On space of integrable quantum field theories

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, X₁, coincides with the composite field (TT¯) built from the components of the energy–momentum tensor. The deformations of quantum field theories generated by X₁ 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.