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.     

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.     

Strong coupling expansions for the mass gap in lattice gauge theories

We derive strong coupling expansions for the mass gap in euclidean lattice gauge theories in any space-time dimension. For gauge groups SU(2), SU(3), Z₂ and Z₃ the series are calculated up to order g^?16. They are used to get rough estimates for the lowest glueball mass in continuum SU(2) and SU(3) gauge theories, assuming a sudden crossover from strong to weak coupling behaviour in the lattice theory.     

Large dimensional lattice gauge theories: (I). Z2 pure gauge system

The transition pattern of lattice gauge theories can be stydied by a variational method based on strong coupling series. For large space-time dimension d, this leads to a 1/d expansion when the parameter βd is kept fixed. The first-order phase transition of the Z₂ pure gauge system is studied here.     

Abelian lattice gauge theories in 3 + 1 dimensions: The linked cluster approach

We use the linked cluster expansion methods of Nickel to derive strong couping series for Z_N abelian gauge theories. These new results together with corresponding estimates using the exact linked cluster expansion algorithm are analysed and compared with previously obtained results for U(1) lattice gauge theory in 3 + 1 dimensions. We confirm the phase structure of these theories as found by other techniques. The critical value of N at which the phase structure of Z_N alters is estimated to be N_C = 4.5 ± 0.2. In each case the string tension estimates using the ELCE algorithm are found to be stable in the presence of a roughening transition.     

Strong-coupling expansions for the off-axis glueball masses

Strong-coupling expansions, up to order g^?4, for the off-axis glueball masses are developed in four-dimensional spacetime for lattice gauge theories with gauge groups SU(2), SU(3), Z₂, Z₃. Glueball mass spectra for the states 0⁺⁺, 2⁺⁺, 1^+? are obtained. Restoration of Lorentz invariance is discussed.     

Monte Carlo studies of SU(N)/ZN lattice gauge theories in four dimensions

Using Monte Carlo techniques on a four-dimensional space-time lattice, we study SU(N)/Z_N gauge theories for N = 3, 4, 5 and 6. We find first-order phase transitions at critical inverse temperatures of β_c = 6.40, 12.0, 19.5 and 32.0 and SU(3)/Z₃,SU(4)/Z₄,SU(5)/Z₅and SU (6)Z₆, respectively.     

Spontaneous symmetry breakings in Z2 gauge theories for doped quantum dimer and eight-vertex models

Behavior of doped fermions in Z₂ gauge theories for the quantum dimer and eight-vertex models is studied. Fermions carry charge and spin degrees of freedom. In the confinement phase of the Z₂ gauge theories, these internal symmetries are spontaneously broken and a superconducting or Neél state appears. On the other hand in the deconfinement-topologically ordered state, all symmetries are respected. From the view point of the quantum dimer and eight-vertex models, this result indicates interplay of the phase structure of the doped fermions and background configuration of the dimer or the eight-vertex groundstate. At the quantum phase transitions in these systems, structure of the doped fermions groundstate and also that of the background dimer or eight-vertex groundstate both change. Translational symmetry breaking induces a superconducting or antiferromagnetic state of the doped fermions.     

On the roughening transition in abelian lattice gauge theories

We study the width of the confining string between static quarks in abelian lattice gauge theories using strong coupling expansions. We consider gauge groups Z_n and U(1) in 3 and 4 dimensions. This extends previous work with Lüscher, where SU(2) and Z₂ were studied. In ν = 3 dimensions we find evidence for a roughening transition. It is characterized by a divergence of the string width for an infinitely far separated quark-antiquark pair, while the string tension remains non-zero. In ν = 4 dimensions for the abelian groups we do not have evidence for a roughening transition away from a phase transition.     

Sufficient condition for confinement of static quarks by a vortex condensation mechanism

We derive a sufficient condition for confinement of static quarks by a vortex condensation mechanism. It admits vortices that are thick at all times at the cost of constraining them to a finite volume Γ_i whose complement is not simply connected. The confining potential V(L) is estimated in terms of the change of free energy of a system enclosed in Γ_i which is induced by a change in vorticity (= singular gauge transformation applied to boundary conditions on ?Γ_i.) For Abelian gauge theories in 3 dimensions the confining Coulomb potential is reproduced as a lower bound.     

Continuum limit of A Z2 lattice gauge theory

Phase diagrams of lattice gauge theories have in several cases lines of first-order transitions ending at points at which continuous (second-order) transitions take place. In the vicinity of this critical point, a continuum field theory may be defined. We have analyzed here a Z₂ gauge plus matter model (which has no formal continuum limit) and identified the critical point with a usual Ø⁴, globally Z₂ invariant, field theory. The analysis relies on a mean field functional formalism and on a loop-wise expansion around it, which is reviewed.     

