatment ◽  
Background Charge

We study a constrained fermionic model involving non-trivial topological gauge configurations. After a path-integral treatment of the topologically trivial degrees of freedom we show that the resulting effective theory is equivalent to a Coulomb gas theory with a "background charge" at infinity plus a b, c ghost system. The Virasoro central charge of the theory is found to be independent of the topological sector.

scholarly journals CONFORMALLY INVARIANT CONSTRAINED FERMION MODELS

1990 ◽  
Vol 05 (12) ◽  
pp. 2313-2330 ◽  
Author(s):  
D. CABRA ◽  
E. MORENO ◽  
C. von REICHENBACH
Keyword(s):  
Path Integral ◽  
Central Charge ◽  
Effective Theory ◽  
Conformally Invariant

We construct constrained fermion models within the path-integral framework. By an appropriate choice of constraints we obtain an effective theory with central charge in the minimal unitary series, its supersymmetric generalization and other well-known series. We also discuss the relation between these constrained fermion models and gauged Wess-Zumino-Witten models.

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 AdS3 wormholes from a modular bootstrap

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Jordan Cotler ◽  
Kristan Jensen
Keyword(s):  
Low Temperature ◽  
Path Integral ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Central Charge ◽  
Three Dimensional ◽  
Single Instance ◽  
Dimensional Gravity ◽  
3D Gravity

Abstract In recent work we computed the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. Here we employ a modular bootstrap to show that the amplitude is completely fixed by consistency conditions and a few basic inputs from gravity. This bootstrap is notably for an ensemble of CFTs, rather than for a single instance. We also compare the 3d gravity result with the Narain ensemble. The former is well-approximated at low temperature by a random matrix theory ansatz, and we conjecture that this behavior is generic for an ensemble of CFTs at large central charge with a chaotic spectrum of heavy operators.

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.

scholarly journals Real-time gravitational replicas: low dimensional examples

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Sean Colin-Ellerin ◽  
Xi Dong ◽  
Donald Marolf ◽  
Mukund Rangamani ◽  
Zhencheng Wang
Keyword(s):  
Variational Principle ◽  
Real Time ◽  
Path Integral ◽  
Central Charge ◽  
Stationary Points ◽  
Two Dimensional ◽  
The Real ◽  
Gravitational Theories ◽  
Low Dimensional ◽  
Analytic Computation

Abstract We continue the study of real-time replica wormholes initiated in [1]. Previously, we had discussed the general principles and had outlined a variational principle for obtaining stationary points of the real-time gravitational path integral. In the current work we present several explicit examples in low-dimensional gravitational theories where the dynamics is amenable to analytic computation. We demonstrate the computation of Rényi entropies in the cases of JT gravity and for holographic two-dimensional CFTs (using the dual gravitational dynamics). In particular, we explain how to obtain the large central charge result for subregions comprising of disjoint intervals directly from the real-time path integral.

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