scholarly journals ANALYTIC MULTI-REGGE THEORY AND THE POMERON IN QCD II: GAUGE-THEORY ANALYSIS

1993 ◽  
Vol 08 (27) ◽  
pp. 4755-4895 ◽  
Author(s):  
ALAN R. WHITE
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Transverse Momentum ◽  
Symmetry Breaking ◽  
Gauge Theories ◽  
Regge Pole ◽  
High Energy ◽  
Asymptotic Freedom ◽  
Regge Theory ◽  
Regge Behavior

The high-energy Regge behavior of gauge theories is studied via the formalism of analytic multi-Regge theory. Perturbative results for spontaneously broken theories are first organized into Reggeon diagrams. Unbroken gauge theories are studied via a Reggeon-diagram infrared analysis of symmetry restoration. Massless fermions play a crucial role and the case of QCD involves the supercritical Pomeron as an essential intermediate stage. An introductory review of the buildup of transverse-momentum diagrams and Reggeon diagrams from leading-log calculations in gauge theories is presented first. It is then shown that the results closely reproduce the general structure for multi-Regge amplitudes derived in Part I of the article, allowing the construction of general Reggeon diagrams for spontaneously broken theories. Next it is argued that, with a transverse-momentum cutoff, unbroken gauge theories can be reached through an infrared limiting process which successively decouples fundamental-representation Higgs fields. The first infrared limit studied is the restoration of SU(2) gauge symmetry. The analysis is dominated by the exponentiation of divergences imposed by Reggeon unitarity and the contribution of massless quarks to Reggeon interactions. Massless quarks also produce “triangle anomaly” transverse-momentum divergences which do not exponentiate but instead are absorbed into a Reggeon condensate — which can be viewed as a “generalized winding-number condensate.” The result is a Reggeon spectrum consistent with confinement and chiral-symmetry breaking, but there is no Pomeron. The analysis is valid when the gauge coupling does not grow in the infrared region, i.e. when a sufficient number of massless quarks is present. An analogy is drawn between the confinement produced by the Reggeon condensate and that produced by regularization of the fermion sea, in the presence of the anomaly, in the two-dimensional Schwinger model. When the analysis is extended to the case of QCD with the gauge symmetry restored to SU(2), the Reggeon condensate can be identified with the Pomeron condensate of supercritical Pomeron theory. In this case, the condensate converts an SU(2) singlet Reggeized gluon to a Pomeron Regge pole — which becomes an SU(3) singlet when the full gauge symmetry is restored, The condensate disappears as SU(3) symmetry is recovered, and in general this limit gives the critical Pomeron at a particular value of the transverse cutoff. If the maximal number of fermions consistent with asymptotic freedom is present, no transverse-momentum cutoff is required. For SU (N) gauge theory it is argued that, when the theory contains many fermions, there are N–2 Pomeron Regge poles of alternating signature. This spectrum of Pomeron trajectories is in direct correspondence with the topological properties of transverse flux tubes characterized by the center ZN of the gauge group. The corresponding Reggeon-field-theory solution of s-channel unitarity should include a representation of ZN in the cutting rules. Finally, the implications of the results for the phenomenological study of the Pomeron as well as for the construction of QCD with a small number of flavors are discussed. Also discussed is the attractive possibility that a flavor doublet of color-sextet quarks could both produce the critical Pomeron in QCD and be responsible for electroweak dynamical-symmetry breaking.

Gauge Theories with Spontaneous Symmetry Breaking

2019 ◽  
pp. 251-264
Author(s):  
Michael E. Peskin
Keyword(s):  
Gauge Symmetry ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Weak Interaction ◽  
Gauge Theories ◽  
High Energy ◽  
High Energy Neutrino ◽  
Neutrino Scattering ◽  
Massive Spin ◽  
Fundamental Equations

This chapter describes theories that combine the ideas of gauge symmetry and spontaneous symmetry breaking. It explains that this combination gives rise to massive spin-1 bosons. This construction is used to propose fundamental equations for the weak interaction. The predictions of these equations for high-energy neutrino scattering are worked out and compared to experiment.

scholarly journals CHIRAL GAUGE THEORIES ON THE LATTICE WITHOUT GAUGE FIXING?

