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Register a new userLattice gauge theories in the presence of a linear gauge-symmetry breaking
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We study the effects of gauge-symmetry breaking (GSB) perturbations in three-dimensional lattice gauge theories with scalar fields. We study this issue at transitions in which gauge correlations are not critical and the gauge symmetry only selects the gauge-invariant scalar degrees of freedom that become critical. A paradigmatic model in which this behavior is realized is the lattice CP(1) model or, more generally, the lattice Abelian-Higgs model with two-component complex scalar fields and compact gauge fields. We consider this model in the presence of a linear GSB perturbation. The gauge symmetry turns out to be quite robust with respect to the GSB perturbation: the continuum limit is gauge-invariant also in the presence of a finite small GSB term. We also determine the phase diagram of the model. It has one disordered phase and two phases that are tensor and vector ordered, respectively. They are separated by continuous transition lines, which belong to the O(3), O(4), and O(2) vector universality classes, and which meet at a multicritical point. We remark that the behavior at the CP(1) gauge-symmetric critical point substantially differs from that at transitions in which gauge correlations become critical, for instance at transitions in the noncompact lattice Abelian-Higgs model that are controlled by the charged fixed point: in this case the behavior is extremely sensitive to GSB perturbations.
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We study perturbations that break gauge symmetries in lattice gauge theories. As a paradigmatic model, we consider the three-dimensional Abelian-Higgs (AH) model with an N-component scalar field and a noncompact gauge field, which is invariant under U(1) gauge and SU(N) transformations. We consider gauge-symmetry breaking perturbations that are quadratic in the gauge field, such as a photon mass term, and determine their effect on the critical behavior of the gauge-invariant model, focusing mainly on the continuous transitions associated with the charged fixed point of the AH field theory. We discuss their relevance and compute the (gauge-dependent) exponents that parametrize the departure from the critical behavior (continuum limit) of the gauge-invariant model. We also address the critical behavior of lattice AH models with broken gauge symmetry, showing an effective enlargement of the global symmetry, from U(N) to O(2N), which reflects a peculiar cyclic renormalization-group flow in the space of the lattice AH parameters and of the photon mass.
By evaluating the so-called Bose-ghost propagator, we present the first numerical evidence of BRST-symmetry breaking for Yang-Mills theory in minimal Landau gauge, i.e. due to the restriction of the functional integration to the first Gribov region in the Gribov-Zwanziger approach. Our data are well described by a simple fitting function, which can be related to a massive gluon propagator in combination with an infrared-free (Faddeev-Popov) ghost propagator. As a consequence, the Bose-ghost propagator, which has been proposed as a carrier of the confining force in minimal Landau gauge, displays a 1/p^4 singularity in the infrared limit.
We consider two-dimensional lattice SU($N_c$) gauge theories with $N_f$ real scalar fields transforming in the adjoint representation of the gauge group and with a global O($N_f$) invariance. Focusing on systems with $N_fge 3$, we study their zero-temperature limit, to understand under which conditions a continuum limit exists, and to investigate the nature of the associated quantum field theory. Extending previous analyses, we address the role that the gauge-group representation and the quartic scalar potential play in determining the nature of the continuum limit (when it exists). Our results further corroborate the conjecture that the continuum limit of two-dimensional lattice gauge models with multiflavor scalar fields, when it exists, is associated with a $sigma$ model defined on a symmetric space that has the same global symmetry as the lattice model.
We consider three-dimensional lattice SU($N_c$) gauge theories with multiflavor ($N_f>1$) scalar fields in the adjoint representation. We investigate their phase diagram, identify the different Higgs phases with their gauge-symmetry pattern, and determine the nature of the transition lines. In particular, we study the role played by the quartic scalar potential and by the gauge-group representation in determining the Higgs phases and the global and gauge symmetry-breaking patterns characterizing the different transitions. The general arguments are confirmed by numerical analyses of Monte Carlo results for two representative models that are expected to have qualitatively different phase diagrams and Higgs phases. We consider the model with $N_c = 3$, $N_f=2$ and with $N_c=2$, $N_f= 4$. This second case is interesting phenomenologically to describe some features of cuprate superconductors.
QCD monopoles are magnetically charged quasiparticles whose Bose-Einstein condensation (BEC) at $T<T_c$ creates electric confinement and flux tubes. The magnetic scenario of QCD proposes that scattering on the non-condensed component of the monopole ensemble at $T>T_c$ plays an important role in explaining the properties of strongly coupled quark-gluon plasma (sQGP) near the deconfinement temperature. In this paper, we study the phenomenon of chiral symmetry breaking and its relation to magnetic monopoles. Specifically, we study the eigenvalue spectrum of the Dirac operator in the basis of fermionic zero modes in an SU(2) monopole background. We find that as the temperature approaches the deconfinement temperature $T_c$ from above, the eigenvalue spectrum has a finite density at $omega = 0$, indicating the presence of a chiral condensate. In addition, we find the critical scaling of the eigenvalue gap to be consistent with that of the correlation length in the 3d Ising model and the BEC transition of monopoles on the lattice.
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