Perturbation theory in terms of superfields and its application to gauge theories

We formulate a perturbation theory in terms of superfields for Lagrangian field theories which are expressable by chiral or general scalar superfields. Especially we consider the generalized QED model of Wess and Zumino where an additional local gauge symmetry is present. Our calculations are manifestly covariant with respect to supersymmetry and local gauge transformations.     

The model for self-dual chiral bosons as a Hodge theory

We consider (1+1) dimensional theory for a single self-dual chiral boson as a classical model for gauge theory. Using the Batalin–Fradkin–Vilkovisky (BFV) technique, the nilpotent BRST and anti-BRST symmetry transformations for this theory have been studied. In this model other forms of nilpotent symmetry transformations like co-BRST and anti-co-BRST, which leave the gauge-fixing part of the action invariant, are also explored. We show that the nilpotent charges for these symmetry transformations satisfy the algebra of the de Rham cohomological operators in differential geometry. The Hodge decomposition theorem on compact manifold is also studied in the context of conserved charges.     

Kaluza–Klein modes of bulk fields in a generalized Randall–Sundrum scenario

We consider a generalised two brane Randall–Sundrum model with non-zero cosmological constant on the visible TeV brane. Massive Kaluza–Klein modes for various bulk fields namely graviton, gauge field and antisymmetric second rank Kalb–Ramond field in a such generalized Randall–Sundrum scenario are determined. The masses for the Kaluza–Klein excitations of different bulk fields are found to depend on the brane cosmological constant indicating interesting consequences in warped brane particle phenomenology.     

Canonical transformations and gauge fixing in the triplectic quantization

We show that the generators of canonical transformations in the triplectic manifold must satisfy constraints that have no parallel in the usual field antifield quantization. A general form for these transformations is presented. Then we consider gauge fixing by means of canonical transformations in this Sp(2) covariant scheme, finding a relation between generators and gauge fixing functions. The existence of a wide class of solutions to this relation nicely reflects the large freedom of the gauge fixing process in the triplectic quantization. Some solutions for the generators are discussed. Our results are then illustrated by the example of Yang-Mills theory.     

CP violation in the general two-Higgs-doublet model: a geometric view

We discuss the CP properties of the potential in the general two-Higgs-doublet model (THDM). This is done in a concise way using real gauge invariant functions built from the scalar products of the doublet fields. The space of these invariant functions, parametrising the gauge orbits of the Higgs fields, is isomorphic to the forward light cone and its interior. CP transformations are shown to correspond to reflections in the space of the gauge invariant functions. We consider CP transformations where no mixing of the Higgs doublets is taken into account as well as the general case where the Higgs basis is not fixed. We present basis independent conditions for explicit CP violation which may be checked easily for any THDM potential. Conditions for spontaneous CP violation, that is CP violation through the vacuum expectation values of the Higgs fields, are also derived in a basis independent way.     

BRST-BV quantization of gauge theories with global symmetries

We consider the general gauge theory with a closed irreducible gauge algebra possessing the non-anomalous global (super)symmetry in the case when the gauge fixing procedure violates the global invariance of classical action. The theory is quantized in the framework of BRST-BV approach in the form of functional integral over all fields of the configuration space. It is shown that the global symmetry transformations are deformed in the process of quantization and the full quantum action is invariant under such deformed global transformations in the configuration space. The deformed global transformations are calculated in an explicit form in the one-loop approximation.     

Lie algebroids,Lie groupoids and TFT

We construct the moduli spaces associated to the solutions of equations of motion (modulo gauge transformations) of the Poisson sigma model with target being an integrable Poisson manifold. The construction can be easily extended to a case of a generic integrable Lie algebroid. Indeed for any Lie algebroid one can associate a BF-like topological field theory which localizes on the space of algebroid morphisms, that can be seen as a generalization of flat connections to the groupoid case. We discuss the finite gauge transformations and discuss the corresponding moduli spaces. We consider the theories both without and with boundaries.     

New Mechanism for Mass Generation of Gauge Field

A new mechanism for mass generation of gauge field is discussed in this paper.By introducing two sets of gauge fields and making the variations of these two sets of gauge fields compensated each other under local gauge transformations,the mass term of gauge fields is introduced into the Lagrangian without violating the local gauge symmetry of the Lagrangian.This model is a renormalizable quantum model.     

