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

TL;DR

This paper investigates the holographic dual of the SL(2,Z) action on 3D conformal field theories with U(1) symmetry within the AdS/CFT framework, providing explicit verification and consistency checks.

Contribution

It offers an explicit verification of the holographic dual of the S operation in AdS/CFT for 3D CFTs with U(1) symmetry and discusses boundary condition prescriptions.

Findings

Verified the holographic dual of the S operation.

Discussed boundary condition prescriptions for deformed boundary CFTs.

Provided consistency checks for the SL(2,Z) action in AdS/CFT context.

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.