On thermodynamics of $ \mathcal{N} = 6 $ superconformal Chern-Simons theory

Abstract

We study thermodynamics of N = 6 superconformal Chern-Simons theory by computing quantum corrections to the free energy. We find that in weakly coupled ABJM theory on R 2 × S 1 , the leading correction is non-analytic in the 't Hooft coupling λ, and is approximately of order λ 2 log(λ) 3 . The free energy is expressed in terms of the scalar thermal mass m, which is generated by screening effects. We show that this mass vanishes to 1-loop order. We then go on to 2-loop order where we find a finite and positive mass squared m 2 . We discuss differences in the calculation between Coulomb and Lorentz gauge. Our results indicate that the free energy is a monotonic function in λ which interpolates smoothly to the N 3/2 behaviour at strong coupling.

Chern–Simons theory with vector fermion matter

“…Such non-analytic behavior in Chern-Simons-matter theories with massless bosons was observed explicitly e.g. in[7],[38]. This non-analyticity has its origin in infrared divergences which are absent in our theory because the only propagating degrees of freedom are the fermions which lack a zero-mode along the thermal circle.…”

Free energy of ABJM theory

“…Hence, they only contribute to lower orders. In this way, we obtain the free energy including the first non-vanishing quantum correction, as already reported on in [15]. Specifically, by combining equations (5.1), (5.2) and (5.3), we find the free energy density 1…”

“…It will be sufficient for our purposes to do this in the static limit, corresponding to no external momentum, since this is the troublesome mode that we want to regularize. To two-loop order, we find the result [15]…”

“…In [15], we computed the quantum corrections to the free field theory result of ABJM [5], allowing us to see whether similar phenomena as in the SYM case also appear in ABJM. Our primary motivation, though, was to see if we can make progress from the field theory side on understanding the strong suppression of the entropy at strong coupling [7] (corrections were computed in [16]).…”

Refined counting of necklaces in one-loop N = 4 $$ \mathcal{N}=4 $$ SYM

“…It is also interesting to study superconformal field theories other than N = 4 SYM, such as β-deformed and γ-deformed theories [36], ABJM model [37], theories with 16 supercharges [38], and quiver gauge theories [39]. Our counting methods should be applicable to integrable models like q-deformed Hubbard model [40], which is a generalization of XXZ spin chain.…”