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A Note on AdS/CFT Dual of SL(2,Z) Action on 3D Conformal Field Theories with U(1) Symmetry

Ho-Ung Yee

Abstract

In this letter, we elaborate on the SL(2,Z) action on three dimensional conformal field theories with U(1) symmetry introduced by Witten, by trying to give an explicit verification of the claim regarding holographic dual of the S operation in AdS/CFT correspondence. A consistency check with the recently proposed prescription on boundary condition of bulk fields when we deform the boundary CFT in a non-standard manner is also discussed.

A Note on AdS/CFT Dual of SL(2,Z) Action on 3D Conformal Field Theories with U(1) Symmetry

Abstract

In this letter, we elaborate on the SL(2,Z) action on three dimensional conformal field theories with U(1) symmetry introduced by Witten, by trying to give an explicit verification of the claim regarding holographic dual of the S operation in AdS/CFT correspondence. A consistency check with the recently proposed prescription on boundary condition of bulk fields when we deform the boundary CFT in a non-standard manner is also discussed.

Paper Structure

This paper contains 4 sections, 51 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Setting up the stage
  3. Holographic dual of the S operation in AdS/CFT
  4. In view of boundary deformations

Figures (1)

  • Figure 1: