Gauge invariant formulation of non-Abelian chiral gauge theories in two dimensions

We study the gauge invariant version of a chiral non-Abelian gauge theory. A local bosonic effective action is obtained and the covariant conservation of the gauge current is verified. A Hamiltonian analysis of the model and of its constraints is performed. We show that the constraints are first class and that no anomalous term appears in the commutators of the gauge group generators. The current algebra of the model is obtained and the gauge fixing is analyzed.     

Supersymmetric gauge theories in quantum mechanics

A general construction for supersymmetric U(1) gauge invariant Hamiltonians in quantum mechanics is given. For a given number of fermionic and bosonic degrees of freedom it is shown that for four supercharges the interactions are determined uniquely, and coincide with the dimensionally reduced N = 1, d = 3 + 1 supersymmetric electrodynamics. With two supercharges one gets models which cannot be obtained through dimensional reduction. For two special choices of a parameter one recovers the dimensionally reduced d = 1 + 1 Weyl supersymmetric and Majorana supersymmetric electrodynamics.     

Superspace approach to quantum gauge theories

We present an approach to quantum gauge theories formulated entirely on a superspace. We show that at the classical level the field equations are the same as in the usual Minkowski-space approach. In particular the a-flatness conditions, which represent the BRS and anti-BRS covariance in the usual approach, appear as field equations. We show that the theory is renormalizable and the a-flatness conditions are stable under renormalization. We speculate about the relevance of this approach to the confinement problem.     

Dynamical fermions in lattice gauge theories: Metropolis and Langevin techniques in two dimensions

A variety of techniques for the inclusion of dynamical fermions in lattice gauge theory is examined. Three pseudo-fermionic techniques that have the characteristics desirable for an unquenched simulation of four-dimensional QCD are studied in detail. Langevin and Metropolis pseudo-fermionic techniques are implemented for a 64×64 lattice on the Distributed Array Processor and their relative merits examined both for free fermions and the lattice Schwinger model.     

Asymptotic freedom in gauge theories and quantum gravity

Restrictions on the structure of a gauge theory which follow from the requirement of asymptotic freedom with respect to all coupling constants are studied. One-loop counterterms for renormalizable gravity with matter are computed. It is shown that for the group O(N), taking into account the contribution of quantum R²-gravity allows one to construct new, asymptotically free gauge theories with a reduced number of spinor multiplets. The results are compared with those obtained earlier for conformal gravity with matter.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 36–41, January, 1990.The authors thank A. O. Barvinskii, I. L. Bukhbinder, and E. S. Fradkin for the discussions.     

On nonlinear gauge theories

In this note, we study non-linear gauge theories for principal bundles, where the structure group is replaced by a Lie groupoid. We follow the approach of Moerdijk–Mr?un and establish its relation with the existing physics literature. In particular, we derive a new formula for the gauge transformation which closely resembles and generalizes the classical formulas found in Yang Mills gauge theories.     

Induced quantum curvature and three-dimensional gauge theories

The effects of quantum holonomy in three-dimensional gauge theories with massless fermions is examined and different definitions of the fermion determinant are discussed. The source of a global gauge and parity anomaly is identified in Schrödinger picture quantization as an induced holonomy that arises from the fermionic sector of the theory. In certain fermion representations this holonomy leads to a global obstruction to imposing either gauge or parity invariance through the implementation of Gauss' law constraint. However, such obstructions can be removed by exploiting renormalization ambiguities inherent in the definition of composite operators.     

Parity anomalies in gauge theories in 2 + 1 dimensions

It is shown that the introduction of massless fermions in an abelian gauge theory in 2 + 1 dimensions does not lead to any parity anomaly despite a non-commutativity of limits in the structure function of the odd part of the vacuum polarisation tensor. However, a parity anomaly does exist in non-abelian theories due to a conflict between gauge invariance under large gauge transformations and the parity symmetry.     

Even more about gauge theories in 1 + 1 dimensions

It is shown that the properly defined background electric field in 1 + 1 dimensional quantum electrodynamics is not limited in magnitude by pair creation effects. Furthermore, the inequivalence of the axial gauge and the Coulomb gauge is pointed out. Applications to quantum chromodynamics are discussed.     

On gauge theories of mass

The classical Einstein–Hilbert action in general relativity extends naturally to a blow-up (in the sense of algebraic geometry) of the usual space of pseudo-Riemannian metrics; this presents the metric tensor _gik$g_{ik}$ as a kind of Goldstone boson associated to the real scalar field defined by its determinant. This seems to be quite compatible with the Higgs mechanism in the standard model of particle physics.     

Two-dimensional lattice gauge theories with superconducting quantum circuits

A quantum simulator of U(1)$U\left(1\right)$ lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.     

String tensions for lattice gauge theories in 2 + 1 dimensions

Compact U(1) and SU(2) lattice gauge theories in 3 euclidean dimensions are studied by standard Monte Carlo techniques. The question of extracting reliable string tensions from these theories is examined in detail, including a comparison of the Monte Carlo Wilson loop data with weak coupling predictions and a careful error analysis: our conclusions are rather different from those of previous investigations of these theories. In the case of U(1) theory, we find that only a tiny range of β values can possibly be relevant for extracting a string tension and we are unable to convincingly demonstrate the expected exponential dependence of the string tension on β. For the SU(2) theory we are able to determine, albeit with rather large errors, a string tension from a study of Wilson loops.     

Simple superconformal field theories in two dimensions

Superconformal field theories with first-order lagrangians, the super BC-systems, are considered on an arbitrary Riemann surface with an arbitrary gravitino field. The corresponding functional integrals are carefully defined, and the Weyl, supersymmetry, and holomorphic anomalies are computed. All the anomalies have a common coefficient. The holomorphic anomaly involves terms quadratic in the gravitino field.     

Consistent gauge-invariant chiral theories in two dimensions

We employ a gauge-invariant point-splitting procedure to solve chiral gauge theories in two dimensions. We present an explicit solution of the chiral Schwinger model. The resulting theory is gauge-invariant and unitary containing a massless physical state. The method is generalizable to higher dimensions.     

Correspondence principle and quantum gauge theories with chiral fermions

The correspondence principle is used to extend nonabelian gauge theories with chiral fermions up to anomaly-free theories by introducing unitary scalar fields. Resulting theories can be treated as a low-energy approximation to left-right theories. This approach fixes the Weinberg angle of the electroweak theory at _w=30°.     

On the Meissner effect in gauge theories

The phase structure of spontaneously broken scalar electrodynamics in an external electromagnetic field is analyzed. With no external field, the spectrum comprises a scalar boson of mass m_H and a vector boson of mass m_W. If m_H ≤ m_W, it is shown that in the tree approximation, as the external field is increased, a first order phase transition to a restored symmetry phase occurs, and the critical field strength is calculated. Below the critical point the external field is completely screened, this being the analogue of the Meissner effect in superconductivity. If m_H > m_W, a third phase, characterized by vortex solutions of the field equations, occurs. Quantum effects, such as pair production in an electric field, are considered at the one (and two) loop level in the massless theory (the Coleman-Weinberg model). The leading correction to the critical magnetic field strength is calculated, and it is shown that for an external electric field the phase transition does not exist.     

The choice of test functions in gauge quantum field theories

We discuss the problem of the choice of test functions in gauge quantum field theories. Analysis of explicitly soluble models suggests that the test function spaces which are suitable for local and covariant formulation of gauge theories are the Gelfand and Shilov spaces , +>1. We also discuss a possible generalization of the spectral condition.