Dynamical supersymmetry breaking and gauge anomalies

Some aspects of supersymmetric gauge theories and discussed. It is shown that dynamical supersymmetry breaking does not occur in supersymmetric QED in higher dimensions. The cancellation of both local (perturbative) and global (non-perturbative) gauge anomalies are also discussed in supersymmetric gauge theories. We argue that there is no dynamical supersymmetry breaking in higher dimensions in any supersymmetric gauge theories free of gauge anomalies. It is also shown that for supersymmetric gauge theories in higher dimensions with a compact connected simple gauge group, when the local anomaly-free condition is satisfied, there can be at most a possibleZ ₂ global gauge anomaly in extended supersymmetricSO(10) (or spin (10)) gauge theories inD=10 dimensions containing additional Weyl fermions in a spinor representation ofSO(10) (or spin (10)). In four dimensions with local anomaly-free condition satisfied, the only possible global gauge anomalies in supersymmetric gauge theories areZ ₂ global gauge anomalies for extended supersymmetricSP(2N) (N=rank) gauge theories containing additional Weyl fermions in a representation ofSP(2N) with an odd 2nd-order Dynkin index.     

Migdal renormalization group approach to deconfinement phase transition

The Migdal renormalization group approach is applied to a finite temperature lattice gauge theory. Imposing the periodic boundary condition in the timelike orientation, the phase structure of the finite temperature lattice gauge system with a gauge groupG in (d+1)-dimensional space is determined by two kinds of recursion equations, describing spacelike and timelike correlations, respectively. One is the recursion equation for ad-dimensional gauge system with the gauge groupG, and the other corresponds to ad-dimensional spin system for which the effective theory is described by the nearest neighbor interaction of the Wilson lines. Detailed phase structure is investigated for theSU(2) gauge theory in (3+1)-dimensional space. Deconfinement phase transition is obtained. Using the recursion equation for the three dimensional spin system of the Wilson lines, it is shown that the flow of the renormalization group trajectories leads to a phase transition of the three dimensional Ising model.     

On the anti-symmetric vierbein in quantum supergravity

We consider the BRS identities for N = 1 supergravity in a covariant gauge. It is shown that, as in the axial gauge, the anti-symmetric part of the vierbein does contribute to the BRS identities, even though one can choose a gauge in which it does not propagate.     

Gauge transformations and quantum mechanics II. Physical interpretation of classical gauge transformations

New gauges are introduced. The potentials, vector and scalar, in these gauges are obtained in closed forms by the Green's function method. These closed form solutions are explicity expressed only in terms of the charge and current densities. The physical interpretation is on how potentials propagate from the charge and current densities. The Coulomb gauge and the Lorentz gauge are special cases of a new gauge defined in this paper. It is called the complete α-Lorentz gauge. The scalar potential propagates at speed αc from the charge density for any positive α. When α is one, the usual solutions for the Lorentz gauge are recovered. When α is not one, our results show that, in order to satisfy the requirement that electromagnetic fields be gauge invariant and in order to conform to Maxwell's interpretation that electromagnetic fields propagate at speed c from the charge and current densities (we only consider the vacuum), the vector potential must contain two mathematically and physically independent gradient components. Furthermore, one such component must propagate at speed αc while the other must at speed c from charge and current densities. Our discussions on the Coulomb gauge are based on the results obtained by letting α go to (positive) infinity. Guided by Maxwell's interpretation, we introduce a new decomposition of the vector potential in the Lorentz gauge into a longitudinal and a transverse component. For an arbitrary charge and current distribution, it is shown that the transverse component will generate all the fields only in the radiation zone. However, for a point charged particle, the transverse component only generates the “free fields”everywhere in the instantaneous rest frame of the charged particle.     

Gauge parameter dependence in the background field gauge and the construction of an invariant charge

By using the enlarged BRS transformations we control the gauge parameter dependence of Green functions in the background field gauge. We show that it is unavoidable — also if we consider the local Ward identity — to introduce the normalization value ξ₀ of the gauge parameter ξ. The dependence of Green functions on ξ₀ is governed by a partial differential equation in a similar manner as the dependence on the normalization point κ is governed by the RG equation. By modifying the Ward identity we are able to construct in 1-loop order a gauge parameter independent combination of 2-point vector and background vector functions. By explicit construction of the next orders we show that this combination can be used to construct a gauge parameter independent RG-invariant charge. However, it is seen that this RG-invariant charge does not satisfy the differential equation of the normalization value ξ₀ of the gauge parameter, and, hence, is not ξ₀-independent as required.     

