Exact finite volume expectation values of $\bar{\Psi} \Psi$ in the Massive Thirring model from light-cone lattice correlators

Abstract

In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operator $\bar{\Psi}\Psi$ between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operator $\bar{\Psi}\Psi$ is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the finite volume spectrum of the theory. Our results for the expectation values coming from the computation of lattice correlators agree with those of the NLIE computations. Previous conjectures for the LeClair-Mussardo-type series representation of the expectation values are also checked.