Moduli Space of BPS Walls in Supersymmetric Gauge Theories

Existence and uniqueness of the solution are proved for the ‘master equation’ derived from the BPS equation for the vector multiplet scalar in the U(1) gauge theory with N _F charged matter hypermultiplets with eight supercharges. This proof establishes that the solutions of the BPS equations are completely characterized by the moduli matrices divided by the V-equivalence relation for the gauge theory at finite gauge couplings. Therefore the moduli space at finite gauge couplings is topologically the same manifold as that at infinite gauge coupling, where the gauged linear sigma model reduces to a nonlinear sigma model. The proof is extended to the U(N _C) gauge theory with N _F hypermultiplets in the fundamental representation, provided the moduli matrix of the domain wall solution is U(1)-factorizable. Thus the dimension of the moduli space of U(N _C) gauge theory is bounded from below by the dimension of the U(1)-factorizable part of the moduli space. We also obtain sharp estimates of the asymptotic exponential decay which depend on both the gauge coupling and the hypermultiplet mass differences.     

SO q (4) quantum mechanics

In this paper we extend our previously discovered exact solution for an SU(2) Yang-Mills-Higgs theory, to the general group SU(N+1). Using the first-order formalism of Bogomolny, an exact, spherically symmetric solution for the gauge and scalar fields is found. This solution is similar to the Schwarzschild solution of general relativity, in that the gauge and scalar fields become infinite on a spherical shell of radiusr ₀=K. However in the Schwarzschild case the singularity at the event horizon is a coordinate singularity while for the present solution the singularity is a true singularity. It is speculated that this solution may give a confinement mechanism for non-Abelian gauge theories, since any particle which carries the SU(N+1) charge would become permanently trapped inside the regionr<r ₀.     

Meron-antimeron solution in Minkowski space

An elementary derivation, using Witten's Ansatz, is given of the elliptic meron-antimeron solution of the (Minkowski) SU(2) gauge theory in the W ₀=0 gauge.     

The CMS experiment at the LHC-status and physics potential

The most general momentum independent dynamical r-matrices are described for the standard Lax representation of the degenerate Calogero-Moser models based on gl _n and those r-matrices whose dynamical dependence can be gauge d away are selected. In the rational case, a non-dynamical r-matrix resulting from gauge transformation is given explicitly as an antisymmetric solution of the classical Yang-Baxter equation that belongs to the Frobenius subalgebra of gl _n consisting of the matrices with vanishing last row.     

Bäcklund Transformation for Supersymmetric Self-Dual Theories for Semisimple Gauge Groups and a Hierarchy of Ai Solutions

We present a Bdcklund transformation (a discrete symmetry transformation) for the self-duality equations for supersymmetric gauge theories in N-extended super-Minkowski space ^4|4N for an arbitrary semisimple gauge group. For the case of anA ₁ gauge algebra we integrate the transformation starting with a given solution and iterating the process we construct a hierarchy of explicit solutions.     

Bogoliubov compensation principle in the electro-weak interaction: value of the gauge constant,muon g-2 anomaly,predictions for Tevatron and LHC

We apply the Bogoliubov compensation principle to the gauge electro-weak interaction to demonstrate the spontaneous generation of an anomalous three-boson gauge invariant effective interaction. The non-trivial solution of the compensation equations uniquely defines the values of the parameters of the theory and the form factor of the anomalous interaction. The contribution of this interaction to the running EW coupling, α _ew(p ²), gives its observable value α _ew(M _W ²)=0.0374, in satisfactory agreement to the experiment. The anomalous three-boson interaction gives a natural explanation of the well-known discrepancy in the muon g−2. The implications for EW studies at Tevatron and LHC are briefly discussed.     

A Plane-Symmetric Magnetized Inhomogeneous Cosmological Models of Perfect Fluid Distribution with Variable Magnetic Permeability in Lyra Geometry

A plane-symmetric magnetized inhomogeneous cosmological model of the universe with time dependent gauge function β for perfect fluid distribution with variable magnetic permeability within the framework of Lyra geometry is investigated. The source of the magnetic field is due to an electric current produced along the z-axis. Thus F ₁₂ is the only non-vanishing component of electromagnetic field tensor F _ij . To get a deterministic solution of Einstein’s modified field equations, the free gravitational field is assumed to be Petrov type-II non-degenerate. For our derived model we obtain the deceleration parameter q=−1 as in the case of de Sitter universe. It has been found that the displacement vector β(t) behaves like cosmological term Λ in the normal gauge treatment and the solution is consistent with the observations. The displacement vector β(t) affects entropy. Some physical and geometric properties of the model are also discussed.     

