Background Gauge Field Research Articles

Instant-Form and Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1-Brane Action in the Presence of a Scalar Axion Field and an <i>U</i>(1) Gauge Field

Recently we have studied the instant-form quantization (IFQ) and the light-front quantization (LFQ) of the conformally gauge-fixed Polyakov D1 brane action using the Hamiltonian and path integral formulations. The IFQ is studied in the equal world-sheet time framework on the hyperplanes defined by the world-sheet time σ0=τ=constant and the LFQ in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time σ+= (τ+σ) =constant. The light-front theory is seen to be a constrained system in the sense of Dirac in contrast to the instant-form theory. However, owing to the gauge anomalous nature of these theories, both of these theories are seen to lack the usual string gauge symmetries defined by the world-sheet reparametrization invariance (WSRI) and the Weyl invariance (WI). In the present work we show that these theories when considered in the presence of background gauge fields such as the NSNS 2-form gauge field Bαβ(σ,τ) or in the presence of U(1) gauge field Aα(σ,τ) and the constant scalar axion field C(σ,τ), then they are seen to possess the usual string gauge symmetries (WSRI and WI). In fact, these background gauge fields are seen to behave as the Wess-Zumino or Stueckelberg fields and the terms containing these fields are seen to behave as Wess-Zumino or Stueckelberg terms for these theories.

Probing Fractionalized Charges

Inspired by the holographic entanglement entropy, for geometries with nonzero abelian charges, we define a quantity which is sensitive to the background charges. One observes that there is a critical charge below the system that is mainly described by the metric, and the effects of the background charges are just via metric's components. For charges above the critical one, the background gauge field plays an essential role. This, in turn, might be used to define an order parameter to probe phases of a system with fractionalized charges.

Constraints on superfluid hydrodynamics from equilibrium partition functions

Following up on recent work in the context of ordinary fluids, we study the equilibrium partition function of a 3+1 dimensional superfluid on an arbitrary stationary background spacetime, and with arbitrary stationary background gauge fields, in the long wavelength expansion. We argue that this partition function is generated by a 3 dimensional Euclidean effective action for the massless Goldstone field. We parameterize the general form of this action at first order in the derivative expansion. We demonstrate that the constitutive relations of relativistic superfluid hydrodynamics are significantly constrained by the requirement of consistency with such an effective action. At first order in the derivative expansion we demonstrate that the resultant constraints on constitutive relations coincide precisely with the equalities between hydrodynamical transport coefficients recently derived from the second law of thermodynamics.

Anisotropic quantum quench in the presence of frustration or background gauge fields: A probe of bulk currents and topological chiral edge modes

Bosons and fermions, in the presence of frustration or background gauge fields, can form manybody ground states that support equilibrium 'charge' or 'spin' currents. Motivated by the experimental creation of frustration or artificial gauge fields in ultracold atomic systems, we propose a general scheme by which making a sudden anisotropic quench of the atom tunneling across the lattice and tracking the ensuing density modulations provides a powerful and gauge invariant route to visualizing diverse equilibrium current patterns. Using illustrative examples of trapped superfluid Bose and normal Fermi systems in the presence of artificial magnetic fluxes on square lattices, and frustrated bosons in a triangular lattice, we show that this scheme to probe equilibrium bulk current order works independent of particle statistics. We also show that such quenches can detect chiral edge currents in gapped topological states, such as quantum Hall or quantum spin Hall insulators.

Topological Flat Bands from Dipolar Spin Systems

We propose and analyze a physical system that naturally admits two-dimensional topological nearly flat bands. Our approach utilizes an array of three-level dipoles (effective S=1 spins) driven by inhomogeneous electromagnetic fields. The dipolar interactions produce arbitrary uniform background gauge fields for an effective collection of conserved hard-core bosons, namely, the dressed spin flips. These gauge fields result in topological band structures, whose band gap can be larger than the corresponding bandwidth. Exact diagonalization of the full interacting Hamiltonian at half-filling reveals the existence of superfluid, crystalline, and supersolid phases. An experimental realization using either ultracold polar molecules or spins in the solid state is considered.

Renormalization constants and beta functions for the gauge couplings of the standard model to three-loop order

We compute the beta functions for the three gauge couplings of the Standard Model in the minimal subtraction scheme to three loops. We take into account contributions from all sectors of the Standard Model. The calculation is performed using both Lorenz gauge in the unbroken phase of the Standard Model and background field gauge in the spontaneously broken phase. Furthermore, we describe in detail the treatment of $\gamma_5$ and present the automated setup which we use for the calculation of the Feynman diagrams. It starts with the generation of the Feynman rules and leads to the bare result for the Green's function of a given process.

Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories

We consider three-dimensional N=2 superconformal field theories on a three-sphere and analyze their free energy F as a function of background gauge and supergravity fields. A crucial role is played by certain local terms in these background fields, including several Chern-Simons terms. The presence of these terms clarifies a number of subtle properties of F. This understanding allows us to prove the F-maximization principle. It also explains why computing F via localization leads to a complex answer, even though we expect it to be real in unitary theories. We discuss several corollaries of our results and comment on the relation to the F-theorem.

