Recent work by Zamolodchikov and others has uncovered a kind of "solvable" irrelevant deformation of two dimensional QFT generated by the composite operator T T .The irrelevant composite operator T T is built with the components of the energy-momentum tensor.The T T deformation can be regarded as a peculiar kind of integrable perturbation of integrable quantum field theories (IQFT).In the holographic dual, this deformation represents a geometric cutoff of the asymptotic region of AdS.The QFT is placed on a Dirichlet boundary at finite radial distance in the bulk.In this thesis we consider the problem of exact integration of the T T deformation of two dimensional quantum field theories, as well as some higher dimensional extensions in the form of T T deformations.When the action can be shown to only depend algebraically on the background metric the solution of the deformation equation on the Lagrangian can be given in closed form in terms of solutions of the (extended) Burgers' equation.We present such examples in two and higher dimensions.
It was noticed many years ago, in the framework of massless RG ows, that the irrelevant composite operator T T, built with the components of the energy-momentum tensor, enjoys very special properties in 2D quantum eld theories, and can be regarded as a peculiar kind of integrable perturbation. Novel interesting features of this operator have recently emerged from the study of eective string theory models. In this paper we study further properties of this distinguished perturbation. We discuss how it aects
The irrelevant composite operator
TTˉ, constructed from components of the stress-energy tensor, exhibits unique properties in two-dimensional quantum field theories and represents a distinctive form of integrable deformation. Significant progress has been made in understanding the bulk aspects of the theory, including its interpretation in terms of coordinate transformations and its connection to topological gravity models. However, the behavior of
TTˉ-deformed theories in the presence of boundaries and defects remains largely unexplored. In this note, we review analytical results obtained through various techniques. Specifically, we study the
TTˉ-deformed exact g-function within the framework of the Thermodynamic Bethe Ansatz and show that the results coincide with those obtained by solving the corresponding Burgers-type flow equation. Finally, we highlight some potentially significant open problems.
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].
Abstract The irrelevant composite operator TT, constructed from components of the stress-energy tensor, exhibits unique properties in two-dimensional quantum field theories and represents a distinctive form of integrable deformation. Significant progress has been made in understanding the bulk aspects of the theory, including its interpretation in terms of coordinate transformations and its connection to topo- logical gravity models. However, the behavior of TT-deformed theories in the pres- ence of boundaries and defects remains largely unexplored. In this note, we review analytical results obtained through various techniques. Specifically, we study the TT-deformed exact g-function within the framework of the Thermodynamic Bethe Ansatz and show that the results coincide with those obtained by solving the corre- sponding Burgers-type flow equation. Finally, we highlight some potentially signif- icant open problems.