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

Figures (8)

• Figure 1: ( a) One out of many possible configurations of fermions in the lowest Landau level on the torus. ( b) The potential generated by integrating out the matter fields selects the configuration where the fermions are localized in a band around $a=0$. The fact that $L \gg \beta$ breaks the symmetry between the two holonomies.
• Figure 2: Bootstrap equation for the scalar self-energy. A filled circle denotes the full scalar propagator. (d) corresponds to the insertion of the $\lambda_6 (\phi^2)^3$ interaction vertex.
• Figure 3: Thermal mass in the regular bosonic theory with $\lambda_6=0$ (blue, lower curve) and critical theory (red, upper curve), with arbitrary normalization.
• Figure 4: Negative free energy in the regular bosonic theory with $\lambda_6=0$ (blue, upper curve) and critical theory (red, lower curve), using arbitrary normalization.
• Figure 5: Bootstrap equation for $\Sigma_F$. A filled circle denotes the exact fermion propagator.