Gauge Field Strength Research Articles

Non-AbelianS-term dark energy and inflation

We study the role that a cosmic triad in the generalized $SU(2)$ Proca theory, specifically in one of the pieces of the Lagrangian that involves the symmetric version $S_{\mu \nu}$ of the gauge field strength tensor $F_{\mu \nu}$, has on dark energy and primordial inflation. Regarding dark energy, the triad behaves asymptotically as a couple of radiation perfect fluids whose energy densities are negative for the $S$ term but positive for the Yang-Mills term. This leads to an interesting dynamical fine-tuning mechanism that gives rise to a combined equation of state parameter $\omega \simeq -1$ and, therefore, to an eternal period of accelerated isotropic expansion for an ample spectrum of initial conditions. Regarding primordial inflation, one of the critical points of the associated dynamical system can describe a prolonged period of isotropic slow-roll inflation sustained by the $S$ term. This period ends up when the Yang-Mills term dominates the energy density leading to the radiation dominated epoch. Unfortunately, in contrast to the dark energy case, the primordial inflation scenario is strongly sensitive to the coupling constants and initial conditions. The whole model, including the other pieces of the Lagrangian that involve $S_{\mu \nu}$, might evade the recent strong constraints coming from the gravitational wave signal GW170817 and its electromagnetic counterpart GRB 170817A.

Torsion in gauge theory

The potential conflict between torsion and gauge symmetry in the Riemann-Cartan curved space-time was noted by Kibble in his 1961 pioneering paper, and has since been discussed by many authors. Kibble suggested that, to preserve gauge symmetry, one should forgo the covariant derivative in favor of the ordinary derivative in the definition of the field strength F_{\mu}{\nu} for massless gauge theories, while for massive vector fields covariant derivatives should be adopted. This view was further emphasized by Hehl and collaborators in their influential 1976 review paper. We address the question of whether this deviation from normal procedure of forgoing covariant derivatives in curved spacetime with torsion could give rise to inconsistencies in the theory, such as the quantum renormalizability of a realistic interacting theory. We demonstrate in this note the one-loop renormalizability of a realistic gauge theory of gauge bosons interacting with Dirac spinors, such as the SU(3) chromodynamics, for the case of a curved Riemann-Cartan spacetime with totally anti-symmetric torsion. This affirmative confirmation is one step towards providing justification for the assertion that the flat-space definition of the gauge field strength should be adopted as the proper definition.

Generalized plane waves in Poincaré gauge theory of gravity

A family of exact vacuum solutions, representing generalized plane waves propagating on the (anti-)de Sitter background, is constructed in the framework of Poincar\'e gauge theory. The wave dynamics is defined by the general Lagrangian that includes all parity even and parity odd invariants up to the second order in the gauge field strength. The structure of the solution shows that the wave metric significantly depends on the spacetime torsion.

A string realisation of Ω-deformed Abelian [formula omitted] theory

The N=2⁎ supersymmetric gauge theory is a massive deformation of N=4, in which the adjoint hypermultiplet gets a mass. We present a D-brane realisation of the (non-)Abelian N=2⁎ theory, and compute suitable topological amplitudes, which are expressed as a double series expansion. The coefficients determine couplings of higher-dimensional operators in the effective supergravity action that involve powers of the anti-self-dual N=2 chiral Weyl superfield and of self-dual gauge field strengths superpartners of the D5-brane coupling modulus. In the field theory limit, the result reproduces the Nekrasov partition function in the two-parameter Ω-background, in agreement with a recent proposal.

ADHM construction of (anti-)self-dual instantons in 4n dimensions

The ADHM construction is a very strong scheme to construct the instantons in four dimensions. We study an ADHM construction of instantons in 4n (n ≥ 2) dimensions by generalizing this scheme. The higher-dimensional ADHM construction generates the 4n-dimensional (anti-)self-dual instantons which satisfy the (anti-)self-dual equation in 4n dimensions: F (n) = ± ∗4nF (n). Here F (n) is the nth wedge products of the gauge field strength 2-form F. We also show that our scheme reproduces the known 4n-dimensional one-instantons and there are multi-instanton solutions of the ’t Hooft type in the dilute instanton gas limit. Moreover, we discuss a Harrington-Shepard type caloron in 4n dimen-sions and this monopole limit.

