Background Gauge Research Articles

On the two-loop divergences in 6D, [formula omitted] SYM theory

We continue studying 6D,N=(1,1) supersymmetric Yang-Mills (SYM) theory in the N=(1,0) harmonic superspace formulation. Using the superfield background field method we explore the two-loop divergences of the effective action in the gauge multiplet sector. It is explicitly demonstrated that among four two-loop background-field dependent supergraphs contributing to the effective action, only one diverges off shell. It is also shown that the divergences are proportional to the superfield classical equations of motion and hence vanish on shell. Besides, we have analyzed a possible structure of the two-loop divergences on general gauge and hypermultiplet background.

Einstein\u2013Yang\u2013Mills theory: gauge invariant charges and linearization instability

We construct the gauge-invariant electric and magnetic charges in Yang–Mills theory coupled to cosmological general relativity (or any other geometric gravity), extending the flat spacetime construction of Abbott and Deser (Phys Lett B 116:259–263, 1982). For non-vanishing background gauge fields, the charges receive non-trivial contribution from the gravity part. In addition, we study the constraints on the first order perturbation theory and establish the conditions for linearization instability: that is the validity of the first order perturbation theory.

A comment on instantons and their fermion zero modes in adjoint QCD_2

The adjoint 2-dimensional QCD with the gauge group SU(N)/Z_NSU(N)/ZN admits topologically nontrivial gauge field configurations associated with nontrivial \pi_1[SU(N)/Z_N] = Z_Nπ1[SU(N)/ZN]=ZN. The topological sectors are labelled by an integer k=0,\ldots, N-1k=0,…,N−1. However, in contrast to QED_2QED2 and QCD_4QCD4, this topology is not associated with an integral invariant like the magnetic flux or Pontryagin index. These instantons may admit fermion zero modes, but there is always an equal number of left-handed and right-handed modes, so that the Atiyah-Singer theorem, which determines in other cases the number of the modes, does not apply. The mod. 2 argument [1] suggests that, for a generic gauge field configuration, there is either a single doublet of such zero modes or no modes whatsoever. However, the known solution of the Dirac problem for a wide class of gauge field configurations indicates the presence of k(N-k) zero mode doublets in the topological sector k. In this note, we demonstrate in an explicit way that these modes are not robust under a generic enough deformation of the gauge background and confirm thereby the conjecture of Ref. [1]. The implications for the physics of this theory (screening vs. confinement issue) are briefly discussed.

Renormalization of the topological charge density in QCD with dimensional regularization

To all orders of perturbation theory, the renormalization of the topological charge density in dimensionally regularized QCD is shown to require no more than an additive renormalization proportional to the divergence of the flavour-singlet axial current. The proof is based on the standard BRS analysis of the QCD vertex functional in the background gauge and exploits the special algebraic properties of the charge density through the Stora–Zumino chain of descent equations.

Can Quantum Thermodynamics Save Time?

The thermal time hypothesis (TTH) is a proposed solution to the problem of time: a coarse-grained state determines a thermal dynamics according to which it is in equilibrium, and this defines the flow of time in generally covariant quantum theories. This article raises a series of objections to the TTH as developed by Alain Connes and Carlo Rovelli. Two technical challenges concern the relationship between thermal time and proper time and the possibility of implementing the TTH in classical theories. Three conceptual problems concern the flow of time in nonequilibrium states and the extent to which the TTH is background independent and gauge invariant.

Instantons, symmetries and anomalies in five dimensions

All five-dimensional non-abelian gauge theories have a U(1)I global symmetry associated with instantonic particles. We describe an obstruction to coupling U(1)I to a classical background gauge field that occurs whenever the theory has a one-form center symmetry. This is a finite-order mixed ’t Hooft anomaly between the two symmetries. We also show that a similar obstruction takes place in gauge theories with fundamental matter by studying twisted bundles for the ordinary flavor symmetry. We explore some general dynamical properties of the candidate phases implied by the anomaly. Finally, we apply our results to supersymmetric gauge theories in five dimensions and analyze the symmetry enhancement patterns occurring at their conjectured RG fixed points.

Hall viscosity in the A phase of superfluid He3

We construct the effective field theory for the A-phase of superfluid $^3$He up to the next-to-leading order in the derivative expansion. To this end, we gauge the internal global symmetries of the theory on the curved space by introducing the background gauge fields and spatial metric so as to expose a hidden local symmetry known as the nonrelativistic diffeomorphism. The nonrelativistic diffeomorphism is particularly useful to yield an additional constraint on the effective field theory and reveal a universal expression for the Hall viscosity in the A-phase. We find it five orders of magnitude larger than that in the B-phase under a magnetic field so that its experimental observation is more feasible by measuring the induced elliptic polarization of sound waves.

A classical complex ϕ4 scalar field in a gauge background

We solve the equations of motion of a complex [Formula: see text] theory coupled to some given gauge field background. The solutions are given in both cylindrical and spherical coordinates and have finite energy.

