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

Mangesh Mandlik,Tomohisa Takimi,Spenta R. Wadia,Shiraz Minwalla,Sachin Jain,Shuichi Yokoyama

doi:10.1007/jhep04(2015)129

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.

Highlights

It has recently been conjectured that U(N ) Chern-Simons theories coupled to a multiplet of fundamental Wilson-Fisher bosons at level k are dual to U(|k| − N ) Chern-Simons theories coupled to fundamental fermions at level −k.1 The evidence for this conjecture is threefold
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 presence of the Wilson lines leads to an additional contribution that we argue to be channel dependent; we argue that the ratio of the additional contributions in the two channels is precisely the given by the factor above, explaining why the ‘bare’ S-matrix computed in this paper has ‘renormalized’ crossing symmetry properties

Summary

Introduction

It has recently been conjectured that U(N ) Chern-Simons theories coupled to a multiplet of fundamental Wilson-Fisher bosons at level k are dual to U(|k| − N ) Chern-Simons theories coupled to fundamental fermions at level −k.1 The evidence for this conjecture is threefold. It has recently been conjectured that U(N ) Chern-Simons theories coupled to a multiplet of fundamental Wilson-Fisher bosons at level k are dual to U(|k| − N ) Chern-Simons theories coupled to fundamental fermions at level −k.1. The evidence for this conjecture is threefold. Second the thermal partition functions of these theories have been computed in the ’t Hooft large N limit and have been shown to match [1, 2, 5, 7,8,9,10]. We would like an explicit construction of the fundamental fermionic field ψa(x) as a function of the fundamental bosonic fields; such a formula cannot, be given precise meaning in the current context as ψa(x) is not gauge invariant and its offshell correlators are ill-defined

Objectives

Methods

Results

Conclusion