Universal signatures of the effective string in finite temperature lattice gauge theories

We study the behaviour of the interquark potential in lattice gauge theories at high temperature, but still in the confining phase, and propose a new observable which could play in this regime the same role played by the Luscher term in the low temperature limit. This quantity is related to the exponent of the power prefactor in the effective string partition function or, equivalently, to the coefficient of the logarithmic correction in the interquark potential and, as for the usual Luscher term, its value does not depend on the particular gauge group under consideration or on the form of the effective string action used to model the flux tube. In this respect it can be considered as a universal signature of the effective string behaviour of the flux tube. As a test of our proposal we studied this quantity with a set of high-precision numerical simulations in the (2+1) dimensional SU(2), SU(3) and SU(4) Yang-Mills theories and in the Z_2 gauge model, always finding a perfect agreement with the predicted values.