The Thermal Free Energy in Large N Chern-Simons-Matter Theories

TL;DR

This paper calculates the thermal free energy of large N Chern-Simons-matter theories at high temperatures, revealing unique eigenvalue distributions and confirming dualities with scalar, fermion, and supersymmetric theories.

Contribution

It provides the first detailed computation of the thermal free energy in these theories, accounting for non-localized eigenvalue distributions at high temperatures.

Findings

Eigenvalue distribution does not localize at high temperatures.

Results are consistent with known dualities between scalar and fermion theories.

Supports the strong-weak coupling duality in N=2 supersymmetric theories.

Abstract

We compute the thermal free energy in large N U(N) Chern-Simons-matter theories with matter fields (scalars and/or fermions) in the fundamental representation, in the large temperature limit. We note that in these theories the eigenvalue distribution of the holonomy of the gauge field along the thermal circle does not localize even at very high temperatures, and this affects the computation significantly. We verify that our results are consistent with the conjectured dualities between Chern-Simons-matter theories with scalar fields and with fermion fields, as well as with the strong-weak coupling duality of the N=2 supersymmetric Chern-Simons-matter theory.