Symmetry Breaking In Gauge Theories Research Articles

Spontaneous symmetry breaking in Lorentz violating background

In this paper, we study spontaneous symmetry breaking of gauge theories in a Lorentz violating background. Here, Lorentz symmetry will be broken down to its subgroup using the formalism of very special relativity. The breaking of the Lorentz symmetry will modify the gauge theories, and this will in turn modify the Higgs mechanisms for such theories. We will explicitly demonstrate that the different Hilbert spaces in various gauges of this theory can be related to each other through the gaugeon formalism. We will also discuss the FFBRST transformation for this theory, and observe that gaugeon formalism can be obtained from same. Thus, by making the BRST parameter finite and field dependent, we can relate different Hilbert spaces in different gauges for a gauge theory with spontaneous symmetry breaking in VSR.

Centre vortex removal restores chiral symmetry

The influence of centre vortices on dynamical chiral symmetry breaking is investigated through the light hadron spectrum on the lattice. Recent studies of the quark propagator and other quantities have provided evidence that centre vortices are the fundamental objects underpinning dynamical chiral symmetry breaking in gauge theory. For the first time, we use the chiral overlap fermion action to study the low-lying hadron spectrum on lattice ensembles consisting of Monte Carlo, vortex-removed, and vortex-projected gauge fields. We find that gauge field configurations consisting solely of smoothed centre vortices are capable of reproducing all the salient features of the hadron spectrum, including dynamical chiral symmetry breaking. The hadron spectrum on vortex-removed fields shows clear signals of chiral symmetry restoration at light values of the bare quark mass, while at heavy masses the spectrum is consistent with a theory of weakly interacting constituent quarks.

Measuring the trilinear neutral Higgs boson couplings in the minimal supersymmetric standard model at e+e− colliders in the light of the discovery of a Higgs boson

We consider the measurement of the trilinear couplings of the neutral Higgs bosons in the minimal supersymmetric standard model (MSSM) at a high energy [Formula: see text] linear collider in the light of the discovery of a Higgs boson at the CERN Large Hadron Collider (LHC). We identify the state observed at the LHC with the lightest Higgs boson [Formula: see text] of the MSSM, and impose the constraints following from this identification, as well as other experimental constraints on the MSSM parameter space. In order to measure trilinear neutral Higgs couplings, we consider different processes where the heavier Higgs boson [Formula: see text] of the MSSM is produced in electron–positron collisions, which subsequently decays into a pair of lighter Higgs boson. We identify the regions of the MSSM parameter space where it may be possible to measure the trilinear couplings of the Higgs boson at a future electron–positron collider. A measurement of the trilinear Higgs couplings is a crucial step in the construction of the Higgs potential, and hence in establishing the phenomena of spontaneous symmetry breaking in gauge theories.

Spontaneous symmetry breaking in gauge theories

The aim of this historical article is to describe the development of the idea of spontaneous symmetry breaking in gauge theories as seen from my perspective as a member of Abdus Salam's group at Imperial College London, UK. Beginning with an account of particle physics in the years after the Second World War, I describe early attempts at constructing a unified theory of weak and electromagnetic interactions, the obstacles encountered and how they were eventually overcome with the mass-generating mechanism incorporating the idea of spontaneous symmetry breaking, one of whose features is the now-famous Higgs boson.

Before, behind and beyond the discovery of the Higgs boson

Before, behind and beyond the discovery of the Higgs boson

Holographic modelling of a light technidilaton

We present a simplified holographic model of chiral symmetry breaking in gauge theory. The chiral condensate is represented by a single scalar field in AdS, with the gauge dynamics input through radial dependence of its mass, representing the running of the anomalous dimension of the qbar q operator. We discuss simple examples of the chiral transition out of the conformal window when the infrared value of the anomalous dimension, \gamma_m, is tuned to one (equivalently the AdS-scalar mass squared is tuned to the Breitenlohner-Freedman bound of -4). The output of the model are the masses of the $\bar{q} q$ scalar meson bound states. We show in an explicit example that if the gradient of the running of the anomalous dimension falls to zero at the scale where the BF bound violation occurs, so that the theory becomes near conformal, then the theory possesses a techni-dilaton state that is parametrically lighter than the dynamically generated quark mass. Indeed the full spectrum of excited meson states also become light (relative to the techni-quark mass) as they approach a conformal spectrum.