A nonlocal approach to the cosmological constant problem

We construct a model in which the cosmological constant is canceled from the gravitational equations of motion. Our model relies on two key ingredients: a nonlocal constraint on the action, which forces the spacetime average of the Lagrangian density to vanish, and a dynamical way for this condition to be satisfied classically with arbitrary matter content. We implement the former condition with a spatially-constant Lagrange multiplier associated with the volume form and the latter by including a free four-form gauge field strength in the action. These two features are enough to remove the cosmological constant from the Einstein equation. The model is consistent with all cosmological and experimental bounds on modification of gravity and allows for both cosmic inflation and the present epoch of acceleration.

Gravity-Induced Four-Fermion Contact Interaction Implies Gravitational Intermediate W and Z Type Gauge Bosons

Coupling fermions to gravity necessarily leads to a non-renormalizable, gravitational four-fermion contact interaction. In this essay, we argue that augmenting the Einstein–Cartan Lagrangian with suitable kinetic terms quadratic in the gravitational gauge field strengths (torsion and curvature) gives rise to new, massive propagating gravitational degrees of freedom. This is to be seen in close analogy to Fermi’s effective four-fermion interaction and its emergent W and Z bosons.

An Application of the General Relativity-type Inversion Formulae: the Derivation of the Fock-Schwinger-Friedmann-Robertson-Walker Christoffel Symbol

Similar relationship between Christoffel symbols and Riemann tensors and between gauge potentials and gauge field strengths enable us to treat the Christoffel symbols just like the gauge fields. Restricting the Christoffel symbol by the Fock-Schwinger (FS) condition one obtains the so-call inversion formulae in general relativity theory. These formulae may be utilized for various applications, including the Christoffel symbol-free formulation of the general relativity and calculating the so-called Fock-Schwinger Christoffel symbols for certain Riemann tensors. Here we will derive the Fock-Schwinger-Friedmann-Robertson-Walker (FSFRW) Christoffel symbols.

Confining and repulsive potentials from effective non-Abelian gauge fields in graphene bilayers

We investigate the effect of shear and strain in graphene bilayers, under conditions where the distortion of the lattice gives rise to a smooth one-dimensional modulation in the stacking sequence of the bilayer. We show that strain and shear produce characteristic Moir\'e patterns which can have the same visual appearance on a large scale, but representing graphene bilayers with quite different electronic properties. The different features in the low-energy electronic bands can be ascribed to the effect of a fictitious non-Abelian gauge field mimicking the smooth modulation of the stacking order. Strained and sheared bilayers show a complementary behavior, which can be understood from the fact that the non-Abelian gauge field acts as a repulsive interaction in the former, expelling the electron density away from the stacking domain walls, while behaving as a confining interaction leading to localization of the electronic states in the sheared bilayers. In this latter case, the presence of the effective gauge field explains the development of almost flat low-energy bands, resembling the form of the zeroth Landau level characteristic of a Dirac fermion field. The estimate of the gauge field strength in those systems gives a magnitude of the order of several tens of Tesla, implying a robust phenomenology that should be susceptible of being observed in suitably distorted bilayer samples.

Anomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological Insulators.

We propose a class of photonic Floquet topological insulators based on staggered helical lattices and an efficient numerical method for calculating their Floquet band structure. The lattices support anomalous Floquet topological insulator phases with vanishing Chern number and tunable topological transitions. At the critical point of the topological transition, the band structure hosts a single unpaired Dirac cone, which yields a variety of unusual transport effects: a discrete analogue of conical diffraction, weak antilocalization not limited by intervalley scattering, and suppression of Anderson localization. Unlike previous designs, the effective gauge field strength can be controlled via lattice parameters such as the interhelix distance, significantly reducing radiative losses and enabling applications such as switchable topological waveguiding.

