Duals of U(N) LGT with staggered fermions

Various approaches to construction of dual formulations of non-abelian lattice gauge theories are reviewed. In the case of U(N) LGT we use a theory of the Weingarten functions to construct a dual formulation. In particular, the dual representations are constructed 1) for pure gauge models in all dimensions, 2) in the strong coupling limit for the models with arbitrary number of flavours and 3) for two-dimensional U(N) QCD with staggered fermions. Applications related to the finite temperature/density QCD are discussed.Comment: 8 pages, Proceedings for the 35th International Symposium on Lattice Field Theory (Lattice 2017

Three-quark potentials in an SU(3)SU(3) effective Polyakov loop model

Three-quark potentials are studied in great details in the three-dimensional $SU(3)$ pure gauge theory at finite temperature, for the cases of static sources in the fundamental and adjoint representations. For this purpose, the corresponding Polyakov loop model in its simplest version is adopted. The potentials in question, as well as the conventional quark--anti-quark potentials, are calculated numerically both in the confinement and deconfinement phases. Results are compared to available analytical predictions at strong coupling and in the limit of large number of colors $N$. The three-quark potential is tested against the expected $\Delta$ and $Y$ laws and the $3q$ string tension entering these laws is compared to the conventional $q\bar{q}$ string tension. As a byproduct of this investigation, essential features of the critical behaviour across the deconfinement transition are elucidated.Comment: 28 pages, 18 figures, 4 tables; some text and a few references added; version accepted for publication on Nucl. Phys.

Critical behavior of the compact 3d U(1) gauge theory on isotropic lattices

We report on the computation of the critical point of the deconfinement phase transition, critical indices and the string tension in the compact three dimensional U(1) lattice gauge theory at finite temperatures. The critical indices govern the behavior across the deconfinement phase transition in the pure gauge U(1) model and are generally expected to coincide with the critical indices of the two-dimensional XY model. We studied numerically the U(1) model for N_t=8 on lattices with spatial extension ranging from L=32 to L=256. Our determination of the infinite volume critical point on the lattice with N_t=8 differs substantially from the pseudo-critical coupling at L=32, found earlier in the literature and implicitly assumed as the onset value of the deconfined phase. The critical index $\nu$ computed from the scaling of the pseudo-critical couplings with the extension of the spatial lattice agrees well with the XY value $\nu$=1/2. On the other hand, the index $\eta$ shows large deviation from the expected universal value. The possible reasons of such behavior are discussed in details.Comment: 15 pages, 7 figures; version accepted for publication on J. Stat. Mech

Critical behavior of 3D Z(N) lattice gauge theories at zero temperature

Three-dimensional $Z(N)$ lattice gauge theories at zero temperature are studied for various values of $N$. Using a modified phenomenological renormalization group, we explore the critical behavior of the generalized $Z(N)$ model for $N=2,3,4,5,6,8$. Numerical computations are used to simulate vector models for $N=2,3,4,5,6,8,13,20$ for lattices with linear extension up to $L=96$. We locate the critical points of phase transitions and establish their scaling with $N$. The values of the critical indices indicate that the models with $N>4$ belong to the universality class of the three-dimensional $XY$ model. However, the exponent $\alpha$ derived from the heat capacity is consistent with the Ising universality class. We discuss a possible resolution of this puzzle. We also demonstrate the existence of a rotationally symmetric region within the ordered phase for all $N\geq 5$ at least in the finite volume.Comment: 25 pages, 4 figures, 8 table