Ue(1)-covariant Rξ gauge for the two-Higgs doublet model

A U _e (1)-covariant R _ξ gauge for the two-Higgs doublet model based on BRST (Becchi-Rouet-Stora-Tyutin) symmetry is introduced. This gauge allows one to remove a significant number of nonphysical vertices appearing in conventional linear gauges, which greatly simplifies the loop calculations, since the resultant theory satisfies QED-like Ward identities. The presence of four ghost interactions in these types of gauges and their connection with the BRST symmetry are stressed. The Feynman rules for those new vertices that arise in this gauge, as well as for those couplings already present in the linear R _ξ gauge but that are modified by this gauge-fixing procedure, are presented.     

On bilocal gauge field theory

The nonlocal gauge group of unitary integral operators U _n (∞) is considered. Gluons in the nonlocal version of QCD are described by the bilocal gauge fields (BGF). The Higgs effect for BGF are discussed. It is shown that the local SU(n) gauge theory can be treated as a local limit of spontaneously broken U _n(∞)/SU(n) BGF theory.     

Characteristic cohomology ofp-form gauge theories

The characteristic cohomologyH ^k _char(d) for an arbitrary set of freep-form gauge fields is explicitly worked out in all form degreesk < n — 1, wheren is the spacetime dimension. It is shown that this cohomology is finite-dimensional and completely generated by the forms dual to the field strengths. The gauge invariant characteristic cohomology is also computed. The results are extended to interactingp-form gauge theories with gauge invariant interactions. Implications for the BRST cohomology are mentioned.     

Superalgebras in N = 1 gauge theories

N = 1 supersymmetric gauge theories with global flavor symmetries contain a gauge invariant W-superalgebra which acts on its moduli space of gauge invariants. With adjoint matter, this superalgebra reduces to a graded Lie algebra. When the gauge group is SO(n_c), with vector matter, it is a W-algebra, and the primary invariants form one of its representation. The same superalgebra exists in the dual theory, but its construction in terms of the dual fields suggests that duality may be understood in terms of a charge conjugation within the algebra. We extend the analysis to the gauge group E₆.     

A unified theory of weak interactions

A gauge model for the weak interactions of the leptons (v _e, e, μ, ν_μ) and the quarks (q _p, q_n,qλ,q _p′) is presented in which deviations from universality, such as the Cabibbo suppression, are explicitly and spontaneously generated. The gauge group is, to begin with SU(4). There are three quartets of Higgs scalars with suitable vacuum expectation values, sufficient and necessary to give masses to all gauge bosons. It turns out that this gauge group is too ‘large’ and fails to account for many observed symmetries of weak interactions, especially electron-muon symmetry. This symmetry corresponds to a discrete transformationR which is an element of SU(4). To accommodate it, the gauge group is restricted to the subgroup of SU(4) which commutes withR. There are now 7 gauge bosons, 4 charged and 3 neutral. One pair of charged bosons is necessarily heavier than the other pair (denotedW ^±) and two neutrals are necessarily heavier than the third (W ⁰). The electron and the muon become massive while the neutrinos and the quark fields remain massless. The dominant charged weak currents coupling toW ^± havee-μ universality and Cabibbo universality for both of whichR-symmetry is essential—the Cabibbo angle is a simple function of the vacuum expectation values. The same symmetry ensurese-μ symmetry and the absence of flavour-changing components in the neutral currents. The currents coupling to the heavier gauge bosons break all these symmetries but these bosons can be made arbitrarily heavy and so are relevant only in the domain of ‘ultraweak’ interactions. The Cabibbo angleϑ _c itself is determined by minimising a very general class of Higgs potentials, leading to a numerical valueϑ _c = ±π/8, | tanϑ _c | = √2 − 1 (an alternative solution | tanϑ _c | = (√2+1) is rejected), independent of the parameters and of the precise form of the potential. This is the ‘bare’ϑ _c; in low energy/momentum transfer processes, this value is renormalised by the structure of the hadrons. A model is given for this renormalisation which reduces the renormalised value of | tanϑ _c | to about 0.2–0.3 from the bare value 0.41. Recent data on highly inelastic neutrino interactions are shown to be not inconsistent with | tanϑ _c | = 0.4.     

