Smirnov and Zamolodchikov recently introduced a new class of two-dimensional quantum field theories, defined through a differential change of any existing theory by the determinant of the energy-momentum tensor. From this
TT flow equation one can find a simple expression for both the energy spectrum and the
S-matrix of the
TT deformed theories. Our goal is to find the renormalized Lagrangian of the
TT deformed theories. In the context of the
TT deformation of an integrable theory, the deformed theory is also integrable and, correspondingly, the
S-matrix factorizes into two-to-two
S-matrices. One may thus hope to be able to extract the renormalized Lagrangian from the
S-matrix. We do this explicitly for the
TT deformation of a free massive scalar, to second order in the deformation parameter. Once one has the renormalized Lagrangian one can, in principle, compute all other observables, such as correlation functions. We briefly discuss this, as well as the relation between the renormalized Lagrangian, the
TT flow equation, and the
S-matrix. We also mention a more general class of integrability-preserving deformations of a free scalar field theory.
Abstract We study perturbative renormalization of the composite operators in the
TT T T ¯ -deformed two-dimensional free field theories. The pattern of renormalization for the stress-energy tensor is different in the massive and massless cases. While in the latter case the canonical stress tensor is not renormalized up to high order in the perturbative expansion, in the massive theory there are induced counterterms at linear order. For a massless theory our results match the general formula derived recently in [1].
That the exact quantum S-matrix of
TT-deformed field theories is known has interesting consequences for their perturbative renormalization. Recent investigations into the interplay between renormalization and integrable deformations have focused on those cases where the (undeformed) seed theories are integrable. In this paper, we study the perturbative renormalization of nonintegrable
TT-deformed field theories, focusing on a theory of scalars with a quartic interaction. We show that in this theory, the 4-point 1-loop S-matrix exhibits features similar to its integrable cousins. We also carry out a similar analysis for the case of an integrable quantum field theory comprising a pair of chiral bosons. Our discussion of this latter theory supplies the first explicit example of a perturbative field theory computation in the formalism due to Sen.
Abstract We explore the analytic structure of the non-perturbative S-matrix in arguably the simplest family of massive non-integrable quantum field theories: the Ising field theory (IFT) in two dimensions, which may be viewed as the Ising CFT deformed by its two relevant operators, or equivalently, the scaling limit of the Ising model in a magnetic field. Our strategy is that of collider physics: we employ Hamiltonian truncation method (TFFSA) to extract the scattering phase of the lightest particles in the elastic regime, and combine it with S-matrix bootstrap methods based on unitarity and analyticity assumptions to determine the analytic continuation of the 2 → 2 S-matrix element to the complex s-plane. Focusing primarily on the “high temperature” regime in which the IFT interpolates between that of a weakly coupled massive fermion and the E8 affine Toda theory, we will numerically determine 3-particle amplitudes, follow the evolution of poles and certain resonances of the S-matrix, and exclude the possibility of unknown wide resonances up to reasonably high energies.
Abstract In this paper, we investigate the partition functions of conformal field theories (CFTs) with the T
T T ¯ deformation on a torus in terms of the perturbative QFT approach. In Lagrangian path integral formalism, the first- and second-order deformations to the partition functions of 2D free bosons, free Dirac fermions, and free Majorana fermions on a torus are obtained. The corresponding Lagrangian counterterms in these theories are also discussed. The first two orders of the deformed partition functions and the first-order vacuum expectation value (VEV) of the first quantum KdV charge obtained by the perturbative QFT approach are consistent with results obtained by the Hamiltonian formalism in literature.
Abstract We compute the leading correction to entanglement entropy in
TT T T ¯ deformed massive QFTs. We show that both for massive scalar and Dirac fermion, the leading order correction to the entanglement entropy of half space comes from the boundary of the entangling surface. For the case of massive scalar, the boundary term is finite while for massive fermion, it diverges logarithmically giving rise to an additional log-square divergence in the entanglement entropy.