Phenomenology of a four generation superstring model

We discuss the quark-lepton phenomenology of a superstring model compactified on aCP ⁴-based Calabi-Yau manifold defined by? _i Z _i ⁵ = 5 _c Z ₁ Z ₂ Z ₃ Z ₄ Z ₅ leading to four fermion generations using the Yukawa couplings calculated by us in a previous paper. We note that maintaining supersymmetry implies that forc?1, one of theU(1)-subgroup ofE ₆ must break at the Planck scale; on the other hand forc?10⁺⁴, an intermediate scale of about 10¹¹ GeV or 10¹⁴ GeV may be generated without destabilizing the gauge hierarchy. The model may have problems with fast proton decay for some choice ofc; however, understanding small neutrino masses remains a problem.     

Finite Group Discretization of Yang-Mills and Einstein Actions

Discrete versions of the Yang-Mills and Einstein actions are proposed for any finite group. These actions are invariant respectively under local gauge transformations and under the analogues of Lorentz and general coordinate transformations. The case Z_n×Z_n×···×Z_n is treated in some detail, recovering the Wilson action for Yang-Mills theories and a new discretized action for gravity.     

Regge behavior under asymptotic freedom

By a new method, we show that the asymptotically free ø₆³ field theory has a point of accumulation of Regge poles but no fixed cut. It is plausible that nonabelian gauge theories have an analogous singularity at j = 1.     

Gauge invariance and renormalization

The renormalization of Abelian and non-Abelian local gauge theories is discussed. It is recalled that whereas Abelian gauge theories are invariant to local c-number gauge transformations δA_μ(x) = ?_μ,…, with □Λ = 0, and to the operator gauge transformation δA_μ(x) = ?_μφ(x), …, δφ(x) = α^?1?·A(x), with □φ = 0, non-Abelian gauge theories are invariant only to the operator gauge transformations $\text{δA}{}_{\mathrm{\mu }}\text{(x) ～}\textcolor{red}{}{}_{\mathrm{\mu }}\text{C(x)}$, …, introduced by Becchi, Rouet and Stora, where

_μ is the covariant derivative matrix and C is the vector of ghost fields. The renormalization of these gauge transformation is discussed in a formal way, assuming that a gauge-invariant regularization is present. The naive renormalized local non-Abelian c-number gauge transformation $\text{δA}{}_{\mathrm{\mu }}\text{(x) = (Z}{}_1\text{/Z}{}_3\text{)gA}{}_{\mathrm{\mu }}\text{(x) ×}\text{Λ}\text{(x)+?}{}_{\mathrm{\mu }}\text{Λ}\text{(x)}$, …, is never a symmetry transformation and is never finite in perturbation theory. Only for $\text{Λ}\text{(x) = (Z}{}_3\text{/Z}{}_1\text{)L}$ with L finite constants or for $\text{Λ}\text{(x) = Ω}\text{z}\text{?}{}_3\text{C(x)}$ with Ω a finite constant does it become a finite symmetry transformation, where $\text{z}\text{?}{}_3$ is the ghost field renormalization constant. The renormalized non-Abelian Ward-Takahashi (Slavnov-Taylor) identities are consequences of the invariance of the renormalized gauge theory to this formation. It is also shown how the symmetry generators are renormalized, how photons appear as Goldstone bosons, how the (non-multiplicatively renormalizable) composite operator A_μ × C is renormalized, and how an Abelian c-number gauge symmetry may be reinstated in the exact solution of many asymptotically fr ee non-Abelian gauge theories.     

Dense stellar matter in asymptotically free gauge theories: I. The high density limit

In asymptotically free gauge theories perturbation theory may be used to obtain the behavior of dense stellar matter. The criteria for the determination of ?_crit, the minimum density above which perturbation theory is valid, are presented. The asymptotic form for the quark-gluon thermodynamic potential is given.     

D=1+2 phase diagram forZ N with a variational method

Trial ground state are constructed which forZ _N gauge theories inD=1+2 dimensions lead to phase diagrams which are in agreement both with theoretical expectations and Monte Carlo results. The nature of the phase transition is correctly predicted for eachN.     

Two-dimensional gauge theories with diagonal SU(N) color

Two-dimensional gauge theories with diagonal SU(N) color symmetry are analyzed in the limit of strong coupling using bosonization techniques. A spectrum of heavy mesons is found in addition to a spectrum of light baryon and baryonium states. Exotic behavior is also found for various values of the {Θ_i} parameters.     

Mean field approach to finite temperature gauge systems

We apply a mean field treatment to theZ ₂ andZ ₃ gauge systems at finite temperature. In the lowest order the deconfinement of fixed electric charges is a second order transition forZ ₂ and a first order transition forZ ₃. Higher order corrections can be calculated using the steepest descent method.     

Chemical potentials in gauge theories

One-loop calculations of the thermodynamic potential Ω are presented for temperature gauge and non-gauge theories. Prototypical formulae are derived which give Ω as a function of both (i) boson and/or fermion chemical potential, and in the case of gauge theories (ii) the thermal vacuum parameter A₀=const (A_μ is the euclidean gauge potential). From these basic abelian gauge theory formulae, the one-loop contribution to Ω can readily be constructed for Yang-Mills theories, and also for non-gauge theories.