Duality and higher temperature phases of large N Chern-Simons matter theories on S 2 × S 1

Abstract

It has been recently demonstrated that the thermal partition function of any large N Chern-Simons gauge theories on S 2 × S 1 , coupled to fundamental matter, reduces to a capped unitary matrix model. The matrix models corresponding to several specific matter Chern-Simons theories at temperature T were determined in [1]. The large N saddle point equations for these theories were determined in the same paper, and were solved in the low temperature phase. In this paper we find exact solutions for these saddle point equations in three other phases of these theories and thereby explicitly determine the free energy of the corresponding theories at all values of T 2 /N . As anticipated on general grounds in [1], our results are in perfect agreement with conjectured level rank type bosonization dualities between pairs of such theories.

Phases of large N vector Chern-Simons theories on S 2 × S 1

“…However it is easily seen that the contribution of the cuts to this integral vanishes 43 . In other words the integral in this expression receives contributions only from the upper gap, where ρ 0 (w) = 1 2πλ .…”

“…43 The reason for this is that h(w) changes sign across a cut. Consequently the principal value -the average of an integral over the upper and lower contour -vanishes over the cut.…”

“…In a similar manner we denote the one lower gap, one upper gap and two gap eigenvalue distributions by ρ lg (λ, ζ, α), ρ ug (λ, ζ, α) and ρ tg (λ, ζ, α) respectively. (C. 43) It follows that level rank duality exchanges the one lower gap and one upper gap solutions.…”

“…We leave this for future work. 48 Level Rank duality of the phase transition points: As we have explained above, for λ < , 48 The analytic proof is given in [43] which is a sequel of this paper.…”

Scattering amplitudes in $$ \mathcal{N} $$ = 3 supersymmetric SU(N) Chern-Simons-matter theory at large N

“…The conjectured bosonization duality has successfully passed a battery of tests in the large N limit, such as thermal partition functions [13][14][15][16], correlation functions of spin s currents [17][18][19][20][21][22][23][24], and S-matrices [25][26][27][28]. As we alluded to earlier, there is significant evidence that the bosonization duality is preserved along RG flows [29,30].…”