1,721,008 research outputs found
Color flux tubes in SU (3) Yang-Mills theory: An investigation with the connected correlator
Full text linkIn this work we perform an investigation of the flux tube between two static color sources in four dimensional SU(3) Yang-Mills theory, using the so-called connected correlator. Contrary to most previous studies we do not use any smoothing algorithm to facilitate the evaluation of the correlator, that is performed using only stochastically exact techniques. We first examine the renormalization properties of the connected operator, then we present our numerical data for the longitudinal chromoelectric component of the flux tube, that are used to extract the dual superconductivity parameters
Three-dimensional phase transitions in multiflavor lattice scalar SO(N_{c}) gauge theories
Full text linkWe investigate the phase diagram and finite-temperature transitions of three-dimensional scalar SO(N_{c}) gauge theories with N_{f}≥2 scalar flavors. These models are constructed starting from a maximally O(N)-symmetric multicomponent scalar model (N=N_{c}N_{f}), whose symmetry is partially gauged to obtain an SO(N_{c}) gauge theory, with O(N_{f}) or U(N_{f}) global symmetry for N_{c}≥3 or N_{c}=2, respectively. These systems undergo finite-temperature transitions, where the global symmetry is broken. Their nature is discussed using the Landau-Ginzburg-Wilson (LGW) approach, based on a gauge-invariant order parameter, and the continuum scalar SO(N_{c}) gauge theory. The LGW approach predicts that the transition is of first order for N_{f}≥3. For N_{f}=2 the transition is predicted to be continuous: It belongs to the O(3) vector universality class for N_{c}=2 and to the XY universality class for any N_{c}≥3. We perform numerical simulations for N_{c}=3 and N_{f}=2,3. The numerical results are in agreement with the LGW predictions
Breaking of Gauge Symmetry in Lattice Gauge Theories
Full text linkWe 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
Three-dimensional Z2 -gauge N -vector models
No full textWe study the phase diagram and critical behaviors of three-dimensional lattice Z2-gauge N-vector models, in which an N-component real field is minimally coupled with Z2-gauge link variables. These models are invariant under global O(N) and local Z2 transformations. They present three phases characterized by the spontaneous breaking of the global O(N) symmetry and by the different topological properties of the Z2-gauge correlations. We address the nature of the three transition lines separating the three phases. The theoretical predictions are supported by numerical finite-size scaling analyses of Monte Carlo data for the N=2 model. In this case, continuous transitions can be observed along both transition lines where the N-component spins order, in the regimes of small and large inverse gauge coupling K. Even though these continuous transitions belong to the same XY universality class, their critical modes turn out to be different. When the gauge variables are disordered (small K), the relevant order-parameter field is a gauge-invariant bilinear combination of the vector field. On the other hand, when the gauge variables are ordered (large K), the order-parameter field is the gauge-dependent N-vector field, whose critical behavior can only be probed by using a stochastic gauge fixing that reduces the gauge freedom
Lattice gauge theories in the presence of a linear gauge-symmetry breaking
Full text linkWe 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 CP1 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 CP1 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
Higher-charge three-dimensional compact lattice Abelian-Higgs models
Full text linkWe consider three-dimensional higher-charge multicomponent lattice Abelian-Higgs (AH) models, in which a compact U(1) gauge field is coupled to an N-component complex scalar field with integer charge q, so that they have local U(1) and global SU(N) symmetries. We discuss the dependence of the phase diagram, and the nature of the phase transitions, on the charge q of the scalar field and the number N≥2 of components. We argue that the phase diagram of higher-charge models presents three different phases, related to the condensation of gauge-invariant bilinear scalar fields breaking the global SU(N) symmetry, and to the confinement and deconfinement of external charge-one particles. The transition lines separating the different phases show different features, which also depend on the number N of components. Therefore, the phase diagram of higher-charge models substantially differs from that of unit-charge models, which undergo only transitions driven by the breaking of the global SU(N) symmetry, while the gauge correlations do not play any relevant role. We support the conjectured scenario with numerical results, based on finite-size scaling analyses of Monte Carlo simuations for doubly charged unit-length scalar fields with small and large number of components, i.e., N=2 and N=25