Self-Dual Strings in Six Dimensions: Anomalies,the <Emphasis Type="Italic">ADE</Emphasis>-Classification,and the World-Sheet <Emphasis Type="Italic">WZW</Emphasis>-Model

We consider the (2,0) supersymmetric theory of tensor multiplets and self-dual strings in six space-time dimensions. Space-time diffeomorphisms that leave the string world-sheet invariant appear as gauge transformations on the normal bundle of the world-sheet. The naive invariance of the model under such transformations is however explicitly broken by anomalies: The electromagnetic coupling of the string to the two-form gauge field of the tensor multiplet suffers from a classical anomaly, and there is also a one-loop quantum anomaly from the chiral fermions on the string world-sheet. Both of these contributions are proportional to the Euler class of the normal bundle of the string world-sheet, and consistency of the model requires that they cancel. This imposes strong constraints on possible models, which are found to obey an ADE-classification. We then consider the decoupled world-sheet theory that describes low-energy fluctuations (compared to the scale set by the string tension) around a configuration with a static, straight string. The anomaly structure determines this to be a supersymmetric version of the level one Wess-Zumino-Witten model based on the group      

The Investigation of Gauge Transformations in the SLq(2) Gauge Field and Thermodynamics Model

Some problems about global transformations in the SLq(2) gauge field and correlative thermodynamics model have been investigated in this paper. We proved that the quantum trace of gauge potential is not gauge-invariant if we compose two GLq(2) gauge transformations. In addition, it has been discovered in SLq(2) thermodynamics model that thermodynamics average of an observable quantity does not satisfy similar gauge invariance. We also found that the thermodynamics average can be only calculated in the case of zero energy gap. This fact shows that the q-deformed energy equation in superconductivity theory is unable to derive naturally from quantum trace model.     

The variational problem and background fields in renormalization group method for lattice gauge theories

We consider the action of a lattice gauge theory on a space of regular gauge field configurations with fixed averages, and we prove that there exists a minimum of this action. The minimum is unique up to gauge transformations. This minimal configuration is called a background field, and it serves as a basis of an expansion and perturbative methods.Work partially supported by the National Science Foundation under Grant PHY 82-03669 and DMS 84-01989     

Universal properties of U(1) gauge theories

The previously known analogies between four-dimensional compact U(1) lattice gauge theories and the two-dimensional planar model are extended to a number of other results. We show that the monopoles in the gauge theory renormalize the coupling constant α by an amount proportional to the susceptibility of the monopole gas. Confinement occurs when this susceptibility diverges. We argue that α is analogous to the critical exponent η of the planar model, and that the transition occurs at a universal critical value α_c.We also define an analogue of the superfluid density for the gauge theory, in terms of the dependence of the free energy on the boundary conditions, and show that it is universally related to α. Finally, we show that the same physics emerges from a continuum U(1) theory with real magnetic monopoles.     

Of Ghosts, Gauge Volumes, and Gauss's Law

The relationship between the canonical operator and the path integral formulation of quantum electrodynamics is analyzed with a particular focus on the implementation of gauge constraints in the two approaches. The removal of gauge volumes in the path integral is shown to match with the presence of zero-norm ghost states associated with gauge transformations in the canonical operator approach. The path integrals for QED in both the Feynman and the temporal gauges are examined and several ways of implementing the gauge constraint integrations are demonstrated. The upshot is to show that both the Feynman and the temporal gauge path integrals are equivalent to the Coulomb gauge path integral, matching the results developed by Kurt Haller using the canonical formalism. In addition, the Faddeev–Popov form for the Feynman gauge and temporal gauge Lagrangian path integrals are derived from the Hamiltonian form of the path integral.     

Lorentz-invariant ensembles of vector backgrounds

We consider gauge field theories in the presence of ensembles of vector backgrounds. While Lorentz invariance is explicitly broken in the presence of any single background, here, the Lorentz invariance of the theory is restored by averaging over a Lorentz-invariant ensemble of backgrounds, i.e., a set of background vectors that is mapped onto itself under Lorentz transformations. This framework is used to study the effects of a non-trivial but Lorentz-invariant vacuum structure or mass dimension two vector condensates by identifying the background with a shift of the gauge field. Up to now, the ensembles used in the literature comprise configurations corresponding to non-zero field tensors together with such with vanishing field strength. We find that even when constraining the ensembles to pure gauge configurations, the usual high-energy degrees of freedom are removed from the spectrum of asymptotic states in the presence of said backgrounds in Euclidean and in Minkowski space. We establish this result not only for the propagators to all orders in the background and otherwise at tree level but for the full propagator.     

