$$ T\overline{T} $$ deformation of classical Liouville field theory

Leoni, Matías

doi:10.1007/jhep07(2020)230

Cited by 13 publications

(14 citation statements)

References 40 publications

(64 reference statements)

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“…Lax pairs of several models including the NLS model were recently found in [37] by using the dynamical coordinate transformation [14]. Their results agree with the previously known Lax pairs of the sine-Gordon and Liouville models [21,38]. It should be possible to apply the method of [37] to the matrix NLS model and the LL model.…”

Section: Discussionsupporting

confidence: 76%

$T\overline{T}$ Deformations of nonrelativistic models

Esper,

Frolov

2021

Preprint

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The light-cone gauge approach to T T deformed models is used to derive the T T deformed matrix nonlinear Schrödinger equation, the Landau-Lifshitz equation, and the Gardner equation. Properties of one-soliton solutions of the T T deformed nonlinear Schrödinger and Korteweg-de Vries equations are discussed in detail. The NLS soliton exhibits the recently discussed phenomenon of widening/narrowing width of particles under the T T deformation. However, whether the soliton's size is increasing or decreasing depends not only on the sign of the deformation parameter but also on soliton and potential parameters. The T T deformed KdV equation admits a one-parameter family of one-soliton solutions in addition to the usual velocity parameter. The extra parameter modifies the properties of the soliton, in particular, it appears in the dispersion relation.

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Section: Discussionsupporting

confidence: 76%

$T\overline{T}$ Deformations of nonrelativistic models

Esper,

Frolov

2021

Preprint

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“…Lax pairs of several models including the NLS model were recently found in [39] by using the dynamical coordinate transformation [14]. Their results agree with the previously known Lax pairs of the sine-Gordon and Liouville models [21,40]. It should be possible to apply the method of [39] to the matrix NLS model and the LL model.…”

Section: Jhep06(2021)101supporting

confidence: 69%

$$ T\overline{T} $$ deformations of non-relativistic models

Chantelle

Фролов

2021

J. High Energ. Phys.

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The light-cone gauge approach to $$ T\overline{T} $$ T T ¯ deformed models is used to derive the $$ T\overline{T} $$ T T ¯ deformed matrix nonlinear Schrödinger equation, the Landau-Lifshitz equation, and the Gardner equation. Properties of one-soliton solutions of the $$ T\overline{T} $$ T T ¯ deformed nonlinear Schrödinger and Korteweg-de Vries equations are discussed in detail. The NLS soliton exhibits the recently discussed phenomenon of widening/narrowing width of particles under the $$ T\overline{T} $$ T T ¯ deformation. However, whether the soliton’s size is increasing or decreasing depends not only on the sign of the deformation parameter but also on soliton and potential parameters. The $$ T\overline{T} $$ T T ¯ deformed KdV equation admits a one-parameter family of one-soliton solutions in addition to the usual velocity parameter. The extra parameter modifies the properties of the soliton, in particular, it appears in the dispersion relation.

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“…The T T -deformed Liouville field theory was studied in [19] where infinite conserved currents were constructed from some ansatz without using the Lax connection. From the discussion in the last subsection, we can present the deformed Lax connections explicitly…”

Section: Examplesmentioning

confidence: 99%

Lax Connections in $T\bar{T}$-deformed Integrable Field Theories

Chen,

Hou,

Tian

2021

Preprint

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In this work, we try to construct the Lax connections of T T -deformed integrable field theories in two different ways. With reasonable assumptions, we make ansatz and find the Lax pairs in the T T -deformed affine Toda theories and the principal chiral model by solving the Lax equations directly. This way is straightforward but maybe hard to apply for general models. We then make use of the dynamical coordinate transformation to read the Lax connection in the deformed theory from the undeformed one. We find that once the inverse of the transformation is available, the Lax connection can be read easily. We show the construction explicitly for a few classes of scalar models, and find consistency with the ones in the first way.

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$$ T\overline{T} $$ deformation of classical Liouville field theory

Abstract: We consider the irrelevant flow of classical Liouville field theory driven by the TT operator. After discussing properties of its exact action and equation of motion we construct an infinite set of conserved currents. We also find its vacuum solutions.

Cited by 13 publications

References 40 publications

$T\overline{T}$ Deformations of nonrelativistic models

$T\overline{T}$ Deformations of nonrelativistic models

$$ T\overline{T} $$ deformations of non-relativistic models

Lax Connections in $T\bar{T}$-deformed Integrable Field Theories

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