Universal low-temperature behavior of two-dimensional lattice scalar chromodynamics
Full text linkWe study the role that global and local non-Abelian symmetries play in two-dimensional (2D) lattice gauge theories with multicomponent scalar fields. We start from a maximally O(M)-symmetric multicomponent scalar model. Its symmetry is partially gauged to obtain an SU(Nc) gauge theory (scalar chromodynamics) with global U(Nf) (for Nc≥3) or Sp(Nf) symmetry (for Nc=2), where Nf>1 is the number of flavors. Correspondingly, the fields belong to the coset SM/SU(Nc) where SM is the M-dimensional sphere and M=2NfNc. In agreement with the Mermin-Wagner theorem, the system is always disordered at finite temperature and a critical behavior only develops in the zero-temperature limit. Its universal features are investigated by numerical finite-size scaling methods. The results show that the asymptotic low-temperature behavior belongs to the universality class of the 2D CPNf-1 field theory for Nc>2 and to that of the 2D Sp(Nf) field theory for Nc=2. These universality classes correspond to 2D statistical field theories associated with symmetric spaces that are invariant under Sp(Nf) transformations for Nc=2 and under SU(Nf) for Nc>2. These symmetry groups are the same invariance groups of scalar chromodynamics, apart from a U(1) flavor symmetry that is present for Nf≥Nc>2, which does not play any role in determining the asymptotic behavior of the model
Three-dimensional lattice multiflavor scalar chromodynamics: interplay between global and gauge symmetries
Full text linkWe study the nature of the finite-temperature transition of the three-dimensional scalar chromodynamics with Nf flavors. These models are constructed by considering maximally O(M)-symmetric multicomponent scalar models, whose symmetry is partially gauged to obtain SU(Nc) gauge theories, with a residual nonabelian global symmetry given by U(Nf) for Nc≥3 and Sp(Nf) for Nc=2, so that M=2NcNf. For Nf=2 and for all values of Nc we investigated, Nc=2, 3, 4, these systems undergo a continuous finite-temperature transition, which belongs to a universality class related to the global symmetry group of the model. For Nc=2, since Sp(2)/Z2=SO(5), it belongs to the O(5) vector universality class. For Nc≥3, since SU(2)/Z2=SO(3), it belongs to the O(3) vector universality class. For Nf≥3, the numerical results show evidence of first-order transitions for any Nc. These results are in agreement with the predictions obtained by using the effective Landau-Ginzburg-Wilson approach in terms of a gauge-invariant order parameter. Our results indicate that the non-Abelian gauge degrees of freedom are irrelevant at the transition. These conclusions are supported by an analysis of gauge-field dependent correlation functions, that are always short ranged, even at the transition
Multicritical point of the three-dimensional Z2 gauge Higgs model
Full text linkWe investigate the multicritical behavior of the three-dimensional Z2 gauge Higgs model at the multicritical point (MCP) of its phase diagram, where one first-order transition line and two continuous Ising-like transition lines meet. The duality properties of the model determine some features of the multicritical behavior at the MCP located along the self-dual line. Moreover, we argue that the system develops a multicritical XY behavior at the MCP, which is controlled by the stable XY fixed point of the three-dimensional multicritical Landau-Ginzburg-Wilson field theory with two competing scalar fields associated with the continuous Z2 transition lines meeting at the MCP. This implies an effective enlargement of the symmetry of the multicritical modes at the MCP to the continuous group O(2). We also provide numerical results to support the multicritical XY scenario
Phase Diagram, Symmetry Breaking, and Critical Behavior of Three-Dimensional Lattice Multiflavor Scalar Chromodynamics
Full text linkWe study the nature of the phase diagram of three-dimensional lattice models in the presence of non-Abelian gauge symmetries. In particular, we consider a paradigmatic model for the Higgs mechanism, lattice scalar chromodynamics with Nf flavors, characterized by a non-Abelian SU(Nc) gauge symmetry. For Nf≥2 (multiflavor case), it presents two phases separated by a transition line where a gauge-invariant order parameter condenses, being associated with the breaking of the residual global symmetry after gauging. The nature of the phase transition line is discussed within two field-theoretical approaches, the continuum scalar chromodynamics, and the Landau-Ginzburg-Wilson (LGW) φ4 approach based on a gauge-invariant order parameter. Their predictions are compared with simulation results for Nf=2, 3 and Nc=2-4. The LGW approach turns out to provide the correct picture of the critical behavior at the transitions between the two phases
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