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

Abstract

The light-cone gauge approach to $T\overline{T}$ deformed models is used to derive the $T\overline{T}$ deformed matrix nonlinear Schrödinger equation, the Landau--Lifshitz equation, and the Gardner equation. Properties of one-soliton solutions of the $T\overline{T}$ 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 $T\overline{T}$ 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 $T\overline{T}$ 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.

arXiv comment34 pages, many figures. V2: minor corrections. V3: Two new comment sections added, accepted for publication in JHEP

References in corpus (30)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Asymptotic Fragility, Near $Ad{S}_2$ Holography and $T\bar{T}$
• Solving the Simplest Theory of Quantum Gravity
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
• Finite-size Effects from Giant Magnons
• The $T\overline{T}$ deformation of quantum field theory as random geometry
• $T\bar{T}$ Partition Function from Topological Gravity
• An integrable Lorentz-breaking deformation of two-dimensional CFTs
• The $\text{T}\bar{\text{T}}$ perturbation and its geometric interpretation
• $T\bar{T}$-deformations in closed form
• Strings on NS-NS Backgrounds as Integrable Deformations
• Generalised Born-Infeld models, Lax operators and the $\text{T}\bar{\text{T}}$ perturbation
• A pedagogical review on solvable irrelevant deformations of 2d quantum field theory
• $T\bar{T}$ Deformations, Massive Gravity and Non-Critical Strings
• On $T\bar{T}$ deformations and supersymmetry
• Supersymmetry and $T\overline{T}$ Deformations
• New Integrable System of 2dim Fermions from Strings on AdS_5 x S^5
• Integrable spin chain for stringy Wess-Zumino-Witten models
• $T\bar{T}$ deformations with $\mathcal{N}=(0,2)$ supersymmetry
• $T\bar{T}$-Deformed Actions and (1,1) Supersymmetry
• $T\bar{T}$ Flows and (2,2) Supersymmetry
• $T\overline{T}$, $\tilde{J}J$, $JT$ and $\tilde{J}T$ deformations
• $T\bar{T}$-like Flows in Non-linear Electrodynamic Theories and S-duality
• Integrable S matrix, mirror TBA and spectrum for the stringy ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$ WZW model
• Geometrizing non-relativistic bilinear deformations
• $T\bar{T}$ deformation of chiral bosons and Chern-Simons AdS${}_3$ gravity
• Irrelevant Deformations of Chiral Bosons
• $T\bar{T}$ deformation of classical Liouville field theory

Cited by in corpus (8)

• On the Classical Integrability of Root-$T\overline{T}$ Flows
• Interacting Chiral Form Field Theories and $T\overline{T}$-like Flows in Six and Higher Dimensions
• Massive gravity generalization of $T\overline{T}$ deformations
• $T\bar{T}$ flow as characteristic flows
• New classical integrable systems from generalized $T\bar{T}$-deformations
• $T\bar{T}$ deformed soft theorem
• Irrelevant and marginal deformed BMS field theories
• On correlators in $T\bar{T}$-deformed conformal field theories