Abstract
Surprising links between the deformation of 2D quantum field theories induced by the composite mathrm{T}overline{mathrm{T}} operator, effective string models and the AdS/CFT correspondence, have recently emerged. The purpose of this article is to discuss various classical aspects related to the deformation of 2D interacting field theories. Special attention is given to the sin(h)-Gordon model, for which we were able to construct the mathrm{T}overline{mathrm{T}} -deformed Lax pair. We consider the Lax pair formulation to be the first essential step toward a more satisfactory geometrical interpretation of this deformation within the integrable model framework.Furthermore, it is shown that the 4D Maxwell-Born-Infeld theory, possibly with the addition of a mass term or a derivative-independent potential, corresponds to a natural extension of the 2D examples. Finally, we briefly comment on 2D Yang-Mills theory and propose a modification of the heat kernel, for a generic surface with genus p and n boundaries, which fully accounts for the mathrm{T}overline{mathrm{T}} contribution.
Highlights
It is shown that the 4D Maxwell-Born-Infeld theory, possibly with the addition of a mass term or a derivative-independent potential, corresponds to a natural extension of the 2D examples
We briefly comment on 2D Yang-Mills theory and propose a modification of the heat kernel, for a generic surface with genus p and n boundaries, which fully accounts for the TTcontribution
Out of all possible bosonic theories corresponding to the Lagrangian density (2.23), we will focus on the TT -deformed classical sine-Gordon model, which corresponds to the case of a single boson field φ interacting with a sine potential
Summary
In [7, 13] it was proven that the energy levels En(R, τ ) associated to the stationary states. With τ = τ (1−τ F0), that is a reparametrization ∆En(R, τ ) → ∆En(R, τ) of the perturbing parameter τ in the energy differences ∆En(R, τ ) = En(R, τ ) − E0(R, τ ) It was argued in [7] that (2.1) is equivalent, up to total derivative terms, to the following fundamental equation for the Lagrangian:. In the N = 1 case, we first obtained the compact form (2.23) performing a resummation of the more complicated, but equivalent, expression given in [13] and subsequently we developed the more direct approach, which again maps (2.21) to a Burgers-type equation The latter technique was independently proposed in [36] and applied to different classes of systems and to models in higher spacetime dimensions.
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