Four-dimensional Gauge Field Research Articles

Zero modes of massive fermions delocalize from axion strings

Massless chiral excitations can arise from the interactions between a fermion and an axion string, propagating along the string and allowing it to superconduct. The properties of these excitations, or zero modes, dictate how the string interacts with light and can thus have important phenomenological consequences. In this paper, we add a nowhere-vanishing Dirac mass for the fermion in the usual model of axion electrodynamics. We find that the zero modes exhibit an interesting phase structure in which they delocalize from the string’s core as the mass increases, up until a critical value past which they disappear. We study this structure from an analytic perspective, with explicit numerical solutions, and via anomaly inflow arguments. Finally, we derive the two-dimensional effective theory of the zero mode and its interactions with the four-dimensional gauge field and show how this effective theory breaks down as the zero modes delocalize.

Chiral solution to the Ginsparg-Wilson equation

We present a chiral solution of the Ginsparg-Wilson equation. This work is motivated by our recent proposal for nonperturbatively regulating chiral gauge theories, where five-dimensional domain wall fermions couple to a four-dimensional gauge field that is extended into the extra dimension as the solution to a gradient flow equation. Mirror fermions at the far surface decouple from the gauge field as if they have form factors that become infinitely soft as the distance between the two surfaces is increased. In the limit of an infinite extra dimension we derive an effective four-dimensional chiral overlap operator which is shown to obey the Ginsparg-Wilson equation, and which correctly reproduces a number of properties expected of chiral gauge theories in the continuum.

Non-Abelian tensor gauge fields

Recently proposed extension of Yang-Mills theory contains non-Abelian tensor gauge fields. The Lagrangian has quadratic kinetic terms, as well as cubic and quartic terms describing non-linear interaction of tensor gauge fields with the dimensionless coupling constant. We analyze particle content of non-Abelian tensor gauge fields. In four-dimensional space-time the rank-2 gauge field describes propagating modes of helicity 2 and 0. We introduce interaction of the non-Abelian tensor gauge field with fermions and demonstrate that the free equation of motion for the spin-vector field correctly describes the propagation of massless modes of helicity 3/2. We have found a new metric-independent gauge invariant density which is a four-dimensional analog of the Chern-Simons density. The Lagrangian augmented by this Chern-Simons-like invariant describes massive Yang-Mills boson, providing a gauge-invariant mass gap for a four-dimensional gauge field theory.

Topological mass generation four-dimensional gauge theory

The Lagrangian of non-Abelian tensor gauge fields describes the interaction of the Yang–Mills and massless tensor bosons of increasing helicities. We have found a metric-independent gauge invariant density which is a four-dimensional analog of the Chern–Simons density. The Lagrangian augmented by this Chern–Simons-like invariant describes massive Yang–Mills boson, providing a gauge-invariant mass gap for a four-dimensional gauge field theory. We present invariant densities which can provide masses to the high-rank tensor bosons.

THE MECHANISM OF MIGDAL RECURSION RELATION AND PHASE DIAGRAMS OF YANG–MILLS FIELDS

In this paper it is shown that the gauge fixing term is not only gauge fixing term in D dimensions, but also the mass term for gauge field in (D+2)-dimensional superspace [or (D-2)-dimensional space], more importantly the kinetic term for the gauge modes g(x) is the so-called (D-2)-dimensional SU (N)× SU (N) principal chiral model. The results conform Migdal's scheme about the connection between four-dimensional gauge field and two-dimensional chiral system. And the recursion relation can be generalized to D dimensions gauge theories with chiral models in D-2 dimensions. With the new local order parameter for Yang–Mills field <g>|D-2, the results are consistent with lattice results qualitatively: there is no phase transition in low dimensions (D≤4), while in higher dimensions first-order phase transition appears between strong coupling region and weak coupling region.

Domain wall fermion and chiral gauge theories on the lattice with exact gauge invariance

We discuss how to construct anomaly-free chiral gauge theories on the lattice with exact gauge invariance in the framework of domain wall fermion. Chiral gauge coupling is realized by introducing a five-dimensional gauge field which interpolates between two different four-dimensional gauge fields at boundaries. The five-dimensional dependence is compensated by a local and gauge-invariant counter term. The cohomology problem to obtain the counter term is formulated in 5+1 dimensional space, using the Chern-Simons current induced from the five-dimensional Wilson fermion. We clarify the connection to the invariant construction based on the Ginsparg-Wilson relation using overlap Dirac operator. Formula for the measure and the effective action of Weyl fermions are obtained in terms of five-dimensional lattice quantities.

Implementation of an iterative map in the construction of (quasi)periodic instantons: Chaotic aspects and discontinuous rotation numbers

An iterative map of the unit disk in the complex plane is used to explore certain aspects of self-dual, four-dimensional gauge fields (quasi)periodic in the Euclidean time. These fields are characterized by two topological numbers and contain standard instantons and monopoles as different limits. The iterations do not correspond directly to a discretized time evolution of the gauge fields. They are implemented in an indirect fashion. First, (t,r,θ,φ) being the standard coordinates, the (r,t) half-plane is mapped on the unit disk in an appropriate way. This provides an (r,t) parametrization of Z0, the starting point of the iterations and makes the iterates increasingly complex functions of r and t. These are then incorporated as building blocks in the generating function of the fields. We explain in what sense and to what extent some remarkable features of our map (indicated in the title) are thus carried over into the continuous time development of the fields. Special features for quasiperiodicity are studied. Spinor solutions and propagators are discussed from the point of view of the mapping. Several possible generalizations are indicated. Some broader topics are also discussed.

On the four-dimensional effective action of strongly coupled heterotic string theory

The low-energy D = 4, N = 1 effective action of the strongly coupled heterotic string is explicitly computed by compactifying the Hořava-Witten theory on the deformed Calabi-Yau three-fold solution due to Witten. It is shown that, to order κ 2 3 , the Kähler potential is identical to that of the weakly coupled theory. Furthermore, the gauge kinetic functions are directly computed to order κ 4 3 and shown to receive a non-vanishing correction. Also, we compute gauge matter terms in the Kahler potential to the order κ 4 3 and find a non-trivial correction to the dilaton term. Part of those corrections arise from background fields that depend on the orbifold coordinate and are excited by four-dimensional gauge field source terms.

Large field renormalization. I. The basic step of the ? operation

We construct the renormalization operation of the expressions connected with the large field regions. This operation, denoted by ℝ, removes the main obstacle to prove the ultraviolet stability of four-dimensional gauge field theories. The proof will be completed in the second part of this paper.

Quantum evolution as a parallel transport

We point out that the evolution of a quantum system can be considered as a parallel transport of unitary operators in Hilbert spaces along the time with respect to a generalized connection. The different quantum representations of the system are shown to correspond to the choices of cross sections in the principal fiber bundle where the generalized connection is defined. This interpre- tation of time evolution allows us to solve the problem of the formulation of the evolution of a quantum particle in a four-dimensional gauge field.

Virtual stationary points

Using ideas from the Morse theory, a type of limiting field configurations is introduced which is expected to yield non-perturbative contributions to coupling constant expansions of topologically non-trivial quantum field theories. Examples are given for two-dimensional non-linear σ models and four-dimensional gauge fields. For the O(3) σ model the complete set is determined. The results are compared with the exact S matrices in two dimensions.