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.

arXiv commentLaTex, 1+15 pages, 1 figure, v2: discussion in terms of deformation theory is added

References in corpus (24)

• AdS/CFT Correspondence and Symmetry Breaking
• A Strong Coupling Test of S-Duality
• Mirror Symmetry in Three Dimensional Gauge Theories
• Multi-Trace Operators, Boundary Conditions, And AdS/CFT Correspondence
• On Mirror Symmetry in Three Dimensional Abelian Gauge Theories
• Topological Disorder Operators in Three-Dimensional Conformal Field Theory
• A universal result on central charges in the presence of double-trace deformations
• "Double-trace" Deformations, Boundary Conditions and Spacetime Singularities
• Monopole Operators and Mirror Symmetry in Three Dimensions
• Multiple-Trace Operators and Non-Local String Theories
• On S-Duality in Abelian Gauge Theory
• Double-trace operators and one-loop vacuum energy in AdS/CFT
• SL(2,Z) Action on Three-Dimensional CFTs and Holography
• Particle-Vortex Duality and the Modular Group: Applications to the Quantum Hall Effect and Other 2-D Systems
• Intertwining Operator Realization of the AdS/CFT Correspondence
• SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry
• Non-Perturbative Solution of Matrix Models Modified by Trace-Squared Terms
• Touching Random Surfaces and Liouville Gravity
• Vortex Dynamics in Self-Dual Chern-Simons Higgs Systems
• Derivation of the Semi-circle Law from the Law of Corresponding States
• Multi-Trace Operators and the Generalized AdS/CFT Prescription
• Duality and the Modular Group in the Quantum Hall Effect
• Large-N expansion, conformal field theory and renormalization-group flows in three dimensions
• Four dimensional Abelian duality and SL(2,Z) action in three dimensional conformal field theory

Cited by in corpus (25)

• Setting the boundary free in AdS/CFT
• Semi-Holographic Fermi Liquids
• Boundary Conditions and Dualities: Vector Fields in AdS/CFT
• Hall Conductivity of Flavor Fields from AdS/CFT
• Generalized symmetries and 2-groups via electromagnetic duality in AdS/CFT
• Gravitational Duality Transformations on (A)dS4
• Soft photon theorems from CFT Ward identites in the flat limit of AdS/CFT
• Holographic anyonic superfluidity
• Holography and magnetohydrodynamics with dynamical gauge fields
• Collective excitations of massive flavor branes
• Universal properties of cold holographic matter
• Intertwining Operator Realization of anti de Sitter Holography
• Collective dynamics and the Anderson-Higgs mechanism in a bona fide holographic superconductor
• Electric-magnetic Duality and Deformations of Three-Dimensional CFT's
• Asymptotic generators of fermionic charges and boundary conditions preserving supersymmetry
• A Monopole Instanton-Like Effect in the ABJM Model
• Non-relativistic anyons from holography
• Modular Symmetry and Fractional Charges in N=2 Supersymmetric Yang-Mills and the Quantum Hall Effect
• Weak-Interacting Holographic QCD
• Boundary conditions for SU(2) Yang-Mills on $Ad{S}_4$
• Can one hear the shape of a wormhole?
• Holographic anyonization: A systematic approach
• Holographic D-brane constructions with dynamical gauge fields
• Wrapped $M5$-branes and complex saddle points
• Investigation of hidden symmetry in $Ad{S}_5$ black hole with Heun equation