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

## TL;DR

This paper explores particle-vortex duality and theta terms within the AdS/CMT framework, analyzing their effects on conductivities and viscosities in 2+1 and 3+1 dimensional theories, including quantum corrections.

## Contribution

It provides a unified approach to understanding dualities and theta effects in AdS/CMT, extending to quantum gravity corrections and fluid dynamics.

## Key findings

- Derived the impact of particle-vortex duality on conductivities.
- Showed how theta terms influence transport properties in AdS/CFT.
- Connected 2+1 and 3+1 dimensional dualities via AdS/CFT.

## 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.