1994 ◽  
Vol 05 (02) ◽  
pp. 327-329
Author(s):  
WOLFGANG BOCK
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Symmetry Breaking ◽  
Continuum Limit ◽  
Gauge Theories ◽  
Gauge Fixing ◽  
The Continuum

We discuss two proposals for a non-perturbative formulation of chiral gauge theories on the lattice. In both cases gauge symmetry is broken by the regularization. We aim at a dynamical restoration of symmetry. If the gauge symmetry breaking is not too severe this procedure could lead in the continuum limit to the desired chiral gauge theory.

SUPERSYMMETRIC TENSOR GAUGE THEORIES

1989 ◽  
Vol 04 (14) ◽  
pp. 1343-1353 ◽  
Author(s):  
T.E. CLARK ◽  
C.-H. LEE ◽  
S.T. LOVE
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Sigma Models ◽  
Gauge Field ◽  
Gauge Theories ◽  
Symmetric Tensor ◽  
Global Symmetry ◽  
Invariant Action ◽  
Symmetry Transformations ◽  
Linear Sigma Models

The supersymmetric extensions of anti-symmetric tensor gauge theories and their associated tensor gauge symmetry transformations are constructed. The classical equivalence between such supersymmetric tensor gauge theories and supersymmetric non-linear sigma models is established. The global symmetry of the supersymmetric tensor gauge theory is gauged and the locally invariant action is obtained. The supercurrent on the Kähler manifold is found in terms of the supersymmetric tensor gauge field.

scholarly journals GAUGE THEORIES AS A GEOMETRICAL ISSUE OF A KALUZA–KLEIN FRAMEWORK

2005 ◽  
Vol 14 (07) ◽  
pp. 1195-1231 ◽  
Author(s):  
FRANCESCO CIANFRANI ◽  
ANDREA MARROCCO ◽  
GIOVANNI MONTANI
Keyword(s):  
Gauge Theory ◽  
Scalar Field ◽  
Symmetry Breaking ◽  
Gauge Theories ◽  
Dimensional Manifold ◽  
Unification Theory ◽  
Klein Theory ◽  
Electroweak Model ◽  
Quark Generation ◽  
Kaluza Klein

We present a geometrical unification theory in a Kaluza–Klein approach that achieve the geometrization of a generic gauge theory bosonic component. We show how it is possible to derive gauge charge conservation from the invariance of the model under extra-dimensional translations and to geometrize gauge connections for spinors, in order to make possible to introducing matter just through free spinorial fields. Then we present the applications to (i) a pentadimensional manifold V4 ⊗ S1 so reproducing the original Kaluza–Klein theory with some extensions related to the rule of the scalar field contained in the metric and to the introduction of matter through spinors with a phase dependance from the fifth coordinate, (ii) a seven-dimensional manifold V4 ⊗ S1 ⊗ S2, in which we geometrize the electroweak model by introducing two spinors for every leptonic family and quark generation and a scalar field with two components with opposite hypercharge responsible for spontaneous symmetry breaking.

Quantum Chromodynamics

2019 ◽  
pp. 169-186
Author(s):  
Michael E. Peskin
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Quantum Chromodynamics ◽  
Strong Interaction ◽  
Experimental Results ◽  
Asymptotic Freedom ◽  
Field Equations ◽  
Abelian Gauge

This chapter introduces non-Abelian gauge symmetry and the associated field equations for spin-1 particles. It proposes the gauge theory Quantum Chromodynamics as the theory of the strong interaction. It describes the property of asymptotic freedom, which explains a number of mysteries in the experimental results shown in the previous three chapters.

scholarly journals Confinement transition of ℤ2 gauge theories coupled to massless fermions: Emergent quantum chromodynamics and SO(5) symmetry

