Conformal Field Theory on a Riemann Surface

1990 ◽  
pp. 33-43
Author(s):  
H. Ooguri
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Conformal Field

scholarly journals SUPERGRAVITY DESCRIPTION OF FIELD THEORIES ON CURVED MANIFOLDS AND A NO GO THEOREM

2001 ◽  
Vol 16 (05) ◽  
pp. 822-855 ◽  
Author(s):  
JUAN MALDACENA ◽  
CARLOS NUÑEZ
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Riemann Surfaces ◽  
Field Theories ◽  
De Sitter ◽  
Curved Manifolds ◽  
Conformal Field ◽  
Low Energies ◽  
M Theory

In the first part of this paper we find supergravity solutions corresponding to branes on worldvolumes of the form Rd×Σ where Σ is a Riemann surface. These theories arise when we wrap branes on holomorphic Riemann surfaces inside K3 or CY manifolds. In some cases the theory at low energies is a conformal field theory with two less dimensions. We find some non-singular supersymmetric compactifications of M-theory down to AdS5. We also propose a criterion for permissible singularities in supergravity solutions. In the second part of this paper, which can be read independently of the first, we show that there are no non-singular Randall-Sundrum or de-Sitter compactifications for large class of gravity theories.

scholarly journals SU(2)k×SU(2)l/SU(2)k+l COSET CONFORMAL FIELD THEORY AND TOPOLOGICAL MINIMAL MODEL ON HIGHER GENUS RIEMANN SURFACE

1993 ◽  
Vol 08 (31) ◽  
pp. 5537-5561 ◽  
Author(s):  
HITOSHI KONNO
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Vertex Operator ◽  
Correlation Functions ◽  
Minimal Model ◽  
The Other ◽  
Operator Formalism ◽  
Conformal Field ◽  
Higher Genus

We consider the Feigin-Fuchs-Felder formalism of the SU (2)k× SU (2)l/ SU (2)k+l coset minimal conformal field theory and extend it to higher genus. We investigate a double BRST complex with respect to two compatible BRST charges, one associated with the parafermion sector and the other associated with the minimal sector in the theory. The usual screened vertex operator is extended to the BRST-invariant screened three-string vertex. We carry out a sewing operation of these vertices and derive the BRST-invariant screened g-loop operator. The latter operator characterizes the higher genus structure of the theory. An analogous operator formalism for the topological minimal model is obtained as the limit l=0 of the coset theory. We give some calculations of correlation functions on higher genus.

A REMARK ON CONFORMAL FIELD THEORIES ON ALGEBRAIC CURVES

1991 ◽  
Vol 06 (12) ◽  
pp. 1103-1107 ◽  
Author(s):  
J. SOBCZYK
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Complex Plane ◽  
Algebraic Curves ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Branching Points ◽  
Branch Covering

We present an argument supporting the conjecture that a conformal field theory (CFT) defined on a Riemann surface viewed as a branch covering of CP 1 can be transformed to a CFT on the complex plane in which the information about branching points was coded into certain conformal field insertions.

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.

CORRELATORS OF CONFORMAL FIELD THEORIES FROM THEIR CHARACTERS

1990 ◽  
Vol 05 (31) ◽  
pp. 2643-2649
Author(s):  
R. P. MALIK ◽  
N. BEHERA ◽  
R. K. KAUL
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Complete Solution ◽  
Arbitrary Point ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Higher Genus

All genus characters define a complete solution of a two-dimensional rational conformal field theory. An arbitrary point correlator can be obtained by an appropriate combination of the pinchings of zero-homology and non-zero-homology cycles of the characters on the higher genus Riemann surface.

scholarly journals The spectrum of marginally-deformed $$ \mathcal{N} $$ = 2 CFTs with AdS4 S-fold duals of type IIB

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Mattia Cesàro ◽  
Gabriel Larios ◽  
Oscar Varela
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Yang Mills ◽  
Conformal Field ◽  
Operator Spectrum ◽  
Two Parameter ◽  
Kaluza Klein

Abstract A holographic duality was recently established between an $$ \mathcal{N} $$ N = 4 non-geometric AdS4 solution of type IIB supergravity in the so-called S-fold class, and a three- dimensional conformal field theory (CFT) defined as a limit of $$ \mathcal{N} $$ N = 4 super-Yang-Mills at an interface. Using gauged supergravity, the $$ \mathcal{N} $$ N = 2 conformal manifold (CM) of this CFT has been assessed to be two-dimensional. Here, we holographically characterise the large-N operator spectrum of the marginally-deformed CFT. We do this by, firstly, providing the algebraic structure of the complete Kaluza-Klein (KK) spectrum on the associated two-parameter family of AdS4 solutions. And, secondly, by computing the $$ \mathcal{N} $$ N = 2 super-multiplet dimensions at the first few KK levels on a lattice in the CM, using new exceptional field theory techniques. Our KK analysis also allows us to establish that, at least at large N, this $$ \mathcal{N} $$ N = 2 CM is topologically a non-compact cylindrical Riemann surface bounded on only one side.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

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