Mixed moduli in 3d N=4 higher-genus quivers

TL;DR

This paper studies the structure of exactly marginal deformations in 3d N=4 gauge theories, revealing a connection between the genus of quiver diagrams and the number of mixed moduli, with implications for holographic duals.

Contribution

It identifies the precise count of mixed moduli in 3d N=4 quiver theories based on their genus and explains limitations of supergravity duals for higher-genus cases.

Findings

Number of single-trace mixed moduli equals the genus for nonabelian unitary gauge group quivers.

Higher-genus quivers have g-dimensional moduli spaces, not fully captured by AdS_4 supergravity.

The superconformal index bounds the number of mixed moduli by the quiver's genus.

Abstract

We analyze exactly marginal deformations of 3d N=4 Lagrangian gauge theories, especially mixed-branch operators with both electric and magnetic charges. These mixed-branch moduli can either belong to products of electric and magnetic current supermultiplets, or be single-trace (non-factorizable). Apart from some exceptional quivers that have additional moduli, 3d N=4 theories described by genus g quivers with nonabelian unitary gauge groups have exactly g single-trace mixed moduli, which preserve the global flavour symmetries. This partly explains why only linear and circular quivers have known AdS_4 supergravity duals. Indeed, for g>1, AdS_4 gauged supergravities cannot capture the entire g-dimensional moduli space even if one takes into account the quantization moduli of boundary conditions. Likewise, in a general Lagrangian theory, we establish (using the superconformal index) that the number of single-trace mixed moduli is bounded below by the genus of a graph encoding how nonabelian gauge groups act on hypermultiplets.