Marginal $T\bar{T}$-Like Deformation and ModMax Theories in Two Dimensions

Abstract

Recently, the ModMax theory has been proposed as a unique conformal nonlinear extension of electrodynamics. We have shown in [1] that this modification can be reproduced a marginal T T -like deformation from pure Maxwell theory. Further, this deformation is solved by using a perturbative approach. In this letter, we will investigate another ModMax-like deformation for a two-dimensional (2D) scalar field theory. In this regard, we first find a marginal T T -like deformation in two dimensions and then reproduce the MM-like Lagrangian from a multiple 2D scalar field theory.

Nonlinear automorphism of the conformal algebra in 2D and continuous $$ \sqrt{T\overline{T}} $$ deformations

“…Thus, eq. ( 3.3) precisely agrees with the flow that has been recently considered in [32,33] and [34] (see also [35,36]), for some concrete examples in the Lagrangian formalism. Indeed, in [32] it was shown that a dimensional reduction of the ModMax theory [38] (see also [39][40][41][42]) to two spacetime dimensions corresponds to the continuous √ T T deformation of N = 2 free bosons, and then extended the deformation to arbitrary N .…”

“…The deformation of free bosons was also addressed in [33] from a more general approach, where it was argued that the deformation should also work well for a wider class of examples, as confirmed in [36]. The same result for free bosons was also obtained in [34] from a perturbative approach. Later on, in [35] it was shown that the flow equation (3.2) in Lagrangian form can be reduced to a set of first order non-linear PDE's by the method of characteristics, and applied them to recover the deformation of free bosons.…”

“…Note that, as it also occurs for the ModMax theory [38] (see also [43]), the equivalence of the deformed Lagrangian action for the free bosons obtained in [32][33][34] and also in [35] with the Hamiltonian action given by (3.7) with (3.8), requires careful implementation of a suitable Legendre transformation. In the case of a single free boson (N = 1) the deformation is trivial because the spectrally flowed energy simplifies as H α = 1 2 Π 2 e −α + e α Φ 2 , so that the momentum is obtained from its own field equation Π = e α Φ.…”

“…T T deformations have also been addressed for field theories in 2D along different approaches and points of view in [32][33][34] (see also [35,36]), and for the deformation of two free harmonic oscillators in classical mechanics [37].…”

The phase diagram of $$ T\overline{T} $$-deformed Yang-Mills theory on the sphere

“…The T T deformation of gauge fields has also been studied in connection with DBI-like theories[28][29][30].…”