A semiclassical formulation of the chiral magnetic effect and chiral anomaly in even d + 1 dimensions

In terms of the matrix valued Berry gauge field strength for the Weyl Hamiltonian in any even space–time dimensions a symplectic form whose elements are matrices in spin indices is introduced. Definition of the volume form is modified appropriately. A simple method of finding the path integral measure and the chiral current in the presence of external electromagnetic fields is presented. It is shown that within this new approach the chiral magnetic effect as well as the chiral anomaly in even [Formula: see text] dimensions are accomplished straightforwardly.

On T-duality of R 2-corrections to DBI action at all orders of gauge field

Recently, it has been observed that in a T-duality invariant world-volume theory in flat spacetime, all orders of gauge field strength and all orders of the D-brane velocity appear in two specific matrices. Using these two matrices, we construct the world-volume couplings of two massless NSNS states at order $\alpha'^2$ and all orders of the velocity and the gauge field strength, by requiring them to be invariant under the linear T-duality. The standard extension $F\rightarrow F+P[B]$, then produces all orders of the pull-back of B-field into the action. We compare the resulting couplings for zero velocity and gauge field strength, with the $\alpha'^2$ terms of the disk-level S-matrix element of two massless NSNS vertex operators in the presence of a constant background B-field. We have found an exact agreement.

Gauge-invariant field-strength correlators for QCD in a magnetic background

We consider the properties of the gauge-invariant two-point correlation functions of the gauge-field strengths for QCD in the presence of a magnetic background field. We discuss the general structure of the correlators in this case and provide the results of an exploratory lattice study for $N_f = 2$ QCD discretized with unimproved staggered fermions. Our analysis provides evidence for the emergence of anisotropies in the non-perturbative part of the correlators and for an increase of the gluon condensate as a function of the external magnetic field.

Photon self-interaction on deformed spacetime

A novel nonlocal four-photon interaction on the deformed spacetime is derived and studied in the three selected models (I, II, III). The first two models (I, II) are obtained via two distinct second-order $\theta$-exact Seiberg-Witten maps of the noncommutative U(1) gauge field strength on Moyal space. The third one (III), inspired by the manifestly gauge invariant structures emerging in the first two, due to the model generality has been constructed with a different set of freedom parameters. The physical relevancy of all models is analyzed by evaluating the four-photon-tadpole diagram, which, when combined with the bubble graph, enables us to fully consider all contributions to the one-loop photon polarization tensor. For an arbitrary noncommutative matrix theta^\mu\nu, the full quadratic IR divergence cancellation in the one-loop photon two-point function is obtained with particular combinations of Seiberg-Witten map/gauge-symmetry freedom parameters in models I and II. Finally, our model III enables complete elimination of all pathological terms in the photon polarization tensor at one-loop order if a special value for the theta matrix is chosen.

θ-exact Seiberg-Witten maps at ordere3

We study two distinct $\ensuremath{\theta}$-exact Seiberg-Witten (SW) map expansions, (I) and (II), respectively, up to order ${e}^{3}$ for the gauge parameter, gauge field, and gauge field strengths of the noncommutative ${\mathrm{U}}_{\ensuremath{\star}}(1)$ gauge theory on the Moyal space. We derive explicitly the closed-form expression for the SW map ambiguity between the two and observe the emergence of several new totally commutative generalized star products. We also identify the additional gauge freedoms within each of the ${e}^{3}$-order field-strength expansions and define corresponding sets of deformation/ratio/weight parameters, $(\ensuremath{\kappa},{\ensuremath{\kappa}}_{i})$ and $(\ensuremath{\kappa},{\ensuremath{\kappa}}_{i}^{\ensuremath{'}})$, for these two SW maps, respectively.

