Entanglement Entropy of 3-d Conformal Gauge Theories with Many Flavors

TL;DR

This paper computes the entanglement entropy and free energy of 3D conformal gauge theories with many flavors, providing evidence for the F-theorem and comparing non-supersymmetric and supersymmetric cases.

Contribution

It introduces a large N_F expansion for free energies of non-supersymmetric gauge theories and verifies results with exact supersymmetric calculations using localization.

Findings

Agreement between 1/N_F expansion and localization results

Evidence supporting the F-theorem in supersymmetric RG flows

Explicit calculations of free energies for theories with many flavors

Abstract

Three-dimensional conformal field theories (CFTs) of deconfined gauge fields coupled to gapless flavors of fermionic and bosonic matter describe quantum critical points of condensed matter systems in two spatial dimensions. An important characteristic of these CFTs is the finite part of the entanglement entropy across a circle. The negative of this quantity is equal to the finite part of the free energy of the Euclidean CFT on the three-sphere, and it has been proposed to satisfy the so called F-theorem, which states that it decreases under RG flow and is stationary at RG fixed points. We calculate the three-sphere free energy of non-supersymmetric gauge theory with a large number N_F of bosonic and/or fermionic flavors to the first subleading order in 1/N_F. We also calculate the exact free energies of the analogous chiral and non-chiral {\cal N} = 2 supersymmetric theories using localization, and find agreement with the 1/N_F expansion. We analyze some RG flows of supersymmetric theories, providing further evidence for the F-theorem.