Auxiliary Gauge Fields Research Articles

Coupling Constants as Conserved Charges in Black Hole Thermodynamics.

In a generic theory of gravity coupled to matter fields, the Smarr formula for black holes does not work properly if the contributions of the coupling constants defining the theory are not incorporated. However, these couplings, such as the cosmological constant or the dimensionful parameters that appear in the Lagrangian, are fixed parameters defining the theory, and they cannot be varied. Here, we present a robust method, applicable to any covariant Lagrangian, that upgrades the role of the couplings from being constants in the theory to being free parameters of the solutions. To this end, for each one of the couplings in a theory, a pair of auxiliary scalar and gauge fields is introduced. The couplings are shown to be conserved charges of the global part of the implemented gauge symmetry. Besides, their conjugate chemical potentials are defined as the electric potential of the corresponding gauge fields on the black hole horizon. Using this method, we systematically extend the first law and the Smarr formula by coupling conserved charges and their conjugate potentials. The thermodynamics of a black hole solution in a quadratic gravity theory is given as an example.

Exact duality and local dynamics in SU(N) lattice gauge theory

We construct exact duality transformations in pure SU(N) Hamiltonian lattice gauge theory in ($2+1$) dimension. This duality is obtained by making a series of iterative canonical transformations on the SU(N) electric vector fields and their conjugate magnetic vector potentials on the four links around every plaquette. The resulting dual description is in terms of the magnetic scalar fields or plaquette flux loops and their conjugate electric scalar potentials. Under SU(N) gauge transformations they both transform like adjoint matter fields. The dual Hamiltonian describes the nonlocal self-interactions of these plaquette flux loops in terms of the electric scalar potentials and with inverted coupling. We show that these nonlocal loop interactions can be made local and converted into minimal couplings by introducing SU(N) auxiliary gauge fields along with new plaquette constraints. The matter fields can be included through minimal coupling. The techniques can be easily generalized to ($3+1$) dimensions.

Reconciling LSND and Super-Kamiokande data through the dynamical Lorentz symmetry breaking in a four-Majorana fermion model

We propose a model of Majorana fermions with quartic self-couplings. These Majorana fermions acquire masses via a type II seesaw mechanism in which the physical eigenstates are identified as a light Majorana fermion and another heavy Majorana fermion. On a physical basis, the quartic self-couplings involve axial currents of these Majorana fermions, and also the interaction of the axial current for the light particle with the heavy particle one. We introduce two auxiliaries gauge fields in this model, and we study the stability conditions of the correspondent effective potential of the model. The ground state of the effective potential introduces two 4-vectors as scales of vacuum expected values, and consequently, the dynamical Lorentz symmetry breaking (DLSB) emerges in the model. We use the expansion of the effective action to calculate the effective Lagrangian up to second order in the auxiliary fields as fluctuations around the ground state. This mechanism generates dynamics for the auxiliary gauge fields, mixed mass terms, longitudinal propagation, and Chern-Simons term through radiative corrections. After the diagonalization, the two gauge fields gain masses through an analogous type II seesaw mechanism in which a gauge boson has a light mass, and the other one acquires a heavy mass. In this scenario of Lorentz symmetry breaking, we obtain the correspondent dispersion relations for the Majorana fermions and the gauge boson fields. Posteriorly, we analyze the neutrino's oscillations in the presence of a DLSB parameter, in the transition $\nu_{e} \rightarrow \nu_{\mu}$. We discuss the parameter space of this transition and show that the DLSB can conciliate the LSND and super-Kamiokande results.

Mass formulae and staticity condition for dark matter charged black holes

The Arnowitt–Deser–Misner formalism is used to derive variations of mass, angular momentum and canonical energy for Einstein–Maxwell dark matter gravity in which the auxiliary gauge field coupled via kinetic mixing term to the ordinary Maxwell one, which mimics properties of hidden sector. Inspection of the initial data for the manifold with an interior boundary, having topology of S^2, enables us to find the generalised first law of black hole thermodynamics in the aforementioned theory. It has been revealed that the stationary black hole solution being subject to the condition of encompassing a bifurcate Killing horizon with a bifurcation sphere, which is non-rotating, must be static and has vanishing magnetic Maxwell and dark matter sector fields, on static slices of the spacetime under consideration.

Ultra-compact spherically symmetric dark matter charged star objects

We study the properties of ultra-compact spherically symmetric dark matter sector star objects, being the solution of Einstein equations with two U(1)-gauge fields. One of them is the ordinary Maxwell field, while the auxiliary gauge field pertains to the hidden sector, and mimics the properties of dark matter. The visible and hidden sectors are coupled by a kinetic mixing term with a coupling constant α. We also investigate the possibility of condensation of charged scalar field around the reflecting dark matter star object. It happens that dark matter sector, both dark matter charge and coupling constant, cause shrinking of the star radius for which the condensation may occur.