Gauge symmetry breaking in gauge theories—in search of clarification

The paper investigates the spontaneous breaking of gauge symmetries in gauge theories from a philosophical angle. Local gauge symmetry itself cannot break spontaneously in quantized gauge theories according to Elitzur's theorem---even though the notion of a spontaneously broken local gauge symmetry is widely employed in textbook expositions of the Higgs mechanism, the standard account of mass generation for the weak gauge bosons in the standard model. Nevertheless, gauge symmetry can be broken in gauge theories, namely, in the form of the breaking of remnant subgroups of the original local gauge group under which the theories typically remain invariant after gauge fixing. The paper discusses the relation between these instances of symmetry breaking and phase transitions and draws some more general conclusions for the philosophical interpretation of gauge symmetries and their breaking.

Evaluation of the Spontaneous Chiral Symmetry Breaking Scale in General Gauge Theories with Non-Perturbative Renormalization Group

We analyze the non-perturbative renormalization group in general vector-like gauge theories. The complete set of local four-fermi operators allowed by the chiral symmetry is taken into account. The beta functions for all those operators with gauge interactions are calculated. Within the four-fermi operator space, we propose two simple methods of evaluating the spontaneous chiral symmetry breaking scale. The large-N part of the system is separately evaluated and approximates the total system very well. Subject Index: 101, 132 1. Introduction Spontaneous chiral symmetry breaking in gauge theories has been an essential subject in particle physics. It will continue to be so in the future even in finite-temperature and finite-density situations.

Condensation of vortex-strings: effective potential contribution through dual actions

Topological excitations are believed to play an important role in different areas of physics. For example, one case of topical interest is the use of dual models of quantum cromodynamics to understand properties of its vacuum and confinement through the condensation of magnetic monopoles and vortices. Other applications are related to the role of these topological excitations, nonhomogeneous solutions of the field equations, in phase transitions associated to spontaneous symmetry breaking in gauge theories, whose study is of importance in phase transitions in the early universe, for instance. Here we show a derivation of a model dual to the scalar Abelian Higgs model where its topological excitations, namely vortex-strings, become manifest and can be treated in a quantum field theory way. The derivation of the nontrivial contribution of these vacuum excitations to phase transitions and its analogy with superconductivity is then made possible and they are studied here.

Universality of spontaneous chiral symmetry breaking in gauge theories

We investigate one-flavor QCD with an additional chiral scalar field. For a large domain in the space of coupling constants, this model belongs to the same universality class as QCD, and the effects of the scalar become unobservable. This is connected to a ``bound-state fixed point'' of the renormalization flow for which all memory of the microscopic scalar interactions is lost. The QCD domain includes a microscopic scalar potential with minima at nonzero field. On the other hand, for a scalar mass term m^2 below a critical value m_c^2, the universality class is characterized by perturbative spontaneous chiral symmetry breaking which renders the quarks massive. Our renormalization group analysis shows how this universality class is continuously connected with the QCD universality class.