Embedding Z′ models in SO(10) GUTs

We embed a theory with Z′ gauge boson (related to an extra U(1) gauge group) into a supersymmetric GUT theory based on SO(10). Two possible sequences of SO(10) breaking via VEVs of appropriate Higgs fields are considered. Gauge coupling unification provides constraints on the low energy values of two additional gauge coupling constants related to Z′ interactions with fermions. Our main purpose is to investigate in detail the freedom in these two values due to different scales of subsequent SO(10) breaking and unknown threshold mass corrections in the gauge RGEs. These corrections are mainly generated by Higgs representations and can be large because of the large dimensions of these representations. To account for many free mass parameters, effective threshold mass corrections have been introduced. Analytic results that show the allowed regions of values of two additional gauge coupling constants have been derived at 1-loop level. For a few points in parameter-space that belong to one of these allowed regions 1-loop running of gauge coupling constants has been compared with more precise running, which is 2-loop for gauge coupling constants and 1-loop for Yukawa coupling constants. 1-loop results have been compared with experimental constraints from electroweak precision tests and from the most recent LHC data.     

The statistical quantum number and gauge groups in parafermi field theory

Properties of a system consisting of a single parafermi field of order p are studied mainly in connection with gauge groups. Following the theory of Drühl, Haag and Roberts, the algebra of observables is classified into four cases according to the types of gauge groups, i.e., SO(p), O(p), U(p), and SU(p). A detailed study is made of irreducible representations of these gauge groups that are realized in the state-vector space of the parafermi field. Superselection operators which give rise to the corresponding superselection rules related to the gauge groups are studied, and their explicit expressions given. The statistical quantum number which we introduced before is found to be nothing other than the eigenvalues of a superselection operator for the gauge group O(p).     

ZN Gauge theories on a lattice and quantum memory

In the present paper we shall study (2+1)-dimensional Z_N gauge theories on a lattice. It is shown that the gauge theories have two phases, one is a Higgs phase and the other is a confinement phase. We investigate low-energy excitation modes in the Higgs phase and clarify relationship between the Z_N gauge theories and Kitaev’s model for quantum memory and quantum computations. Then we study effects of random gauge couplings (RGC) which are identified with noise and errors in quantum computations by Kitaev’s model. By using a duality transformation, it is shown that time-independent RGC give no significant effects on the phase structure and the stability of quantum memory and computations. Then by using the replica methods, we study Z_N gauge theories with time-dependent RGC and show that nontrivial phase transitions occur by the RGC.     

VII. Difficulties in fixing the gauge in non-Abelian gauge theories

Some problems arising from the use of the Coulomb gauge in SU(2) Yang-Mills theory are discussed. It is shown that: i) the transversality condition does not fix the gauge uniquely (Gribov ambiguity); ii) there exist physical configurations that cannot be described by a continuous A_μ in the Coulomb gauge.     

A gravitating SO(3, 1) gauge field

In this article, we postulate SO(3, 1) as a local symmetry of any relativistic theory. This is equivalent to assuming the existence of a gauge field associated with this noncompact group. This SO(3, 1) gauge field is the spinorial affinity which usually appears when we deal with weighting spinors, which, as is well known, cannot be coupled to the metric tensor field. Furthermore, according to the integral approach to gauge fields proposed by Yang, it is also recognized that in order to obtain models of gravity we have to introduce ordinary affinities as the gauge field associated with GL(4) (the local symmetry determined by the parallel transport). Thus if we assume both L(4) and SO(3, 1) as local independent symmetries we are led to analyze the dynamical gauge system constituted by the Einstein field interacting with the SO(3, 1) Weyl-Yang gauge field. We think this system is a possible model of strong gravity. Once we give the first-order action for this Einstein-Weyl-Yang system we study whether the SO(3, 1) gauge field could have a tetrad associated with it. It is also shown that both fields propagate along a unique characteristic cone. Algebraic and differential constraints are solved when the system evolves along a null coordinate. The unconstrained expression for the action of the system is found working in the Bondi gauge. That allows us to exhibit an explicit expression of the dynamical generator of the system. Its signature turns out to be nondefinite, due to the nondefinite contribution of the Weyl-Yang field, which has the typical spinorial behavior. A conjecture is made that such an unpleasant feature could be overcome in the quantized version of this model.     

