Unitarity, crossing symmetry and duality of the S-matrix in large N Chern-Simons theories with fundamental matter

Abstract

We present explicit computations and conjectures for 2 → 2 scattering matrices in large N U(N ) Chern-Simons theories coupled to fundamental bosonic or fermionic matter to all orders in the 't Hooft coupling expansion. The bosonic and fermionic S-matrices map to each other under the recently conjectured Bose-Fermi duality after a level-rank transposition. The S-matrices presented in this paper may be regarded as relativistic generalization of Aharonov-Bohm scattering. They have unusual structural features: they include a non-analytic piece localized on forward scattering, and obey modified crossing symmetry rules. We conjecture that these unusual features are properties of S-matrices in all Chern-Simons matter theories. The S-matrix in one of the exchange channels in our paper has an anyonic character; the parameter map of the conjectured Bose-Fermi duality may be derived by equating the anyonic phase in the bosonic and fermionic theories.

A test of bosonization at the level of four-point functions in Chern-Simons vector models

“…We hope to return to this off-shell ladder diagram in the future. We note that the on-shell four point function is calculated to all orders in [6], and its supersymmetric generalization [13].…”

“…These theories, which have been intensively studied in the past few years [1][2][3][4][5][6][7][8][9][10][11][12][13], are particularly interesting because they provide examples of non-supersymmetric dualities. For instance, they are widely believed to be dual to Vasiliev higher-spin gauge theories (see [14] for a review).…”

A symmetry breaking scenario for QCD3

“…They were motivated by ideas in 2 + 1d field theory [19][20][21][22][23][24], supersymmetric quantum field theory [9,[25][26][27][28][29][30][31][32][33][34][35][36], and string theory [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. Roughly speaking, these dualities shed light on theories with small N f not larger than the Chern-Simons level in the fermionic theory.…”

A master bosonization duality

“…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]).…”