Abstract
In this paper we explicitly carry out the perturbative renormalization of the Toverline{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 Toverline{T} -deformed integrable field theory. Remarkably, the renormalized Lagrangian is qualitatively very different from its classical counterpart.
Highlights
Recently in two dimensions [3, 4] and has received wide attention in the past few years as the theory is solvable
In this paper we explicitly carry out the perturbative renormalization of the T T-deformed free massive Dirac fermion in two dimensions up to second order in the coupling constant
We demonstrate that the renormalized Lagrangian is unambiguously determined by demanding that it gives the correct S-matrix of a T T-deformed integrable field theory
Summary
Several aspects of integrability, two-dimensional quantum field theories and T T-deformations are discussed. In two dimensional integrable theories the S-matrix of any scattering process factorizes into two-to-two S-matrices and there is no particle production [31]–[37]. Two dimensional kinematics of the two-to-two scattering processes have the unique property that the incoming momenta of the particles equal the outgoing momenta of the particles This fact and the Lorentz invariance implies that the S-matrix, denoted by S(θ), will only be a function of the difference of rapidities, θ = θ1 − θ2. We will be restricted to the low-energy regime of the T T-deformed theories In this regime these are quantum field theories and can be studied perturbatively in the T T-coupling λ around λ = 0 [8, 30, 42]–[46].4
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