Constraints on fluid dynamics from equilibrium partition functions

We study the thermal partition function of quantum field theories on arbitrary stationary background spacetime, and with arbitrary stationary background gauge fields, in the long wavelength expansion. We demonstrate that the equations of relativistic hydrodynamics are significantly constrained by the requirement of consistency with any partition function. In examples at low orders in the derivative expansion we demonstrate that these constraints coincide precisely with the equalities between hydrodynamical transport coefficients that follow from the local form of the second law of thermodynamics. In particular we recover the results of Son and Surowka on the chiral magnetic and chiral vorticity flows, starting from a local partition function that manifestly reproduces the field theory anomaly, without making any reference to an entropy current. We conjecture that the relations between transport coefficients that follow from the second law of thermodynamics agree to all orders in the derivative expansion with the constraints described in this paper.

The gravity dual of supersymmetric gauge theories on a biaxially squashed three-sphere

We present the gravity dual to a class of three-dimensional N=2 supersymmetric gauge theories on a biaxially squashed three-sphere, with a non-trivial background gauge field. This is described by a 1/2 BPS Euclidean solution of four-dimensional N=2 gauged supergravity, consisting of a Taub–NUT–AdS metric with a non-trivial instanton for the graviphoton field. The holographic free energy of this solution agrees precisely with the large N limit of the free energy obtained from the localized partition function of a class of Chern–Simons quiver gauge theories. We also discuss a different supersymmetric solution, whose boundary is a biaxially squashed Lens space S3/Z2 with a topologically non-trivial background gauge field. This metric is of Eguchi–Hanson–AdS type, although it is not Einstein, and has a single unit of gauge field flux through the S2 cycle.

The gravity dual of supersymmetric gauge theories on a squashed three-sphere

We present the gravity dual to a class of three-dimensional N=2 supersymmetric gauge theories on a U(1)×U(1)-invariant squashed three-sphere, with a non-trivial background gauge field. This is described by a supersymmetric solution of four-dimensional N=2 gauged supergravity with a non-trivial instanton for the graviphoton field. The particular gauge theory in turn determines the lift to a solution of eleven-dimensional supergravity. We compute the partition function for a class of Chern–Simons quiver gauge theories on both sides of the duality, in the large N limit, finding precise agreement for the functional dependence on the squashing parameter. This constitutes an exact check of the gauge/gravity correspondence in a non-conformally invariant setting.

Primordial fluctuations from inflation with a triad of background gauge fields

We study the linear perturbation of the recently proposed model of inflation where a uniform gauge-kinetic coupling of the inflaton to multiple vector fields breaks the cosmic no-hair conjecture while maintaining the isotropy. We derive the general quadratic action for the perturbation and calculate the power spectra of scalar and tensor modes at the end of inflation by in-in formalism. It is shown that the model predicts slightly red spectra and the tensor-to-scalar ratio tends to be suppressed. The comparison with the data from WMAP 7-year does not impose strong constraints on the parameters and both weak- and strong- gauge-field regimes are consistent with the current observations.

Do we need Feynman diagrams for higher order perturbation theory?

We compute the two loop and three loop corrections to the beta function for Yang–Mills theories in the background gauge field method and using the background gauge field as the only source. The calculations are based on the separation of the one loop effective potential into zero and positive modes contributions and are entirely analytical. No two or three loop Feynman diagrams are considered in the process.

Arbitrage-free self-organizing markets with GARCH properties: Generating them in the lab with a lattice model

We extend our studies of a quantum field model defined on a lattice having the dilation group as a local gauge symmetry. The model is relevant in the cross-disciplinary area of econophysics. A corresponding proposal by Ilinski aimed at gauge modeling in non-equilibrium pricing is realized as a numerical simulation of the one-asset version. The gauge field background enforces minimal arbitrage, yet allows for statistical fluctuations. The new feature added to the model is an updating prescription for the simulation that drives the model market into a self-organized critical state. Taking advantage of some flexibility of the updating prescription, stylized features and dynamical behaviors of real-world markets are reproduced in some detail.

“Charged” particle’s tunneling from rotating black holes

The behavior of a scalar field theory near the event horizon in a rotating black hole background can be effectively described by a two dimensional field theory in a gauge field background. Based on this fact, we proposal that the quantum tunneling from rotating black hole can be treated as "charged" particle' s tunneling process in its effectively two dimensional metric. Using this viewpoint and considering the corresponding "gauge charge" conservation, we calculate the non-thermal tunneling rate of Kerr black hole and Myers-Perry black hole, and results are consistent with Parikh-Wilczek's original result for spherically symmetric black holes. Especially for Myers-Perry black hole which has multi-rotation parameters, our calculation fills in the gap existing in the literature applying Parikh-Wilczek's tunneling method to various types black holes. Our derivation further illuminates the essential role of effective gauge symmetry in Hawking radiation from rotating black holes.