Spontaneous symmetry breaking in gauge theories via Bose-Einstein condensation

We propose a mechanism leading naturally to spontaneous symmetry breaking in a gauge theory. The Higgs field is assumed to have global and gauged internal symmetries. We associate a nonzero chemical potential with one of the globally conserved charges commuting with all the gauge transformations. This induces a negative mass squared for the Higgs field, triggering the spontaneous symmetry breaking of the global and local symmetries. The mechanism is general and we test the idea for the electroweak theory in which the Higgs sector is extended to possess an extra global Abelian symmetry. With this symmetry we associate a nonzero chemical potential. The Bose-Einstein condensation of the Higgs bosons leads, at the tree level, to modified dispersion relations for the Higgs field, while the dispersion relations of the gauge bosons and fermions remain undisturbed. The latter are modified through higher order corrections. We have computed some corrections to the vacuum polarizations of the gauge bosons and fermions. To quantify the corrections to the gauge boson vacuum polarizations with respect to the standard model we considered the effects on the T parameter. We finally derive the one loop modified fermion dispersion relations.

Symmetry breaking of gauge theories via internal space dynamics

In this paper, I explain how gauge symmetry can be broken in a geometric way, \`{a} la Kaluza-Klein. In higher dimensional gravitational theories, one usually considers the extra dimensions to be ``frozen'' in time. However, the internal manifold is actually a dynamic entity. For example, its metric can change even if one expects its topological properties to be invariant. It is conceivable then, that at an earlier epoch the internal manifold made a geometric transition from say a maximally symmetric metric space to a less symmetric one. We know in a Kaluza-Klein reduction scheme, the massless gauge bosons are associated with the Killing vectors of the internal manifold. After the transition of the internal manifold, the gauge bosons associated with the broken Killing isometries will pick up a mass thereby breaking the gauge invariance partially. In this paper, I explore this idea, work out the mass of broken gauge bosons for some simple examples, and also point out how a mechanism similar to that of Higgs may be at work.

Dynamical chiral symmetry breaking in gauge theories with extra dimensions

We investigate dynamical chiral symmetry breaking in vector-like gauge theories in $D$ dimensions with ($D-4$) compactified extra dimensions, based on the gap equation (Schwinger-Dyson equation) and the effective potential for the bulk gauge theories within the improved ladder approximation. The non-local gauge fixing method is adopted so as to keep the ladder approximation consistent with the Ward-Takahashi identities. Using the one-loop $\bar{\rm MS}$ gauge coupling of the truncated KK effective theory which has a nontrivial ultraviolet fixed point (UV-FP) $g_*$ for the (dimensionless) bulk gauge coupling ${\hat g}$, we find that there exists a critical number of flavors, $N_f^{\rm crit}$ ($\simeq 4.2, 1.8$ for $D=6, 8$ for SU(3) gauge theory): For $N_f > N_f^{\rm crit}$, the dynamical chiral symmetry breaking takes place not only in the ``strong-coupling phase'' (${\hat g} >g_*$) but also in the ``weak-coupling phase'' (${\hat g} <g_*$) when the cutoff is large enough. For $N_f < N_f^{\rm crit}$, on the other hand, only the strong-coupling phase is a broken phase and we can formally define a continuum (infinite cutoff) limit, so that the physics is insensitive to the cutoff in this case. We also perform a similar analysis using the one-loop ``effective gauge coupling''. We find the $N_f^{\rm crit}$ turns out to be a value similar to that of the $\bar{\rm MS}$ case, notwithstanding the enhancement of the coupling compared with that of the $\bar{\rm MS}$.

INTRODUCTION TO THE NON-PERTURBATIVE RENORMALIZATION GROUP AND ITS RECENT APPLICATIONS

We introduce the basic ideas and the framework of the non-perturbative renormalization group particularly for pedestrians using elementary examples. First we briefly review the history of the renormalization theory and the renormalization group. We will make it clear that the modern renormalization theory is constructed on the idea of the renormalization group and it is quite a new type of theory in physics. Then we derive the exact non-perturbative renormalization group equation and set up its systematic approximation method. The lowest order approximation called the local potential approximation is applied to scalar theories with the ferromagnetic transition and quantum mechanics with tunneling. We compare our results with other methods, and will show that the non-perturbative renormalization group method is promising since it gives fairly good results already in the lowest order approximation and it does not suffer any divergent series expansion. As a typical application in high energy physics, we analyze the dynamical chiral symmetry breaking in gauge theories and investigate the chiral phase structures. Our new method improves results by the ladder Schwinger–Dyson equation so that the physical results might be less gauge dependent.