Unified description of spin transport, weak antilocalization, and triplet superconductivity in systems with spin-orbit coupling

This work uncovers a hitherto unknown connection between different effects mediated by spin-orbit coupling in nanostructures: spin transport, weak antilocalization, and spin-triplet superconductivity. The authors show that all these phenomena can be described by a tool borrowed from the theory of superconductivity -- the linearized Eilenberger equation, generalized to include the spin-orbit coupling as a non-Abelian background gauge field. Furthermore, this approach enables the description of the aforementioned phenomena in a simpler and more intuitive manner compared to other methods.

Computing real time correlation functions on a hybrid classical/quantum computer

Quantum devices may overcome limitations of classical computers in studies of nuclear structure functions and parton Wigner distributions of protons and nuclei. In this talk, we discuss a worldline approach to compute nuclear structure functions in the high energy Regge limit of QCD using a hybrid quantum computer, by expressing the fermion determinant in the QCD path integral as a quantum mechanical path integral over 0 + 1-dimensional fermionic and bosonic world-lines in background gauge fields. Our simplest example of computing the well-known dipole model result for the structure function F2 in the high energy Regge limit is feasible with NISQ era technology using few qubits and shallow circuits. This example can be scaled up in complexity and extended in scope to compute structure functions, scattering amplitudes and other real-time correlation functions in QCD, relevant for example to describe non-equilibrium transport of quarks and gluons in a Quark-Gluon-Plasma.

Gauge copies and the fate of background independence in Yang-Mills theories: A leading order analysis

In this work we investigate the effects of the Gribov prescription to get rid of zero-modes of the Faddeev-Popov operator, at one-loop order in perturbation theory, in the Landau-DeWitt gauge. Quantum fluctuations are taken around a transverse background gauge field. The one-loop effective action is explicitly computed, and the behavior of the gauge and ghost fields propagators are carefully investigated. At one-loop and for generic transverse background configurations the effective action is found to be \textit{not} background invariant, as expected, due to a non-vanishing background contribution. The gauge field propagator has the same form as in the case {where the} background is a trivial field, $i.e.$ with complex conjugate poles, which are modified by the corresponding gap equation. The ghost-anti-ghost propagator still displays its enhanced $\sim p^{-4}$ behavior.

Path integral calculation of heat kernel traces with first order operator insertions

We study generalized heat kernel coefficients, which appear in the trace of the heat kernel with an insertion of a first-order differential operator, by using a path integral representation. These coefficients may be used to study gravitational anomalies, i.e. anomalies in the conservation of the stress tensor. We use the path integral method to compute the coefficients related to the gravitational anomalies of theories in a non-abelian gauge background and flat space of dimensions 2, 4, and 6. In 4 dimensions one does not expect to have genuine gravitational anomalies. However, they may be induced at intermediate stages by regularization schemes that fail to preserve the corresponding symmetry. A case of interest has recently appeared in the study of the trace anomalies of Weyl fermions.

Symmetry-enriched quantum spin liquids in (3 + 1)d

We use the intrinsic one-form and two-form global symmetries of (3+1)d bosonic field theories to classify quantum phases enriched by ordinary (0-form) global symmetry. Different symmetry-enriched phases correspond to different ways of coupling the theory to the background gauge field of the ordinary symmetry. The input of the classification is the higher-form symmetries and a permutation action of the 0-form symmetry on the lines and surfaces of the theory. From these data we classify the couplings to the background gauge field by the 0-form symmetry defects constructed from the higher-form symmetry defects. For trivial two-form symmetry the classification coincides with the classification for symmetry fractionalizations in (2 + 1)d. We also provide a systematic method to obtain the symmetry protected topological phases that can be absorbed by the coupling, and we give the relative ’t Hooft anomaly for different couplings. We discuss several examples including the gapless pure U(1) gauge theory and the gapped Abelian finite group gauge theory. As an application, we discover a tension with a conjectured duality in (3 + 1)d for SU(2) gauge theory with two adjoint Weyl fermions.

Non-Abelian Aharonov-Bohm caging in photonic lattices

Aharonov-Bohm (AB) caging is the localization effect in translational-invariant lattices due to destructive interference induced by penetrated magnetic fields. While current research focuses mainly on the case of Abelian AB caging, here we go beyond and develop the non-Abelian AB caging concept by considering the particle localization in a 1D multi-component rhombic lattice with non-Abelian background gauge field. In contrast to its Abelian counterpart, the non-Abelian AB cage depends on both the form of the nilpotent interference matrix and the initial state of the lattice. This phenomena is the consequence of the non-Abelian nature of the gauge potential and thus has no Abelian analog. We further propose a circuit quantum electrodynamics realization of the proposed physics, in which the required non-Abelian gauge field can be synthesized by the parametric conversion method, and the non-Abelian AB caging can be unambiguously demonstrated through the pumping and the steady-state measurements of only a few sites on the lattice. Requiring only currently available technique, our proposal can be readily tested in experiment and may pave a new route towards the investigation of exotic photonic quantum fluids.

