Boundary S-matrix in a (2,0) theory of AdS_{3} Supergravity

TL;DR

This paper explores two formulations of (2,0) supergravity with gravitational Chern-Simons terms, focusing on their boundary S-matrix and implications for dual conformal field theories, especially in the gauge+fermionic sector.

Contribution

It compares first and second order formalisms of (2,0) supergravity with Chern-Simons terms and analyzes their boundary S-matrix in the gauge+fermionic sector.

Findings

First order formalism solutions form a subset of second order solutions.

Boundary S-matrix computed in the gauge+fermionic sector.

Higher derivative terms influence the boundary S-matrix.

Abstract

We will discuss two inequivalent generalizations of the standard (2,0) supergravity action gr-qc/9501018 to include gravitational Chern-Simons term. One is in the first order formalism where we treat \omega_{M}^{ab} as independent and the other is in the second order formalism where \omega_{M}^{ab} is determined in terms of other fields via a standard constraint equation. The two theories have different equations of motion and the solutions to the equations of motion of the first order theory spans only a subset of those of the second order theory. We will be interested in computing the boundary S-matrix, describing correlation functions in a dual conformal field theory, in this sector and hence we use the equations of motion coming out of the first order theory. We restrict ourselves to the gauge+fermionic sector of the theory to compute the boundary S-matrix. We will also look at the effect of higher derivative terms on the boundary S-matrix obtained using the standard supergravity action.