The Higgs SU(2) model with fixed Higgs length is usually believed to have two different phases at high gauge coupling (β), separated by a line of first order transitions but not distinuguished by any typical symmetry associated with a local order parameter, as first proved by Fradkin and Shenker. We show that in regions of the parameter space where it is usually supposed to be a first order phase transition only a smooth crossover is in fact present.
We perform a detailed study of the phase diagram of the lattice Higgs SU(2) model with fixed Higgs field length. Consistently with previsions based on the Fradkin Shenker theorem we find a first order transition line with an endpoint whose position we determined. The diagram also shows cross-over lines: the cross-over corresponding to the pure SU(2) bulk is also present at nonzero coupling with the Higgs field and merges with the one that continues the line of first order transition beyond the critical endpoint. At high temperature the first order line becomes a crossover, whose position moves…
Yang-Mills-Higgs theory is quite a remarkable theory in that it shows very different behaviors without phase transitions. It is dominated by the Brout-Englert-Higgs mechanism in some domain of the phase diagram, while it is essentially QCD-like in another. It is expected that albeit there is no qualitative difference, there are substantially quantitative differences throughout the spectrum. This is investigated using lattice theory for the case of the scalar singlet channel for more than a hundred different points in the phase diagram. It is found that the results deviate partly substantially …
We investigate gauge theories based on the smallest exceptional simple lie group G(2). Our first model considered here is G(2) Yang-Mills coupled to a fundamental Higgs field. In 4 spacetime dimensions we explore the phase diagram of the theory, showing that at larger Higgs masses the first order deconfinement phase transition turns into a crossover and therefore connects the low temperature confined phase with the high temperature deconfined phase. The second model investigated is G(2) Yang-Mills coupled to fundamental fermions. It shares many features with QCD, especially fermionic baryons, …
Yang-Mills-Higgs theory, being the standard-model Higgs sector for a suitable choice of gauge and custodial group, offers a rich set of physics. In particular, in some region of its parameter space it has QCD-like behavior, while in some other region it is Higgs-like. Therefore, it is possible to study a plethora of phenomena within a single theory. Here, the physics of the standard-model version is studied using lattice gauge theory. To this end, the low-lying spectrum in several different channels is obtained for more than 140 different sets of bare parameters throughout the phase diagram. T…
According to recent work of Greensite and Matsuyama, the Higgs phase of a gauge Higgs theory is distinguished from the confinement and massless phases by the spontaneous breaking of a global center subgroup of the gauge group, and by confinement type. This is contrary to the notion that there is no essential distinction between the Higgs and confinement phases when the Higgs field is in the fundamental representation of the gauge group. Although this new symmetry breaking order parameter has been investigated in $D=4$ dimensions, there is so far no check in a non-abelian gauge theory containin…
We study the phase diagram and mass spectrum of an $SU(2)$ Gauge-Higgs Unification scenario on a five-dimensional orbifold.We observe spontaneous symmetry breaking within the Higgs phase of the theory and, in the vicinity of a newly discovered phase, we find that the ratio of Higgs to gauge boson masses takes a Standard Model-like value. Precisely in this region of the phase diagram, we observe dimensional reduction via localisation.