Renormalization of the Asymptotically Expanded Yang–Mills Spectral Action

We study renormalizability aspects of the spectral action for the Yang–Mills system on a flat 4-dimensional background manifold, focusing on its asymptotic expansion. Interpreting the latter as a higher-derivative gauge theory, a power-counting argument shows that it is superrenormalizable. We determine the counterterms at one-loop using zeta function regularization in a background field gauge and establish their gauge invariance. Consequently, the corresponding field theory can be renormalized by a simple shift of the spectral function appearing in the spectral action.This manuscript provides more details than the shorter companion paper, where we have used a (formal) quantum action principle to arrive at gauge invariance of the counterterms. Here, we give in addition an explicit expression for the gauge propagator and compare to recent results in the literature.

(2, 0) supersymmetry and the light-cone description of M5-branes

AbstractInarXiv:1007.2982a novel system of equations which propagate in one null and four space directions were obtained as the on-shell conditions for the six-dimensional (2, 0) superalgebra. In this paper we show how this system reduces to one-dimensional motion on instanton moduli space. Quantization leads to the previous light-cone proposal of the (2, 0) theory, generalized to include a potential that arises on the Coulomb branch as well as couplings to background gauge and self-dual two-form fields.

SpontaneousCPviolation in quark scattering from QCDZ(3)interfaces

In this paper, we explore the possibility of spontaneous CP violation in the scattering of quarks and anti-quarks from QCD Z(3) domain walls. The CP violation here arises from the nontrivial profile of the background gauge field $(A_{0})$ between different Z(3) vacua. We calculate the spatial variation of $A_{0}$ across the Z(3) interface from the profile of the Polyakov loop $L(\vec{x})$ for the Z(3) interface and calculate the reflection of quarks and antiquarks using the Dirac equation. This spontaneous CP violation has interesting consequences for the relativistic heavy-ion collision experiments, such as baryon enhancement at high $P_{T}$. It also acts as a source of additional J/$\psi$ suppression. We also discuss its implications for the early universe.

String Gauge Symmetries in the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of Background Gauge Fields

Recently we have studied the instant-form quantization (IFQ) and the light-front quantization (LFQ) of the conformally gauge-fixed Polyakov D1 brane action using the Hamiltonian and path integral formulations. The IFQ is studied in the equal world-sheet time framework on the hyperplanes defined by the world- sheet time σ0 = τ = constant and the LFQ in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time . The light-front theory is seen to be a constrained system in the sense of Dirac in contrast to the instant-form theory. However, owing to the gauge anomalous nature of these theories, both of these theories are seen to lack the usual string gauge symmetries defined by the world-sheet reparametrization invariance (WSRI) and the Weyl invariance (WI). In the present work we show that these theories when considered in the presence of background gauge fields such as the NSNS 2-form gauge field or in the presence of gauge field and the constant scalar axion field , then they are seen to possess the usual string gauge symmetries (WSRI and WI). In fact, these background gauge fields are seen to behave as the Wess-Zumino/Stueckelberg fields and the terms containing these fields are seen to behave as Wess-Zumino or Stueckelberg terms for these theories.

Some properties of two Nambu-Jona-Lasinio -type models with inputs from lattice QCD

We investigate the phase diagram of the so-called Polyakov--Nambu--Jona-Lasinio (PNJL) model at finite temperature and nonzero chemical potential. The calculations are performed in the light and strange quark sectors ($u$, $d$, $s$), which includes the 't Hooft instanton induced interaction term that breaks the axial symmetry, and the quarks are coupled to the (spatially constant) temporal background gauge field. On one hand, a special attention is payed to the critical end point (CEP). The strength of the flavor-mixing interaction alters the CEP location, since when it becomes weaker the CEP moves to low temperatures and can even disappear. On the other hand, we also explore the connection between QCD, a nonlocal Nambu--Jona-Lasinio type model and the Landau gauge gluon propagator. Possible links between the quenched gluon propagator and low energy hadronic phenomenology are investigated.

Calculation of renormalized fermion effective actions in radially symmetric non-Abelian backgrounds

Our recent method to calculate renormalized functional determinants, the partial wave cutoff method, is extended for the evaluation of 4-D fermion one-loop effective action with arbitrary mass in certain types of radially symmetric, non-Abelian, background gauge fields (including instanton-like and instanton-antiinstanton-like configurations). A detailed study on functional determinants for matrix-valued radial differential operators is presented, explicating both our analytic treatment on the high partial wave contribution and the application of the generalized Gel'fand-Yaglom formula to determine the low partial wave contribution. In general, some numerical work is needed for the low partial wave part. In the massless limit, however, the factorizable nature of our partial-wave radial differential operators can be exploited to evaluate semi-analytically even the low partial wave part, and we thus have the full fermion effective action calculated explicitly in a class of non-Abelian background gauge fields. With nonzero mass, we also perform necessary numerical analysis as regards the low partial wave contribution to produce numerically exact results for the massive effective action. Comparing these against the results of the large mass expansion, the validity range of the large mass expansion is addressed. Also studied is the fermion mass dependence of the effective instanton-antiinstanton interaction.