Solving the Dynamical Chiral Symmetry Breaking by Non-Perturbative Renormalization Group

We introduce the basic notions and the framework of the non-perturbative renormaliza­ tion group (NPRG) particularly for pedestrians using elementary examples. We derive an exact NPRG equation and set up its approximation method. The lowest order approxima­ tion called the local potential approximation (LPA) is applied to scalar theories with the ferromagnetic transition and quantum mechanics with tunneling. We compare our results with other methods, and will show that NPRG is very promising since it does not suffer any divergent series expansion. Then we analyze the dynamical chiral symmetry breaking in gauge theories and get the chiral phase structures. The LPA NPRG improves results by the ladder Schwinger-Dyson equation in a gauge independent way.

Spontaneously unbroken symmetry and gauge-invariant effective action

It is shown how spontaneous symmetry breaking in gauge theories may be described by assigning vacuum expectation values only to gauge-invariant, renormalizable, composite operators. This description is primarily of use in analyzing the dynamics of symmetry-breaking phase transitions in the early universe. The abelian Higgs model is studied in detail. The theory is formulated most naturally in a unitary gauge, which is shown to be (essentially) renormalizable. The effective action is calculated in a gradient expansion. It is renormalizable, manifestly gauge invariant, and free from singularities which afflict the conventional effective potential. The extension to non-abelian theories is discussed, also in a unitary gauge. Although this gauge is generally not renormalizable, it is expected that finite results can be obtained for gauge-invariant quantities.

QUANTUM CORRECTIONS EFFECT ON THE COUPLING OF THE GRAVITATIONAL AND SCALAR FIELDS AND SPONTANEOUSLY INDUCED GRAVITY

Gravity induced by the spontaneous symmetry breaking in gauge theories is studied. All calculations are carried out with an accuracy provided by the one-loop approximation. It appears that in an effective potential of the scalar field φ a parameter ε of a nonminimal coupling of φ with a curvature is a function of φ. Under zero energy density of the stable vacuum &lt;φ&gt;0 = µ it is proved that the induced gravitational constant G ind is finite only if µε′(µ) = −2ε(µ). Hence it follows that if gravity is induced indeed then its theory necessarily has the structure of the Einstein's theory for gravitation: G ind is positive and invariable (at zero temperature). Within the limitations imposed by the model, the T-dependence of G ind is exponentially relaxed.

Chiral Symmetry Breaking and Nonperturbative Scale Anomaly in Gauge Field Theories

The nonperturbative dynamics of chiral and scale symmetry breaking in asymptotically free and non-asymptotically free (with an ultraviolet stable fixed point) vector-like gauge theories is inves­ tigated. In the two-loop approximation analytical expressions for the chiral and gluon condensates are obtained. The hypothesis about a soft behaviour at small distances of composite operators in non-asymptotically free gauge theories with a fixed point is put forward and substantiated. It is shown that in these theories the form of the scale anomaly depends on the type of the phase in coupling constant to which it relates. The two component conception of scale symmetry breaking in gauge theories is suggested. The mass relation for the singlet scalar fermion-antifermion bound state is obtained. The important ingredient of this approach is a large (d'2) dynamical dimension of composite chiral fields. The application of this approach to QeD and technicolour models is discussed.

On the character of scalar symmetry breaking in gauge theories

It is shown that the phenomenon of spontaneous breaking of an approximate scale symmetry in gauge theories and the PCAC dynamics are incompatible.

On the dynamics of tumbling gauge theories

The dynamics of symmetry breaking in gauge theories without fundamental scalars is investigated. The method of determining the way of the vacuum rearrangement in these theories is elaborated.