The BRS algebra of a free minimal differential algebra

We construct the Weil and the universal BRS algebras of theories that can have as a gauge symmetry a free minimal differential (Sullivan) algebra, the natural extension of Lie algebras allowing the definition of p-form gauge potentials (p > 1). The geometrical meaning of these p-form gauge potentials can be understood with the notion of a Quillen superconnection.     

Hidden local gauge invariance in integrable magnetic chains

It is shown that local gauge transformations preserve the integrability of one-dimensional quantum Heisenberg chains. Abelian U(1) gauge transformations associated to z-rotations appear in the XXZ model which is worked out in detail. The exact energy spectrum derived by the Bethe ansatz turns out to be gauge-invariant whereas the eigenvectors are explicitly gauge-dependent. Isotropic XXX chains exhibit SU(2) ⊗ Z₂ gauge invariance properties and anisotropic XYZ chains possess discrete Z₂ ⊗ Z₂ gauge invariance.     

Gauge dependence of renormalization group parameters in ghost-free non-abelian gauge theories

We discuss the gauge dependence of the renormalization group parameters in a class of ghost-free non-abelian gauge theories. We show, using the n-dimensional regularization with the “minimal” renormalization procedure, that these parameters are gauge independent.     

Topologically non-trivial gauge configurations and the heterotic string

The contribution to the heterotic string of topologically non-trivial gauge configurations is studied. In the σ-model approach, it is proved that this kind of gauge configuration does not contribute to gauge anomalies. The ß = 0 condition is also analyzed.     

SU(2) gauge symmetry and anomaly of the S = 12 antiferromagnetic Heisenberg model in 2 + 1 dimensions

On the basis of the local SU (2) symmetry of the Heisenberg model, we show that the model, in a continuum limit, reduces to a problem of massless fermions coupled to an SU(2) gauge field in three space-time dimensions. The effective gauge field action changes by ± π ⦶ n ⦶ under a large gauge transformation with winding number n. To restore the gauge invariance, a parity- nonconserving, topological term is needed in the effective action. The physical implications are conjectured.     

Topological Geon Black Holes in Einstein-Yang-Mills Theory

We construct topological geon quotients of two families of Einstein-Yang-Mills black holes. For Künzle??s static, spherically symmetric SU(n) black holes with n?>?2, a geon quotient exists but generically requires promoting charge conjugation into a gauge symmetry. For Kleihaus and Kunz??s static, axially symmetric SU(2) black holes a geon quotient exists without gauging charge conjugation, and the parity of the gauge field winding number determines whether the geon gauge bundle is trivial. The geon??s gauge bundle structure is expected to have an imprint in the Hawking-Unruh effect for quantum fields that couple to the background gauge field.     

Yukawa-type potential besides newtonian potential in Poincaré gauge theory of gravitation

It is shown that the spin gauge fields with non-zero mass mediate the Yukawa-type interactions besides the short-range spin-spin interactions in the Poincaré gauge theory of gravitation. The interaction range of spin gauge fields is determined from the coupling constants. The coupling constant in front of the R(W) term is bounded by the requirement of a non-oscillating solution.     

Instanton zero modes and β-functions in gauged supergravity

We prove that one loop infinities in N?3 gauged O(N) supergravities are produced only by zero modes both on de Sitter and gauge instanton backgrounds. This strongly suggests (in analogy with the super Yang-Mills case) that instantons may be used for establishing exact β-functions in supergravities. We also derive the general formula for the number of gauge instanton zero modes for arbitrary spin and find that the “magnetic moment” part of the contribution in the gauge β-function is completely due to zero modes.     

Exact analysis of Coulomb gauge vacuum degeneracies in (2 + 1) dimensions

The solutions of the two-dimensional euclidean σ-model provide an infinite number of pure gauge field configurations satisfying the Coulomb gauge condition, in (2 + 1) dimensions. For vacuum gauge fields associated with finite action instanton solutions of the σ-model, we find that the winding number n configuration leads to n negative eigenvalues for the ghost operator, up to a finite calculable degeneracy.