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.

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.

FROM LOOPS TO FIELDS IN 2D QUANTUM GRAVITY

1992 ◽  
Vol 07 (11) ◽  
pp. 2601-2634 ◽  
Author(s):  
GREGORY MOORE ◽  
NATHAN SEIBERG
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Zero Mode ◽  
Integral Transform ◽  
Target Space ◽  
Two Dimensional ◽  
And Topology ◽  
The Matrix ◽  
Dimensional Gravity ◽  
Infinite Set

We discuss a target space field theory of macroscopic loops W(ℓ,…) in two-dimensional gravity. The propagator <W(ℓ1)W(ℓ2)> and topology-changing amplitudes <W(ℓ1)W(ℓ2)W(ℓ3)> (string interactions) are considered as off-shell Euclidean Green's functions in this field theory. In the course of the analysis, we identify a new set of operators in the c = 1 system and interpret them in two-dimensional gravity. We also identify an infinite set of new conserved charges in the c = 1 system which are associated with the special states in the theory. The analysis also shows that the eigenvalue coordinate of the matrix model and a zero mode of the Liouville field are not functionally related but are conjugate variables in an integral transform.

Gravité quantique et modèles de matrices

1991 ◽  
Vol 69 (7) ◽  
pp. 837-854 ◽  
Author(s):  
David Sénéchal
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Gravity ◽  
Orthogonal Polynomials ◽  
Matrix Models ◽  
Continuum Limit ◽  
Two Dimensional ◽  
Planar Approximation ◽  
Conformal Field ◽  
The Matrix

A review of the main results recently obtained in the study of two-dimensional quantum gravity is offered. The analysis of two-dimensional quantum gravity by the methods of conformal field theory is briefly described. Then the treatment of quantum gravity in terms of matrix models is explained, including the notions of continuum limit, planar approximation, and orthogonal polynomials. Correlation fonctions are also treated, as well as phases of the matrix models.

AN EXPLICIT COMPUTATION FOR THE BOSE-FERMI EQUIVALENCE ON RIEMANN SURFACES OF GENUS g

1989 ◽  
Vol 04 (17) ◽  
pp. 4437-4447
Author(s):  
NOUREDDINE CHAIR
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Partition Function ◽  
Quadratic Form ◽  
Riemann Surfaces ◽  
Partition Functions ◽  
Explicit Computation ◽  
Dimensional Torus ◽  
Conformal Field

The instanton sum in the partition function for D bosons on a Riemann surface of genus g, with values in a general D-dimensional torus, TD = RD/ΛD is given explicitly. When the rational metric Q of the lattice, ΛD, is the identity we get the bosonization formula of Alvarez-Gaumé et al. for SO( 2D ). If Q is orthogonal, in the bosonization formula, we get the theta function associated with the quadratic form Q, if Q is generic we get rational Conformal Field Theory. Also we look for conditions on a twisted spin bundle LE, which may ensure that our partition functions arise from some generalized bosonization formulas.

ON THE KOSTERLITZ–THOULESS TRANSITION ON COMPACT RIEMANN SURFACES

1993 ◽  
Vol 07 (03) ◽  
pp. 171-182 ◽  
Author(s):  
ACHILLES D. SPELIOTOPOULOS ◽  
HARRY L. MORRISON
Keyword(s):  
Field Theory ◽  
Riemann Surface ◽  
Partition Function ◽  
Riemann Surfaces ◽  
Compact Riemann Surface ◽  
Constant Density ◽  
Two Dimensional ◽  
Coulombic Interaction ◽  
Density Limit ◽  
Compact Riemann Surfaces

A Lagrangian for the two-dimensional vortex gas is derived from a general microscopic Lagrangian for 4 He atoms on an arbitrary compact Riemann Surface without boundary. In the constant density limit the vortex Hamiltonian obtained from this Lagrangian is found to be the same as the Kosterlitz and Thouless Coulombic interaction Hamiltonian. The partition function for the Kosterlitz–Thouless ensemble on the general compact is formulated and mapped into the sine–Gordon field theory.

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.

TWO-DIMENSIONAL QUANTUM GRAVITY ON A DISK

1992 ◽  
Vol 07 (06) ◽  
pp. 521-532 ◽  
Author(s):  
YOSHIAKI TANII ◽  
SHUN-ICHI YAMAGUCHI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Gravity ◽  
Correlation Functions ◽  
Two Dimensional ◽  
Field Approach ◽  
Conformal Field ◽  
Boundary Operators ◽  
Point Correlation ◽  
The Continuum

We study a two-dimensional conformal field theory coupled to quantum gravity on a disk. Using the continuum Liouville field approach, we compute three-point correlation functions of boundary operators. The structure of momentum singularities is different from that of correlation functions on a sphere and is more complicated. We also compute four-point functions of boundary operators and three-point functions of two boundary operators and one bulk operator.

STABILIZED MATRIX MODELS FOR NONPERTURBATIVE TWO-DIMENSIONAL QUANTUM GRAVITY

1994 ◽  
Vol 09 (21) ◽  
pp. 3751-3771 ◽  
Author(s):  
JOSHUA FEINBERG
Keyword(s):  
Nonperturbative Effects ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Two Dimensional ◽  
Hartree Fock ◽  
Kdv Hierarchy ◽  
Multicritical Points ◽  
Dimensional Gravity ◽  
Arbitrary Weight ◽  
Genus Expansion

A thorough analysis of stochastically stabilized Hermitian one-matrix models for two-dimensional quantum gravity at all its (2, 2k − 1) multicritical points is made. It is stressed that only the zero fermion sector of the supersymmetric Hamiltonian, i.e. the forward Fokker–Planck Hamiltonian, is relevant for the analysis of bosonic matter coupled to two-dimensional gravity. Therefore, supersymmetry breaking is not the physical mechanism that creates nonperturbative effects in the case of points of even multicriticality k. Nonperturbative effects in the string coupling constant g str result in a loss of any explicit relation to the KdV hierarchy equations in the latter case, while maintaining the perturbative genus expansion. As a by-product of our analysis it is explicitly proved that polynomials orthogonal relative to an arbitrary weight exp (−βV (x)) along the whole real line obey a Hartree–Fock equation.

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 Multiple phases in a generalized Gross-Witten-Wadia matrix model

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Jorge G. Russo ◽  
Miguel Tierz
Keyword(s):  
Partition Function ◽  
Matrix Models ◽  
Characteristic Polynomial ◽  
Matrix Model ◽  
Phase Structure ◽  
Unitary Matrix ◽  
Two Dimensional ◽  
Toeplitz Determinants ◽  
Dimensional Parameter ◽  
Planar Limit

Abstract We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large N results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large N (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

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