A different kind of string

Journal of High Energy Physics 2015.1 (2015): 105 reproduced by permission of Scuola Internazionale Superiore di Studi Avanzati (SISSA)In U(1) lattice gauge theory in three spacetime dimensions, the problem of confinement can be studied analytically in a semi-classical approach, in terms of a gas of monopoles with Coulomb-like interactions. In addition, this theory can be mapped to a spin model via an exact duality transformation, which allows one to perform high-precision numerical studies of the confining potential. Taking advantage of these properties, we carried out an accurate investigation of the effective string describing the low-energy properties of flux tubes in this confining gauge theory. We found striking deviations from the expected Nambu-Goto-like behavior, and, for the first time, evidence for contributions that can be described by a term proportional to the extrinsic curvature of the effective string worldsheet. Such term is allowed by Lorentz invariance, and its presence in the infrared regime of the U(1) model was indeed predicted by Polyakov several years ago. Our results show that this term scales as expected according to Polyakov’s solution, and becomes the dominant contribution to the effective string action in the continuum limit. We also demonstrate analytically that the corrections to the confining potential induced by the extrinsic curvature term can be related to the partition function of the massive perturbation of a c = 1 bosonic conformal field theory. The implications of our results for SU(N) Yang-Mills theories in three and in four spacetime dimensions are discussedThis work is supported by the Spanish MINECO (grant FPA2012-31686 and “Centro de Excelencia Severo Ochoa” programme grant SEV-2012-0249

First-order phase transitions in Yang-Mills theories and the density of state method

When studied at finite temperature, Yang-Mills theories in 3+1 dimensions display the presence of confinement/deconfinement phase transitions, which are known to be of first order - the SU(2) gauge theory being the exception. Theoretical as well as phenomenological considerations indicate that it is essential to establish a precise characterization of these physical systems in proximity of such phase transitions. We present and test a new method to study the critical region of parameter space in non-Abelian quantum field theories on the lattice, based upon the logarithmic linear relaxation (LLR) algorithm. We apply this method to the SU(3) Yang-Mills lattice gauge theory, and perform extensive calculations with one fixed choice of lattice size. We identify the critical temperature, and measure interesting physical quantities near the transition. Among them, we determine the free energy of the model in the critical region, exposing for the first time its multivalued nature with a numerical calculation from first principles, providing this novel evidence in support of a first-order phase transition. This study sets the stage for future high-precision measurements, by demonstrating the potential of the method