Replica-deformation of the SU(2)-invariant Thirring model via solutions of the qKZ equation

TL;DR

This paper demonstrates that replica-deformed form factors of the SU(2)-invariant Thirring model can be derived from solutions of the qKZ equation, linking deformed and original form factors through a one-to-one correspondence.

Contribution

It establishes a connection between replica-deformed form factors and solutions of the qKZ equation, providing a method to compute deformed form factors in the model.

Findings

Replica-deformed form factors correspond to solutions of the rational $sl_2$-type qKZ equation.

Modulo conserved charge solutions, deformed form factors are in one-to-one correspondence with those at level zero.

Conjecture of deformed form factors of the Noether current in the SU(2)-invariant Thirring model.

Abstract

The response of an integrable QFT under variation of the Unruh temperature has recently been shown to be computable from an S-matrix preserving (`replica') deformation of the form factor approach. We show that replica-deformed form factors of the SU(2)-invariant Thirring model can be found among the solutions of the rational $sl_2$-type quantum Knizhnik-Zamolodchikov equation at generic level. We show that modulo conserved charge solutions the deformed form factors are in one-to-one correspondence to the ones at level zero and use this to conjecture the deformed form factors of the Noether current in our model.