We consider three-dimensional lattice SU(Nc) gauge theories with degenerate multicomponent (Nf>1) complex scalar fields that transform under the fundamental representation of the gauge SU(Nc) group and of the global U(Nf) invariance group, interacting with the most general quartic potential compatible with the global (flavor) and gauge (color) symmetries. We investigate the phase diagrams, identifying the low-temperature Higgs phases and their global and gauge symmetries, and the critical behaviors along the different transition lines. In particular, we address the role of the quartic scalar p…
We determine the phase diagram of the Abelian-Higgs model in one spatial dimension and time (1+1D) on a lattice. We identify a line of first order phase transitions separating the Higgs region from the confined one. This line terminates in a quantum critical point above which the two regions are connected by a smooth crossover. We analyze the critical point and find compelling evidences for its description as the product of two non-interacting systems, a massless free fermion and a massless free boson. However, we find also some surprizing results that cannot be explained by our simple picture…
The SU(2)-Higgs model, with a single Higgs field in the fundamental representation and a quartic self-interaction, has a Higgs region and a confinement region which are analytically connected in the parameter space of the theory; these regions thus represent a single phase. The effect of multiple Higgs fields on this phase structure is examined via Monte Carlo lattice simulations. For the case of N>=2 identical Higgs fields, there is no remaining analytic connection between the Higgs and confinement regions, at least when Lagrangian terms that directly couple different Higgs flavours are omitt…
We study the phases and phase transition lines of the finite temperature G(2) Higgs model. Our work is based on an efficient local hybrid Monte-Carlo algorithm which allows for accurate measurements of expectation values, histograms and susceptibilities. On smaller lattices we calculate the phase diagram in terms of the inverse gauge coupling $β$ and the hopping parameter $κ$. For $κ\to 0$ the model reduces to G(2) gluodynamics and for $κ\to\infty$ to SU(3) gluodynamics. In both limits the system shows a first order confinement-deconfinement transition. We show that the first order transitions…
We study two different SU(2) gauge-scalar theories in 3 and 4 spacetime dimensions. Firstly, we focus on the 3 dimensional SU(2) theory with multiple Higgs fields in the adjoint representation, that can be mapped to cuprate systems in condensed matter physics which host a rich phase diagram including high-Tc superconductivity. It has been proposed that the theory with 4 adjoint Higgs fields can be used to explain the physics of hole-doped cuprates for a wide range of parameters. We show exploratory results on the phase diagram of the theory. On the other hand, we are interested in the 4 dimens…
We show that the Higgs and confinement phases of a gauge Higgs theory, with the Higgs field in the fundamental representation of the gauge group, are distinguished both by a broken or unbroken realization of the global center subgroup of the gauge group, and by the type of confinement in each phase. This is color confinement in the Higgs phase, and a stronger property, which we call "separation-of-charge" confinement, in the confining phase.
We 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>1 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 S…
We discuss the non-thermal phase structure of a chirally invariant Higgs-Yukawa model on the lattice in the presence of a higher dimensional $Φ^6$-term. For the exploration of the phase diagram we use analytical, lattice perturbative calculations of the constraint effectice potential as well as numerical simulations. We also present first results of the effects of the $Φ^6$-term on the lower Higgs boson mass bounds.
We study a chirally invariant Higgs-Yukawa model regulated on a space-time lattice. We calculate Higgs boson resonance parameters and mass bounds for various values of the mass of the degenerate fermion doublet. Also, first results on the phase transition temperature are presented. In general, this model may be relevant for BSM scenarios with a heavy fourth generation of quarks.
The phases of a lattice gauge model for the massive Yang-Mills are investigated. The phase diagram supports the recent conjecture on the large energy behavior of nonlinearly realized massive gauge theories (i.e. mass a` la Stueckelberg, no Higgs mechanism), envisaging a Phase Transition (PT) to an asymptotically free massless Yang-Mills theory.
A spectrum of localized excitations of isolated static fermions has been discovered in several different gauge Higgs theories. In lattice numerical simulations, we show that the charged elementary particles can have the spectrum of excitations in the Higgs phase of SU(3) gauge Higgs theory, $q=2$ Abelian Higgs theory, Landau-Ginzburg theory, and in chiral U(1) gauge Higgs theory. Possibly these excited states of the isolated fermions can be observed in ARPES studies of conventional superconductors. Also, we consider that similar kinds of excitations could exist in other gauge Higgs theories, s…
Deconfinement-Higgs continuity in ${\rm SU(2)}$ adjoint Higgs model at finite temperature
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Department of Physics, Graduate School of Science, Kobe University（神户大学理学研究科物理学系）；Department of Physics, and Research and Education Center for Natural Sciences, Keio University（庆应义塾大学自然科学教育研究中心及物理学系）
The Fradkin-Shenker theorem proves analyticity in a region that connects Higgs to confinement regimes, precluding a phase transition. This conflicts with a simpler analyticity argument applicable to any symmetry-breaking phase transition that requires the phase diagram to be bifurcated. A flaw in the Fradkin-Shenker and related Osterwalder-Seiler proofs is found which removes this paradox. Higgs and Confinement regions are everywhere separated by a phase boundary. A new order parameter allowing this transition to be traced with Monte-Carlo simulations without gauge fixing is introduced.
We propose that the Higgs phase of a gauge Higgs theory is the phase of spontaneously broken custodial symmetry, and present a new gauge invariant order parameter for custodial symmetry breaking which is very closely analogous to the Edwards-Anderson order parameter for spin glasses. Custodial symmetry is a global symmetry acting on the Higgs field alone, and we show here that the spin glass transition in gauge Higgs theories, from a QCD-like phase to a Higgs phase of broken custodial symmetry, coincides with the transition between two distinct types of confinement. These are color confinement…
