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.
Highlights
An interesting open issue in lattice gauge theory is to understand and model the behavior of the so-called “spacelike string tension” [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] across the deconfinement transition
We study the effective string description of spacelike Polyakov loop correlators at finite temperature with the goal of describing the behavior of the spacelike string tension in the vicinity of the deconfinement transition
Under particular conditions, our result can be interpreted as the partition function of the TTdeformation of the 2d quantum field theory describing a compactified bosonic field and that this mapping allows a deeper insight on the behavior of the spacelike observables of the theory
Summary
An interesting open issue in lattice gauge theory is to understand and model the behavior of the so-called “spacelike string tension” [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] across the deconfinement transition. When the perturbation parameter t is positive within the sign convention employed in Eq (1.1) it can be shown that the perturbed partition function is unique and that it satisfies a differential equation originating from the Burgers equation for the energy levels [20]; this allows us to determine many of its properties, both at the perturbative and at the nonperturbative level in t In this respect, the effective string theory approach, which allows us to construct in an explicit way the partition function of the perturbed model for any value of the perturbing parameter, represents a perfect laboratory to test the above approaches and, another aim of our paper is to extend the range of explicitly known partition functions to the TTperturbation of the CFT of a compactified boson. IV will be devoted to a discussion of potential applications of our results and to some concluding remarks
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