Spin and Abelian Electromagnetic Duality¶on Four-Manifolds

We investigate the electromagnetic duality properties of an Abelian gauge theory on a compact oriented four-manifold by analysing the behaviour of a generalised partition function under modular transformations of the dimensionless coupling constants. The true partition function is invariant under the full modular group but the generalised partition function exhibits more complicated behaviour depending on topological properties of the four-manifold concerned. It is already known that there may be “modular weights” which are linear combinations of the Euler number and Hirzebruch signature of the four-manifold. But sometimes the partition function transforms only under a subgroup of the modular group (the Hecke subgroup). In this case it is impossible to define real spinor wave-functions on the four-manifold. But complex spinors are possible provided the background magnetic fluxes are appropriately fractional rather than integral. This gives rise to a second partition function which enables the full modular group to be realised by permuting the two partition functions, together with a third. Thus the full modular group is realised in all cases. The demonstration makes use of various constructions concerning integral lattices and theta functions that seem to be of intrinsic interest. Received: 5 June 2000 / Accepted: 9 October 2000     

Supergravity as a gauge theory of supersymmetry

In a new approach to supergravity we consider the gauge theory of the 14-dimensional supersymmetry group. The theory is constructed from 14×4 gauge fields, 4 gauge fields being associated with each of the 14 generators of supersymmetry. The gauge fields corresponding to the 10 generators of the Poincaré subgroup are those normally associated with general relativity, and the gauge fields corresponding to the 4 generators of supersymmetry transformations are identified with a Rarita-Schwinger spinor. The transformation laws of the gauge fields and the Lagrangian of lowest degree are uniquely constructed from the supersymmetry algebra. The resulting action is shown to be invariant under these gauge transformations if the translation associated field strength vanishes. It is shown that the second-order form of the action, which is the same as that previously proposed, is invariant without constraint.     

Superholomorphic structures,moment maps,and super self-dual Yang-Mills connections over super Riemann surfaces

We consider the space of superconnections with certain curvature constraints over super Riemann surfaces. We define a moment map over that space to the dual of the super Lie algebra of gauge transformations. The zero set of this moment map corresponds to the super self-dual Yang-Mills equations in two dimensions. This result generalizes the recently proposed scheme for the nonsupersymmetric case. The superfield equations also arise from super self-dual Yang-Mills equations in four dimensions by dimensional reduction.     

Gauge hierarchies and mass bounds

We consider the effects of weak symmetry breaking by radiative corrections in a scheme of gauge hierarchies. We obtain new mass bounds on heavy fermions and show how discovery of a Higgs boson may distinguish between two different approaches to hierarchial spontaneous gauge symmetry breakdown. If there are no intrinsic mass scales below ～10¹⁵ GeV then discovery of a Higgs boson at ～9 GeV implies the existence of heavy fermions.     

Linear bosonic quantum field theories arising from causal variational principles

We describe discrete symmetries of two-dimensional Yang–Mills theory with gauge group G associated with outer automorphisms of G, and their corresponding defects. We show that the gauge theory partition function with defects can be computed as a path integral over the space of twisted G-bundles and calculate it exactly. We argue that its weak-coupling limit computes the symplectic volume of the moduli space of flat twisted G-bundles on a surface. Using the defect network approach to generalised orbifolds, we gauge the discrete symmetry and construct the corresponding orbifold theory, which is again two-dimensional Yang–Mills theory but with gauge group given by an extension of G by outer automorphisms. With the help of the orbifold completion of the topological defect bicategory of two-dimensional Yang–Mills theory, we describe the reverse orbifold using a Wilson line defect for the discrete gauge symmetry. We present our results using two complementary approaches: in the lattice regularisation of the path integral, and in the functorial approach to area-dependent quantum field theories with defects via regularised Frobenius algebras.

     

QCD on an Infinite Lattice

We construct a mathematically well–defined framework for the kinematics of Hamiltonian QCD on an infinite lattice in ${\mathbb{R}^3}$ , and it is done in a C*-algebraic context. This is based on the finite lattice model for Hamiltonian QCD developed by Kijowski, Rudolph e.a.. To extend this model to an infinite lattice, we need to take an infinite tensor product of nonunital C*-algebras, which is a nonstandard situation. We use a recent construction for such situations, developed by Grundling and Neeb. Once the field C*-algebra is constructed for the fermions and gauge bosons, we define local and global gauge transformations, and identify the Gauss law constraint. The full field algebra is the crossed product of the previous one with the local gauge transformations. The rest of the paper is concerned with enforcing the Gauss law constraint to obtain the C*-algebra of quantum observables. For this, we use the method of enforcing quantum constraints developed by Grundling and Hurst. In particular, the natural inductive limit structure of the field algebra is a central component of the analysis, and the constraint system defined by the Gauss law constraint is a system of local constraints in the sense of Grundling and Lledo. Using the techniques developed in that area, we solve the full constraint system by first solving the finite (local) systems and then combining the results appropriately. We do not consider dynamics.