On the $T\bar{T}$ deformation of the compactified boson and its interpretation in Lattice Gauge Theory

Abstract

We study the effective string description of space-like Polyakov loop correlators at finite temperature with the goal of describing the behaviour of the space--like string tension in the vicinity of the deconfinement transition. To this end we construct the partition function of the Nambu-Goto effective string theory in presence of a compact transverse direction of length $L$ equal to the inverse temperature. We then show that, under particular conditions, our result can be interpreted as the partition function of the $T\bar{T}$ deformation of the 2d quantum field theory describing a compactified bosonic field and that this mapping allows a deeper insight on the behaviour of the space-like observables of the theory. In particular we show, by imposing that the spectrum of the model obeys the inviscid Burgers equation, that the $T\bar{T}$ deformations follow well defined trajectories in the parameter space $(\sigma ,L)$ of the model, where $\sigma$ is the string tension, which are characterized by a constant value of the dimensionless compactification radius $\rho =L\sqrt{\sigma /2\pi }$. We discuss the potential usefulness of these results for studying the space--like string tension of the underlying Lattice Gauge Theory and its behaviour across the deconfinement transition.

28 pages, 2 figures. V2: expanded comments in sections 2.2, 2.3 and 4

References in corpus (9)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• The Spatial String Tension, Thermal Phase Transition, and AdS/QCD
• The Spatial String Tension and Dimensional Reduction in QCD
• The partition function of interfaces from the Nambu-Goto effective string theory
• Spatial string tension of finite temperature QCD matter in gauge/gravity duality
• The Spatial String Tension in the Deconfined Phase of SU(N) Gauge Theory and Gauge/String Duality
• TTbar deformation and the light-cone gauge
• Abelian spatial string tension in finite temperature SU(2) gauge theory

Cited by in corpus (5)

• $T\overline{T}$ deformation in SCFTs and integrable supersymmetric theories
• Sampling the lattice Nambu-Goto string using Continuous Normalizing Flows
• Fine corrections in the effective string describing SU(2) Yang-Mills theory in three dimensions
• $T\overline{T}$-deformation of $q$-Yang-Mills theory
• Deforming the ODE/IM correspondence with $\mathrm{T}\bar{\mathrm{T}}$