Anomalous transport independent of gauge fields

We show that three-dimensional trace anomalies lead to new universal anomalous transport effects on a conformally-flat spacetime with background scalar fields. In contrast to conventional anomalous transports in quantum chromodynamics (QCD) or quantum electrodynamics (QED), our current is independent of background gauge fields. Therefore, our anomalous transport survives even in the absence of vector-like external sources. By manipulating background fields, we suggest a setup to detect our anomalous transport. If one turns on scalar couplings in a finite interval and considers a conformal factor depending just on (conformal) time, we find anomalous transport localized at the interfaces of the interval flows perpendicularly to the interval. The magnitude of the currents is the same on the two interfaces but with opposite directions. Without the assumption on scalar couplings, and only assuming the conformal factor depending solely on (conformal) time as usually done in cosmology, one also finds the three-dimensional Hubble parameter naturally appears in our current.

Scalar sunset diagram at finite temperature with imaginary square masses

We evaluate the finite temperature scalar sunset diagram with imaginary square masses, that appears in the Gribov-Zwanziger approach to Yang-Mills (YM) theory beyond one-loop order. Since YM theory at finite temperature is governed by center-symmetry and the Polyakov loop, we also include the possibility of a constant temporal background gauge field in the form of color-dependent imaginary chemical potentials.

Dirac equation on a square waveguide lattice with site-dependent coupling strengths and the gravitational Aharonov-Bohm effect

The main objective of this work is to present a theoretical proposal for an implementation of the $(2 + 1)$-dimensional Dirac equation in classical gravitational and electromagnetic backgrounds in a two-dimensional waveguide array. For this, a framework for achieving site-dependent effective coupling constants in two-dimensional waveguide arrays is developed. Implementability of the Dirac equation under the proposed scheme puts minor demands on gauge and spacetime backgrounds; however, a wide array of physical spacetimes, such as all vacuum and static solutions, prove to be implementable. As an interesting and instructive example, we discuss a tabletop realization of the gravitational Aharonov-Bohm effect: After devising a thought experiment in which signatures of the gravitational Aharonov-Bohm effect could be detected, we briefly discuss how the analogue of such a setting can in principle be implemented using the proposed waveguide setup.

Deconfined, massive quark phase at high density and compact stars: A holographic study

In Hoyos et al. (arXiv:1603.02943) a holographic D3/D7 system was used to describe a deconfined yet massive quark phase of QCD at finite density, concluding that the equation of state of such a phase was not stiff enough to support exotic dense stars. That analysis used a hard quark mass to represent the dynamical mass and assumed a conformal gauge background. Here we phenomenologically adjust the D3/D7 system to include a running anomalous dimension for the quark condensate. This introduces a dynamical mechanism for chiral symmetry breaking yet the model still has a deconfined massive phase at intermediate densities. We show that these systems, dependent on the running profile in the deep IR, generate much stiffer equations of state and non-monotonic behaviour in the speed of sound. The results suggest that these equations of state may be closer to supporting hybrid stars with quark cores.

Skyrmions and spin waves in frustrated ferromagnets at low applied magnetic field

A continuum model of frustrated ferromagnets is analyzed in detail in the regime of low applied magnetic field, $H_0<1/4$, where the ground state is a spatially varying conical spiral. By changing variables to a corotating spin field, the model is reformulated as a gauged sigma model in a fixed background gauge, allowing the construction of stable isolated Skyrmions, and stable multi-Skyrmion clusters, which approach the conical ground state at spatial infinity. Owing to the spatial anisotropy induced by the ground state, these Skyrmions exhibit only discrete symmetries, and are of neither N\'eel nor Bloch type. These Skyrmions are continuously connected to the more familar solutions in the high field regime ($H_0>1/4$), acquiring axial symmetry in the limit $H_0\rightarrow 1/4$. The propagation of small amplitude spin waves through the conical ground state is also analyzed and is found to depend strongly on both $H_0$ and propagation direction relative to the ground state. In contrast to spin waves in the high field regime ($H_0>1/4$) there is no spectral gap: waves may propagate with any angular frequency.

Heterotic strings on (K3 \xd7 T2)/\u21243 and their dual Calabi-Yau threefolds

In this paper we study compactifications of the mathcal{N} = 2 heterotic E8× E8 string on (K3 × T2)/ℤ3 with various gauge backgrounds and calculate the topological couplings in the effective supergravity action that arise from one-loop amplitudes. We then identify candidates for dual type IIA compactifications on Calabi-Yau threefolds and compare the heterotic results with the corresponding topological string amplitudes. We find that the dual Calabi-Yau geometries are K3 fibrations that are also genus one fibered with three- sections. Moreover, we show that the intersection form on the polarization lattice of the K3 fibration has to be three times the intersection form on the Narain lattice Γ1,1.