Holographic model for the paramagnetism/antiferromagnetism phase transition

In this paper we build a holographic model of paramagnetism/antiferromagnetism phase transition, which is realized by introducing two real antisymmetric tensor fields coupling to the background gauge field strength and interacting with each other in a dyonic black brane background. In the case without external magnetic field and in low temperatures, the magnetic moments condense spontaneously in antiparallel manner with the same magnitude and the time reversal symmetry is also broken spontaneously (if boundary spatial dimension is more than 2, spatial rotational symmetry is broken spontaneously as well), which leads to an antiferromagnetic phase. In the case with weak external magnetic field, the magnetic susceptibility density has a peak at the critical temperature and satisfies the Curie-Weiss law in the paramagnetic phase of antiferromagnetism. In the strong external magnetic field case, there is a critical magnetic field $B_c$ in antiferromagnetic phase: when magnetic field reaches $B_c$, the system will return into the paramagnetic phase by a second order phase transition.

Universal constraints on axions from inflation

We consider the presence of an axion like particle, $\sigma$, with a generic $CP$ violating axial coupling of the form $ (\alpha \, \sigma/f) F \tilde{F}$, where $F_{\mu\nu}$ is the gauge field strength of a generic abelian $U(1)$ gauge group, not necessarily associated with the standard electromagnetism, and $f$ is the decay constant of the axion. It has previously been demonstrated that if the axion is identified with the inflaton, such an interaction can lead to measurable cosmological signatures (non-Gaussian modifications of the curvature perturbation spectrum) depending on the parameter $\xi= \alpha \dot{\sigma}/ (f H)$. In the present paper we will show that the generation of curvature perturbation at horizon crossing due to the axial coupling has a universal form and remains unmodified in terms of the $\xi$ parameter even if the axion, $\sigma$, is not identified with the inflaton. As a consequence, it does not appear to be possible to generate CMB tensor perturbations through this mechanism, larger than the vacuum ones, without violating the observational constraints unless we combine this mechanism with a curvaton or if the $\sigma$ field becomes heavy and decays during inflation. Even in this last case there are non-trivial constraints coming from the slow-roll evolution of the curvature perturbation on super horizon scales which should be taken into account. We also comment on implications for inflationary models where axions play an important role as, for example, models of natural inflation where more than one axion are included and models where the curvaton is an axion.

Note on the self-duality of gauge fields in topologically nontrivial spacetime

We show the derivation of the self-duality relation of abelian higher-form gauge field strength in the topologically nontrivial spacetime background. The so-called Pasti-Sorokin-Tonin action for the self-dual abelian gauge field assumes that the spacetime topology is trivial to derive the self-duality relation using a gauge transformation of the action. In this paper we find a new gauge transformation of the same theory and show that this new gauge transformation enables us to derive the self-duality relation even in the topologically nontrivial spacetime background.

On Lagrangian approach to self-dual gauge fields in spacetime of nontrivial topology

We study the Lagrangian description of chiral bosons, p-form gauge fields with (anti-)self-dual gauge field strengths, in D=2p+2 dimensional spacetime of nontrivial topology. We show that the manifestly Lorentz and diffeomorphism invariant Pasti-Sorokin-Tonin (PST) approach is consistent and produces the (anti-)self-duality equation also in topologically nontrivial spacetime. We discuss in what circumstances the nontrivial topology makes difference between two disconnected, `da-timelike' and `da-spacelike' branches of the PST system, the gauge fixed version of which are described by not manifestly invariant Henneaux-Teitelboim (HT) and Perry-Schwarz (PS) actions, respectively.

EXACT SOLUTIONS AND CANONICAL REDUCTION OF THE SELF-DUAL YANG MILLS EQUATIONS TO SOME NONLINEAR EVOLUTION EQUATIONS

The (constrained) canonical reduction of four-dimensional self- dual Yang-Mills (SDYM) theory to two-dimensional Burgers equation, Hunter- Saxton equation and Nonlinear diffusion equation are considered. On the other hand, other methods and transformations are developed to obtain exact solu- tions for the original two dimensional Burgers equation, Hunter-Saxton equa- tion and Nonlinear diffusion. The corresponding gauge potential Aµ and the gauge field strengths Fµν are also obtained. For these nonlinear evolution equations (NLEEs) which describe pseudo- spherical surfaces (pss) two new exact solution classes are generated from known solutions by using the Backlund transformations with the aid of Mathematica , either the seed solution is constant or a traveling wave.