Particle-vortex duality and theta terms in AdS/CMT applications

Abstract

In this paper we study particle-vortex duality and the effect of theta terms from the point of view of AdS/CMT constructions. We can construct the duality in 2+1 dimensional field theories with or without a Chern-Simons term, and derive an effect on conductivities, when the action is viewed as a response action. We can find its effect on 3+1 dimensional theories, with or without a theta term, coupled to gravity in asymptotically AdS space, and derive the resulting effect on conductivities defined in the spirit of AdS/CFT. AdS/CFT then relates the 2+1 dimensional and the 3+1 dimensional cases naturally. Quantum gravity corrections, as well as more general effective actions for the abelian vector, can be treated similarly. We can use the fluid/gravity correspondence, and the membrane paradigm, to define shear and bulk viscosities $\eta$ and $\zeta$ for a gravity plus abelian vector plus scalar system near a black hole, and define the effect of the S-duality on it.

arXiv comment39 pages, no figures; references added

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Cited by in corpus (5)

• Duality Constraints on Thermal Spectra of 3d Conformal Field Theories and 4d Quasinormal Modes
• Wiedemann-Franz laws and $Sl(2,\mathbb{Z})$ duality in AdS/CMT holographic duals and one-dimensional effective actions for them
• S-duality, entropy function and transport in $Ad{S}_4/CM{T}_3$
• Duality and modular symmetry in the quantum Hall effect from Lifshitz holography
• A renormalisation group equation for transport co-efficients in (2+1)-dimensions derived from the AdS/CMT correspondence