Note on massless bosonic states in two-dimensional field theories

TL;DR

This paper demonstrates that in certain two-dimensional super-renormalizable theories, the parity-odd current correlator reveals massless bosonic states, with specific counts depending on the supersymmetry and symmetry groups involved.

Contribution

It provides a general method to identify massless bosonic states via current correlators in two-dimensional theories with specific symmetries.

Findings

Massless poles in current correlators indicate massless bosonic states.

$ ext{N}=(2,2)$ theories have one massless boson per momentum.

$ ext{N}=(4,4)$ theories have at least three massless bosons.

Abstract

In a wide class of $G_L\times G_R$ invariant two-dimensional super-renormalizable field theories, the parity-odd part of the two-point function of global currents is completely determined by a fermion one-loop diagram. For any non-trivial fermion content, the two-point function possesses a massless pole which corresponds to massless bosonic physical states. As an application, we show that two-dimensional $\mathcal{N}=(2,2)$ supersymmetric gauge theory without a superpotential possesses $U(1)_L\times U(1)_R$ symmetry and contains one massless bosonic state per fixed spatial momentum. The $\mathcal{N}=(4,4)$ supersymmetric pure Yang-Mills theory possesses $SU(2)_L\times SU(2)_R$ symmetry, and there exist at least three massless bosonic states.