T T ¯ deformation of the compactified boson and its interpretation in lattice gauge theory

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. 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 TT¯ deformation 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. In particular we show, by imposing that the spectrum of the model obeys the inviscid Burgers equation, that the TT¯ deformations follow well-defined trajectories in the parameter space (σ,L) of the model, where σ is the string tension, which are characterized by a constant value of the dimensionless compactification radius ρ=Lσ/2π. We discuss the potential usefulness of these results for studying the spacelike string tension of the underlying lattice gauge theory and its behavior across the deconfinement transition.