SUSCEPTIBILITY FOR 2-d GRAVITY COUPLED TO SO(2,1) BF SYSTEM

1991 ◽  
Vol 06 (32) ◽  
pp. 2965-2972
Author(s):  
MARCO PICCO ◽  
JEAN-CHRISTOPHE WALLET
Keyword(s):  
Partition Function ◽  
Gauge Group ◽  
Two Dimensional ◽  
Continuum Approach ◽  
Topological Theory ◽  
Dimensional Gravity ◽  
The Continuum

We consider two-dimensional gravity in the presence of a system of fields described by an action which can be derived from a topological theory with gauge group SO(2,1). Working in the continuum approach, we extract the area dependence of the partition function and deduce the susceptibility for the theory. The inclusion of D massless scalars gives a susceptibility depending linearly on D. We finally discuss our results.

A COMPACT BOSON COUPLED TO TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (15) ◽  
pp. 2743-2754 ◽  
Author(s):  
NORISUKE SAKAI ◽  
YOSHIAKI TANII
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Riemann Surfaces ◽  
Partition Functions ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
The Continuum ◽  
Continuum Field

The radius dependence of partition functions is explicitly evaluated in the continuum field theory of a compactified boson, interacting with two-dimensional quantum gravity (noncritical string) on Riemann surfaces for the first few genera. The partition function for the torus is found to be a sum of terms proportional to R and 1/R. This is in agreement with the result of a discretized version (matrix models), but is quite different from the critical string. The supersymmetric case is also explicitly evaluated.

scholarly journals Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Fridrich Valach ◽  
Donald R. Youmans
Keyword(s):  
Quantum Mechanics ◽  
Partition Function ◽  
Gauge Group ◽  
Path Integral ◽  
Coadjoint Orbits ◽  
Two Dimensional ◽  
Edge States ◽  
Class Constraint ◽  
Action Functional ◽  
Bf Theory

Abstract We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

scholarly journals SUPERLOOP EQUATIONS AND TWO-DIMENSIONAL SUPERGRAVITY

1992 ◽  
Vol 07 (21) ◽  
pp. 5337-5367 ◽  
Author(s):  
L. ALVAREZ-GAUMÉ ◽  
H. ITOYAMA ◽  
J.L. MAÑES ◽  
A. ZADRA
Keyword(s):  
Partition Function ◽  
Discrete Model ◽  
Continuum Limit ◽  
Basic Assumption ◽  
Scaling Limit ◽  
Integrable Hierarchy ◽  
Two Dimensional ◽  
Virasoro Constraints ◽  
Double Scaling Limit ◽  
The Continuum

We propose a discrete model whose continuum limit reproduces the string susceptibility and the scaling dimensions of (2, 4m) minimal superconformal models coupled to 2D supergravity. The basic assumption in our presentation is a set of super-Virasoro constraints imposed on the partition function. We recover the Neveu-Schwarz and Ramond sectors of the theory, and we are also able to evaluate all planar loop correlation functions in the continuum limit. We find evidence to identify the integrable hierarchy of nonlinear equations describing the double scaling limit as a supersymmetric generalization of KP studied by Rabin.

TETRACRITICAL ISING MODEL COUPLED TO THE TWO-DIMENSIONAL GRAVITY

1992 ◽  
Vol 07 (19) ◽  
pp. 4487-4499
Author(s):  
ALOK KUMAR ◽  
JNANADEVA MAHARANA
Keyword(s):  
Ising Model ◽  
Central Charge ◽  
Continuum Theory ◽  
Two Dimensional ◽  
Operator Approach ◽  
Modular Invariant ◽  
Lax Operator ◽  
Dimensional Gravity ◽  
Ade Classification ◽  
The Continuum

Nonperturbative string equations are found explicitly for a central charge c=4/5 model coupled to the two-dimensional quantum gravity in the Lax operator approach proposed by Douglas. These string equations are used to derive the scaling behavior of several correlation functions on the sphere and it is shown that they agree with the calculations of the continuum theory. The model, identified with the diagonal modular invariant in the ADE classification, corresponds to the tetracritical Ising model.

CONTINUUM SCHWINGER-DYSON EQUATIONS AND UNIVERSAL STRUCTURES IN TWO-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (08) ◽  
pp. 1385-1406 ◽  
Author(s):  
MASAFUMI FUKUMA ◽  
HIKARU KAWAI ◽  
RYUICHI NAKAYAMA
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Square Root ◽  
Two Dimensional ◽  
Kp Hierarchy ◽  
Kdv Hierarchy ◽  
The One ◽  
Matter Fields ◽  
The Continuum

We study the continuum Schwinger-Dyson equations for nonperturbative two-dimensional quantum gravity coupled to various matter fields. The continuum Schwinger-Dyson equations for the one-matrix model are explicitly derived and turn out to be a formal Virasoro condition on the square root of the partition function, which is conjectured to be the τ function of the KdV hierarchy. Furthermore, we argue that general multi-matrix models are related to the W algebras and suitable reductions of KP hierarchy and its generalizations.

CRITICAL MODELS COUPLED TO TWO-DIMENSIONAL GRAVITY IN THE CONTINUUM

1991 ◽  
Vol 06 (14) ◽  
pp. 1261-1268 ◽  
Author(s):  
YUNHAI CAI ◽  
GEORGE SIOPSIS
Keyword(s):  
Matrix Model ◽  
Correlation Functions ◽  
Minimal Model ◽  
Fock Space ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Dimensional Gravity ◽  
The Continuum

We discuss minimal conformal field theories M(p,q) coupled to 2-dimensional gravity in the continuum. We find a transformation that enables us to relate all models with p=2 to each other. We identify the Fock space in each model and calculate correlation functions. We thus show that the k-th multi-critical matrix model corresponds to the non-unitary minimal model with q=2k−1.

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.

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