2018 ◽  
Vol 115 (30) ◽  
pp. E6987-E6995 ◽  
Author(s):  
Snir Gazit ◽  
Fakher F. Assaad ◽  
Subir Sachdev ◽  
Ashvin Vishwanath ◽  
Chong Wang
Keyword(s):  
Monte Carlo ◽  
Gauge Theory ◽  
Symmetry Breaking ◽  
Monte Carlo Simulations ◽  
Quantum Monte Carlo ◽  
Gauge Theories ◽  
Square Lattice ◽  
Dirac Fermion ◽  
Topological Order ◽  
Continuous Transition

We study a model of fermions on the square lattice at half-filling coupled to an Ising gauge theory that was recently shown in Monte Carlo simulations to exhibit Z2 topological order and massless Dirac fermion excitations. On tuning parameters, a confining phase with broken symmetry (an antiferromagnet in one choice of Hamiltonian) was also established, and the transition between these phases was found to be continuous, with coincident onset of symmetry breaking and confinement. While the confinement transition in pure gauge theories is well-understood in terms of condensing magnetic flux excitations, the same transition in the presence of gapless fermions is a challenging problem owing to the statistical interactions between fermions and the condensing flux excitations. The conventional scenario then proceeds via a two-step transition, involving a symmetry-breaking transition leading to gapped fermions followed by confinement. In contrast, here, using quantum Monte Carlo simulations, we provide further evidence for a direct, continuous transition and also find numerical evidence for an enlarged SO(5) symmetry rotating between antiferromagnetism and valence bond solid orders proximate to criticality. Guided by our numerical finding, we develop a field theory description of the direct transition involving an emergent nonabelian [SU(2)] gauge theory and a matrix Higgs field. We contrast our results with the conventional Gross–Neveu–Yukawa transition.

scholarly journals Phase transitions for SU(N) gauge theories with arbitrary number of flavors

2015 ◽  
Vol 30 (34) ◽  
pp. 1550203 ◽  
Author(s):  
Renata Jora
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Gauge Theory ◽  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Gauge Theories ◽  
Chiral Symmetry Breaking ◽  
Small Region ◽  
New Phase ◽  
Strong Confinement

We study the phase diagram of an [Formula: see text] gauge theory in terms of the number of colors [Formula: see text] and flavors [Formula: see text] with emphasis on the confinement and chiral symmetry breaking phases. We argue that as opposed to SUSY QCD there is a small region in the [Formula: see text] plane where the theory has the chiral symmetry broken but it is unconfined. The possibility of a new phase with strong confinement and chiral symmetry breaking is suggested.

ANALYTIC MULTI-REGGE THEORY AND THE POMERON IN QCD I: THE SUPER-CRITICAL POMERON

1991 ◽  
Vol 06 (11) ◽  
pp. 1859-1959 ◽  
Author(s):  
ALAN R. WHITE
Keyword(s):  
Field Theory ◽  
Matrix Theory ◽  
Spectral Component ◽  
High Energy ◽  
Vector Particle ◽  
Regge Theory ◽  
Regge Behavior ◽  
Energy Behavior ◽  
S Matrix ◽  
Full Structure

The formalism of analytic multi-Regge theory is developed as a basis for the study of abstract critical and super-critical pomeron high-energy behavior and for related studies of the Regge behavior of spontaneously broken gauge theories and the pomeron in QCD. Asymptotic domains of analyticity for multiparticle amplitudes are shown to follow from properties of field theory and S-matrix theory. General asymptotic dispersion relations are then derived for such amplitudes in which the spectral components are described by the graphical formalism of hexagraphs. Further consequences are distinct Sommerfeld-Watson representations for each hexagraph spectral component, together with a complete set of angular momentum plane unitarity equations which control the form of all multi-Regge amplitudes. Because of this constraint of “reggeon unitarity” the critical pomeron solution of the reggeon field theory gives the only known “non-trivial” unitary high-energy S-matrix. By exploiting the full structure of multi-Regge amplitudes as the pomeron becomes super-critical, one can study the simultaneous modification of hadrons and the pomeron. The result is a completely consistent description of the super-critical pomeron appearing in hadron scattering. Reggeon unitarity is satisfied in the super-critical phase by the appearance of a massive “gluon” (Reggeized vector particle) coupling pair-wise to the pomeron.

Sign in / Sign up

Export Citation Format

Share Document