Perturbative renormalization of the $$ \mathrm{T}\overline{\mathrm{T}} $$-deformed free massive Dirac fermion

Abstract

Abstract In this paper we explicitly carry out the perturbative renormalization of the $$ T\overline{T} $$ T T ¯ -deformed free massive Dirac fermion in two dimensions up to second order in the coupling constant. This is done by computing the two-to-two S-matrix using the LSZ reduction formula and canceling out the divergences by introducing counterterms. We demonstrate that the renormalized Lagrangian is unambiguously determined by demanding that it gives the correct S-matrix of a $$ T\overline{T} $$ T T ¯ -deformed integrable field theory. Remarkably, the renormalized Lagrangian is qualitatively very different from its classical counterpart.