Ghostbusters in f (R) supergravity

f (R) supergravity is known to contain a ghost mode associated with higher-derivative terms if it contains Rn with n greater than two. We remove the ghost in f (R) supergravity by introducing auxiliary gauge field to absorb the ghost. We dub this method as the ghostbuster mechanism [1]. We show that the mechanism removes the ghost super-multiplet but also terms including Rn with n ≥ 3, after integrating out auxiliary degrees of freedom. For pure supergravity case, there appears an instability in the resultant scalar potential. We then show that the instability of the scalar potential can be cured by introducing matter couplings in such a way that the system has a stable potential.

A gauged linear formulation for flag-manifold σ-models

We formulate σ-models of a flag manifold with a zero-curvature representation in the form of a theory of linear “matter fields” interacting with auxiliary gauge fields.

Cosmological aspects of a unified dark energy and dust dark matter model

Recently, a model of modified gravity plus single scalar field was proposed, in which the scalar couples both to the standard Riemannian volume form given by the square root of the determinant of the Riemannian metric, as well as to another non-Riemannian volume form given in terms of an auxiliary maximal rank antisymmetric tensor gauge field. This model provides an exact unified description of both dark energy (via dynamically generated cosmological constant) and dark matter (as a “dust” fluid due to a hidden nonlinear Noether symmetry). In this paper, we test the model against Supernovae type Ia experimental data and investigate the future Universe evolution which follows from it. Our results show that this model has very interesting features allowing various scenarios of Universe evolution and in the same time perfectly fits contemporary observational data. It can describe exponentially expanding or finite expanding Universe and moreover, a Universe with phase transition of first kind. The phase transition occurs to a new, emerging at some time ground state with lower energy density, which affects significantly the Universe evolution.

Higher gauge theories from Lie n-algebras and off-shell covariantization

We analyze higher gauge theories in various dimensions using a supergeometric method based on a differential graded symplectic manifold, called a QP-manifold, which is closely related to the BRST-BV formalism in gauge theories. Extensions of the Lie 2-algebra gauge structure are formulated within the Lie n-algebra induced by the QP-structure. We find that in 5 and 6 dimensions there are special extensions of the gauge algebra. In these cases, a restriction of the gauge symmetry by imposing constraints on the auxiliary gauge fields leads to a covariantized theory. As an example we show that we can obtain an off-shell covariantized higher gauge theory in 5 dimensions, which is similar to the one proposed in [1] (arxiv:1206.5643).

Non‐abelian T‐duality of Pilch‐Warner background

In this work we obtain the non‐abelian T‐dual geometry of the well‐known Pilch‐Warner supergravity solution in its infrared point. We derive the dual metric and the NS two‐form by gauging the isometry group of the initial theory and integrating out the introduced auxiliary gauge fields. Then we use the Fourier‐Mukai transform from algebraic geometry to find the transformation rules of the R‐R fields. The dual background preserves the supersymmetry of the original one due to the fact that the Killing spinor does not depend on the directions on which the N‐AT‐D is performed. Finally, we consider two different pp‐wave limits of the T‐dual geometry by performing Penrose limits for two light‐like geodesics.

Unified dark energy and dust dark matter dual to quadratic purely kinetic K-essence

We consider a modified gravity plus single scalar-field model, where the scalar Lagrangian couples symmetrically both to the standard Riemannian volume-form (spacetime integration measure density) given by the square root of the determinant of the Riemannian metric, as well as to another non-Riemannian volume-form in terms of an auxiliary maximal-rank antisymmetric tensor gauge field. As shown in a previous paper, the pertinent scalar-field dynamics provides an exact unified description of both dark energy via dynamical generation of a cosmological constant, and dark matter as a “dust” fluid with geodesic flow as a result of a hidden Noether symmetry. Here we extend the discussion by considering a non-trivial modification of the purely gravitational action in the form of $$f(R) = R - \alpha R^2$$ generalized gravity. Upon deriving the corresponding “Einstein-frame” effective action of the latter modified gravity-scalar-field theory we find explicit duality (in the sense of weak versus strong coupling) between the original model of unified dynamical dark energy and dust fluid dark matter, on one hand, and a specific quadratic purely kinetic “k-essence” gravity–matter model with special dependence of its coupling constants on only two independent parameters, on the other hand. The canonical Hamiltonian treatment and Wheeler–DeWitt quantization of the dual purely kinetic “k-essence” gravity–matter model is also briefly discussed.

