Perturbative renormalization of the $$ \mathrm{T}\overline{\mathrm{T}} $$ -deformed free massive Dirac fermion
Anshuman Dey (The Racah Institute of Physics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Jerusalem, 91904, Israel); Aryeh Fortinsky (The Racah Institute of Physics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Jerusalem, 91904, Israel)
In this paper we explicitly carry out the perturbative renormalization of the $$ T\overline{T} $$ -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 $$ T\overline{T} $$ -deformed integrable field theory. Remarkably, the renormalized Lagrangian is qualitatively very different from its classical counterpart.