Gauge theory of two-dimensional spin- Heisenberg antiferromagnet

A gauge theory of the spin- Heisenberg antiferromagnet (HA) on a two-dimensional square lattice is developed, which is based on the diagonal G_D of the group product SO(3)×SU(2). For classical gauge fields G_D is homeomorphic to SO(3). The structure of the theory is such that the quantum spin- field propagates on the background gauge field. For special gauges the excitations of the spin-field are computed and compared to the excitations of the O(3) σ model for the same gauge. The significance of negative excitational modes with respect to a semiclassical actionГ_sc of the spin- HA is discussed. Some properties ofГ_sc represented as a chiral SO(3) model in a continuum representation are worked out.     

Light Quark Hadron Mass Scale

With a symmetry procedure based on Noether's theorem, the field equation of motion is obtained from the Dirac Hamiltonian H(D_μ) of a massless quark interacting with a gluon. The equation of motion is the Yang-Mills equation with external current which is spin-dependent and follows from the group algebra. In addition to the pure gauge solution we find a gauge covariant solution which follows from current conservation and sets the mass scale m₀/M = g². This gluon field is due to the density of dipole moments squared and represents four harmonic oscillators with quadratic constraints; the gluon can be written as a string potential or as a 1/x potential with a sharp cutoff. The chiral symmetry group G^spin × G^D gives the light quark hadron degenerate multiplet mass spectrum in terms of m₀[SU(2) × SU(2)] with the spinorial decomposition and the multipole breaks into dipoles. Scaling from atomic lengths it is found that g = em₀/nM for light quarks is the quark charge e/3 renormalized by m₀/M and g is magnetic. Thus quarks occur at the ends of spinning magnetic strings with dipole lengths ∼m₀⁻¹. The mass scale is that of a degenerate magnetic multipole with charge n = 3, 4… .     

Gauge symmetries of electroweak interactions

By considering the symmetries associated with baryon number and lepton number conservation as gauge symmetries, the underlying gauge symmetry of weak electromagnetic interactions is shown to beSU(2) _L ×U(1)×U(1)Baryon×U(1)_Lepton. If right-handed currents exist on a par with the observed left-handed ones, then the full symmetry of electroweak interactions that emerges isSU(2)_L×SU(2)_R×U(1)_Baryon×U(1)_Lepton. These symmetries offer a rich spectrum of massive neutral gauge bosons, one of which is the massive neutral boson of the standardSU(2) _L ×U(1) _Y model.     

An energy-momentum tensor in gauge theories

We consider the renormalization of the twist two, dimension four gauge invariant operator O_μν⁽¹⁾ = − F_μσF_νσ − g_{μν 0}. By using the general theory of renormalization of gauge invariant operators, we find the gauge noninvariant operator O⁽²⁾ with which it mixes. We construct a finite combination of O⁽¹⁾ and O⁽²⁾ and show that it is an acceptable energy momentum tensor for gauge theories. We compare our energy momentum tensor with that constructed by Freedman, Muzinich, and Weinberg.     

Quantum Wall Crossing in $${{\mathcal N}=2}$$ Gauge Theories

We study refined and motivic wall-crossing formulas in N=2{{\mathcal N}=2} supersymmetric gauge theories with SU(2) gauge group and N _f < 4 matter hypermultiplets in the fundamental representation. Such gauge theories provide an excellent testing ground for the conjecture that “refined = motivic.”     

Color Superconductivity in Supersymmetric Gauge Theories

The studies of superconductivity, dual superconductivity and color superconductivity have been undertaken through the breaking of supersymmetric gauge theories which automatically incorporate the condensation of monopoles and dyons leading to confining and superconducting phases. Constructing the total effective Lagrangian of N=2 SU(2) gauge theory with N _f =2 quark multiplets and quark chemical potential at classical and quantum levels, it has been demonstrated that baryon number symmetry is spontaneously broken as a consequence of the SU(2) strong gauge dynamics and the color superconductivity dynamically takes space at the non-SUSY vacuum.