Amir Masoud Ghezelbash

Logarithmic conformal field theories and AdS correspondence

We generalize the Maldacena correspondence to the logarithmic conformal field theories. We study the correspondence between field theories in (d+1)-dimensional AdS space and the d-dimensional logarithmic conformal field theories in the boundary of AdSd+1. Using this correspondence, we get the n-point functions of the corresponding logarithmic conformal field theory in d-dimensions.

Interacting spinors-scalars and AdS/CFT correspondence

Abstract By taking the interacting spinor-scalar theory on the AdSd+1 space we calculate the boundary CFT correlation functions using AdS/CFT correspondence.

The moduli space and monodromies of the N = 2 supersymmetric Yang-Mills theory with any Lie gauge groups

Abstract We propose a unified scheme for finding the hyperelliptic curve of N = 2 SUSY YM theory with any Lie gauge groups. Our general scheme gives the well-known results for the classical gauge groups and the exceptional G 2 group. In particular, we present the curve for the exceptional gauge groups F 4 , E 6,7,8 and check the consistency condition for them. The exact monodromies and the dyon spectrum of these theories are determined. We note that for any Lie gauge groups, the exact monodromies could be obtained only from the Cartan matrix.

Global conformal invariance in D dimensions and logarithmic correlation functions

Abstract We define transformation of multiplets of fields (Jordan cells) under the D-dimensional conformal group, and calculate two and three point functions of fields, which show logarithmic behaviour. We also show how by a formal differentiation procedure, one can obtain n-point function of logarithmic field theory from those of ordinary conformal field theory.

Logarithmic N=1 superconformal field theories

Abstract We study the logarithmic superconformal field theories. Explicitly, the two-point functions of N =1 logarithmic superconformal field theories (LSCFT) when the Jordan blocks are two (or more) dimensional, and when there are one (or more) Jordan block(s) have been obtained. Using the well known three-point functions of N =1 superconformal field theory (SCFT), three-point functions of N =1 LSCFT are obtained. The general form of N =1 SCFTs four-point functions is also obtained, from which one can easily calculate four-point functions in N =1 LSCFT.

Gauged noncommutative Wess-Zumino-Witten models

Abstract We investigate the Kac–Moody algebra of noncommutative Wess–Zumino–Witten model and find its structure to be the same as the commutative case. Various kinds of gauged noncommutative WZW models are constructed. In particular, noncommutative U(2)/U(1) WZW model is studied and by integrating out the gauge fields, we obtain a noncommutative non-linear σ -model.

Quantizing field theories in noncommutative geometry and the correspondence between anti de Sitter space and conformal field theory

Abstract By using the approach of non-commutative geometry, we study spinors and scalars on the two layers AdS d +1 space. We have found that in the boundary of two layers AdS d +1 space, by using the AdS/CFT correspondence, we have a logarithmic conformal field theory. This observation propose a way to get the quantum field theory in the context of non-commutative geometry.

PERIODS AND PREPOTENTIAL IN N = 2 SUPERSYMMETRIC E6 YANG-MILLS THEORY

Abstract We obtain the periods and one-instanton coefficient of the N =2 supersymmetric Yang-Mills theory with the exceptional gauge group E 6 . These calculations are based on the E 6 spectral curve and the obtained one-instanton coefficient is in agreement with the microscopic results.

GAUGING OF LORENTZ GROUP WZW MODEL BY ITS NULL SUBGROUP

We consider the standard vector gauging of Lorentz group SO(3, 1) WZW model by its non-semisimple null Euclidean subgroup in two dimensions E(2). The resultant effective action of the theory is seen to describe a one-dimensional bosonic field in the presence of external charge that we interpret as a Liouville field. By gauging a boosted SO(3) subgroup, we find that in the limit of the large boost, the theory can be interpreted as an interacting Toda theory. We take also the generalized nonstandard bilinear form for SO(3, 1) and gauge both SO(3) and E(2) subgroups and discuss the resultant theories.

VECTOR-CHIRAL EQUIVALENCE IN NULL GAUGED WZNW THEORY

We consider the standard vector and chiral gauged WZNW models gauged by their maximal null subgroups and show that they can be mapped to each other by a special transformation. We give an explicit expression for the map in the case of the classical Lie groups AN, BN, CN, DN, and note its connection with the duality map for the Riemannian globally symmetric spaces.