On space of integrable quantum field theories

TL;DR

This paper investigates how 2D integrable quantum field theories can be deformed while preserving integrability, revealing a universal structure of scalar operators linked to conserved quantities and exploring their effects on the theories' S-matrices and form factors.

Contribution

It introduces a universal class of integrable deformations generated by scalar fields associated with conserved currents, including the special case of the $(Tar T)$ deformation, and analyzes their properties.

Findings

Infinitely many integrable deformations generated by scalar fields $X_s$.

The scalar $X_1$ coincides with the $(Tar T)$ operator.

Deformations by $X_1$ are solvable even for non-integrable theories.

Abstract

We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields $X_s$, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars $X_s$ are built from the components of the associated conserved currents in a universal way. The first of these scalars, $X_1$, coincides with the composite field $(T{\bar T})$ built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by $X_1$ are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations $X_s$ are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators $X_s$ in sine-Gordon theory. We also make some remarks on the problem of UV completeness of such integrable deformations.