The thermal free energy in large N Chern-Simons-matter theories

A master bosonization duality

“…For k = N f , the theory in Phase I is SU(N ) 0 which we expect JHEP01(2018)031 For N f < k the U theories also have four phases, while for N f = k they have five. We have 19) and Phase IV' only exists when N f = k. For N f < k, Phase III' splits into Phases IIIa' and IIIb' depending on whether the fermions have a negative or positive mass. For N f = k, Phase IV' splits into Phases IVa' and IVb' with the same.…”

“…At large N, k, with N/k finite, they are dual to a peculiar theory of gravity known as Vasiliev theory [4][5][6]. These theories are in fact solvable in this limit, and much is known of their thermal physics and scattering amplitudes [4][5][6][19][20][21]. Away from N = k = N f = 1, they imply a web of dualities for gauge theories with product gauge groups and (bi)fundamental matter [22], known as quiver gauge theories, and have been embedded intro string theory [23] (see also [24]).…”

“…At large N , these dualities appear to be inherited from a three-dimensional version of Seiberg duality [33,34], and there is some expectation that the non-supersymmetric bosonization dualities are always the offspring of a parent supersymmetric duality (see e.g. [19,[33][34][35][36]). …”

ABJ theory in the higher spin limit

“…Note that the Newton constant G HS in (2.3) is a duality invariant. The HS free energy (2.4) has a few favorable features: (1) The leading 1/G HS term is linear in M , as opposed to M 2 as would be expected from the U(M ) vector degrees of freedom, and the dependence on the PV phase θ 0 is qualitatively similar to that of the N = 2 theory in [103] which exhibits the invariance under θ 0 ↔ π 2 − θ 0 . (2) The leading 1/M correction, the first logarithmic term in (2.4), is consistent with the one-loop free energy of the N = 6 HS theory whose contribution comes solely from the U(N ) gauge fields, as calculated in section 4, up to the ambiguity of the constant γ.…”

Baryons, monopoles and dualities in Chern-Simons-matter theories

“…In the SU(N ) theory the eigenvalues sum up to zero (up to an overall shift by a multiple of 2π), and the quantization applies to the difference between any pair of eigenvalues. This quantization has important effects for the thermodynamical behavior of these theories, which was analyzed in the large N limit in [28,29] (following [1]). …”