Abelian Field Theory Research Articles

From physical symmetries to emergent gauge symmetries

Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.

Nonrelativistic limit of the abelianized ABJM model and the ADS/CMT correspondence

We consider the nonrelativistic limit of the abelian reduction of the massive ABJM model proposed in [1], obtaining a supersymmetric version of the Jackiw-Pi model. The system exhibits an $$ \mathcal{N}=2 $$ Super-Schrodinger symmetry with the Jackiw-Pi vortices emerging as BPS solutions. We find that this (2 + 1)-dimensional abelian field theory is dual to a certain (3+1)-dimensional gravity theory that differs somewhat from previously considered abelian condensed matter stand-ins for the ABJM model. We close by commenting on progress in the top-down realization of the AdS/CMT correspondence in a critical string theory.

Topologically stratified energy minimizers in a product Abelian field theory

We study a recently developed product Abelian gauge field theory by Tong and Wong hosting magnetic impurities. We first obtain a necessary and sufficient condition for the existence of a unique solution realizing such impurities in the form of multiple vortices. We next reformulate the theory into an extended model that allows the coexistence of vortices and anti-vortices. The two Abelian gauge fields in the model induce two species of magnetic vortex-lines resulting from Ns vortices and Ps anti-vortices (s=1,2) realized as the zeros and poles of two complex-valued Higgs fields, respectively. An existence theorem is established for the governing equations over a compact Riemann surface S which states that a solution with prescribed N1, N2 vortices and P1,P2 anti-vortices of two designated species exists if and only if the inequalities|N1+N2−(P1+P2)|<|S|π,|N1+2N2−(P1+2P2)|<|S|π, hold simultaneously, which give bounds for the ‘differences’ of the vortex and anti-vortex numbers in terms of the total surface area of S. The minimum energy of these solutions is shown to assume the explicit valueE=4π(N1+N2+P1+P2), given in terms of several topological invariants, measuring the total tension of the vortex-lines.

Path integral approach to eikonal and next-to-eikonal exponentiation

We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed coordinate-momentum space representation, a charged particle interacting with a soft gauge field is represented as a Wilson line for a semi-infinite line segment, together with calculable fluctuations. Combining such line segments, we show that exponentiation in an abelian field theory follows immediately from standard path-integral combinatorics. In the non-abelian case, we consider color singlet hard interactions with two outgoing external lines, and obtain a new viewpoint for exponentiation in terms of ``webs'', with a closed form solution for their corresponding color factors. We investigate and clarify the structure of next-to-eikonal corrections.

Coexistence of Vortices and Antivortices in an Abelian Gauge Theory

We present an Abelian field theory model that allows the coexistence of vortices and antivortices. Some of the interesting properties are that the magnetic flux is proportional to the difference of the numbers of vortices and antivortices but the energy is proportional to the sum of these numbers. In the context of cosmology, these vortices represent cosmic strings and antistrings with opposite magnetic charges. In addition to the above properties, we show that the total quantized curvature is proportional to the sum of the numbers of strings and antistrings which also determines the completeness of the gravitational metric.

Asymptotic properties of the Chern-Simons Abelian field theory with matter in distorted space-time

The asymptotic behavior of the Chern-Simons field theory with matter in a deformed space is investigated. The asymptotic forms of effective charges are considered.

Study of the phase structure of abelian field theories through non-lattice, non-perturbative calculations

A recently proposed approach to gauge field theories, by which one formulates them non-locally and subsequently approaches locality arbitrarily close, is applied to U(1) gauge theories. We test the possibility that the aformentioned methodology might introduce a measure in the functional integral which supports non-perturbative calculations in the continuum. In particular, we are able to carry relevant calculations pertaining to the expectation value of Wilson's loop operator in 3 + 1, 2 + 1 and 1 + 1 dimensions. The results are similar to ones obtained through the lattice regularization of U(1) gauge theory, with the important difference that in our case they refer to continuum, U(1) gauge theory, as a function of the bare coupling constant. We further solidify the validity of our approach by conducting a calculation referring to the 2-dimensional scalar Heisenberg model, remaining always in the continuum.

Study of the phase structure of abelian field theories through non-lattice, non-perturbative calculations

Study of the phase structure of abelian field theories through non-lattice, non-perturbative calculations

Color flux and Yang-Mills structure-a dynamical model

In view of the basic difficulties of QCD to bring the confinement hypothesis to a calculational level, a field-theoretic flux tube model with local color gauge invariance is set up which exhibits triality confinement ab initio. This is achieved by an appropriate formulation of Gauss' law using the tube operator as canonical degree of freedom. Along the tube there are vectorlike gauge-invariant color excitations related to splitting and to the short-distance behavior. They receive their degrees of freedom from the tube oscillations and thus are a realization of Polyakov's program. The quarkless system averaged over the directions of the flux tubes passing through a given world point reproduces the pure Yang-Mills equations. The guide to the model is the loop-space formulation of the confining Gauss law of the abelian confinement theory. Basically we generalize to a nonabelian gauge structure not a local abelian field theory but directly the loop-space formulation of the abelian confinement theory.

Spinor Bethe-Salpeter equation with generalized ladder kernels and the Goldstein problem

The spinor Bethe-Salpeter equation is investigated for tightly bound fermion pairs. The covariant interaction kernel contains contributions of vector and axial-vector gluons within the framework of the Stückelberg formalism. The free gluon propagators of the strict ladder approximation are replaced by a convenient spectral form. This generalized ladder model can be extended to a large class of gauge field theories by specifying the spectral functions. The model-independent O(4) analysis of the Wick-rotated wave functions is carried out by using a complete set of four-dimensional scalar, vector, and tensor spherical harmonics. At vanishing center-of-mass energy, the radial Bethe-Salpeter equations can be classified in six disconnected sectors. All these equations are recorded in a general form which provides a study of the gauge dependence of the wave functions at short distances. Illustrative calculations are based on a simple Abelian field theory. In two Goldstein equations the leading singular term of the kernel may be absent by cancellation. In addition, one obtains a generalized Goldstein equation in which the kernel includes a gauge-independent marginally singular term. It is discussed how corrections of the large-distance behavior of the singular Goldstein kernel can lead to normalizable bound-state solutions without introducing a short-distance cutoff. Exact and numerical solutions are presented by using a simple parametrization of the kernel. In other sectors, the noncanonical angular behavior of the solutions may be avoided by prescribing a complex mass for the Stückelberg ghosts.