Dark energy and dark matter from hidden symmetry of gravity model with a non-Riemannian volume form

We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume forms (covariant integration measure densities) on the spacetime manifold – one standard Riemannian given by $$\sqrt{-g}$$ (square root of the determinant of the pertinent Riemannian metric) and another non-Riemannian volume form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless “dust” fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from the above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding an appropriate perturbation, which breaks the above hidden symmetry and along with this couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe’s epoch without evolution pathologies.

Membrane quantum mechanics

We consider the multiple M2-branes wrapped on a compact Riemann surface and study the arising quantum mechanics by taking the limit where the size of the Riemann surface goes to zero. The IR quantum mechanical models resulting from the BLG-model and the ABJM-model compactified on a torus are N=16 and N=12 superconformal gauged quantum mechanics. After integrating out the auxiliary gauge fields we find OSp(16|2) and SU(1,1|6) quantum mechanics from the reduced systems. The curved Riemann surface is taken as a holomorphic curve in a Calabi–Yau space to preserve supersymmetry and we present a prescription of the topological twisting. We find the N=8 superconformal gauged quantum mechanics that may describe the motion of two wrapped M2-branes in a K3 surface.

Chern-Simons theory of multicomponent quantum Hall systems

The Chern-Simons approach has been widely used to explain fractional quantum Hall states in the framework of trial wave functions. In the present paper, we generalise the concept of Chern-Simons transformations to systems with any number of components (spin or pseudospin degrees of freedom), extending earlier results for systems with one or two components. We treat the density fluctuations by adding auxiliary gauge fields and appropriate constraints. The Hamiltonian is quadratic in these fields and hence can be treated as a harmonic oscillator Hamiltonian, with a ground state that is connected to the Halperin wave functions through the plasma analogy. We investigate several conditions on the coefficients of the Chern-Simons transformation and on the filling factors under which our model is valid. Furthermore, we discuss several singular cases, associated with symmetric states.

Doped kagome system as exotic superconductor

A Chern-Simons theory for the doped spin-1/2 kagome system is constructed, from which it is shown that the system is an exotic superconductor that breaks time-reversal symmetry. It is also shown that the system carries minimal vortices of flux $hc/4e$ (as opposed to the usual $hc/2e$ in conventional superconductors) and contains fractional quasiparticles (including fermionic quasiparticles with semionic mutual statistics and spin-1/2 quasiparticles with bosonic self-statistics) in addition to the usual spin-1/2 fermionic Bogoliubov quasiparticles. Two Chern-Simons theories---one with an auxiliary gauge field kept and one with the auxiliary field and a redundant matter field directly eliminated---are presented and shown to be consistent with each other.

On the problem of multiple M2 branes

A simplified version of 3d BL theory is considered, which allows any number N of M2 branes in d=11. The underlying 3-algebra structure is provided by degenerate U(N) Nambu bracket [X,Y,Z] = tr(X) [Y,Z] + tr(Y) [Z,X] + tr(Z) [X,Y], the corresponding f^{abcd} is not totally antisymmetric and extended supersymmetry of the action remains to be checked. All the fields, including auxiliary non-propagating gauge fields, are in adjoint representation of SU(N) and the only remnant of 3-algebra structure is an octuple of gauge singlets, acquiring vacuum expectation value in transition to D2 branes in d=10.

Coupling of fermions to the three-dimensional noncommutativeCPN−1model: Minimal and supersymmetric extensions

We consider the coupling of fermions to the three-dimensional noncommutative ${\mathrm{CP}}^{N\ensuremath{-}1}$ model. In the case of minimal coupling, although the infrared behavior of the gauge sector is improved, there are dangerous (quadratic) infrared divergences in the corrections to the two-point vertex function of the scalar field. However, using superfield techniques we prove that the supersymmetric version of this model with ``antisymmetrized'' coupling of the Lagrange multiplier field is renormalizable up to the first order in $1/N.$ The auxiliary spinor gauge field acquires a nontrivial (nonlocal) dynamics with generation of Maxwell and Chern-Simons noncommutative terms in the effective action. Up to $1/N$ order all divergences are only logarithmic so that the model is free from nonintegrable infrared singularities.

(2+1)-dimensional noncommutativeCPN−1model

We investigate possible extensions of the $(2+1)$-dimensional ${\mathrm{CP}}^{N\ensuremath{-}1}$ model to noncommutative space. Up to the leading nontrivial order of $1/N,$ we prove that the model restricted to the left fundamental representation of the gauge group is renormalizable and does not have dangerous infrared divergences. In contrast, if the basic field $\ensuremath{\varphi}$ transforms in accord with the adjoint representation, infrared singularities are present in the two-point function of the auxiliary gauge field and also in the leading correction to the self-energy of the $\ensuremath{\varphi}$ field. These infrared divergences may produce nonintegrable singularities leading at higher orders to a breakdown of the $1/N$ expansion. Gauge invariance of the renormalization procedure is also discussed.

7D bosonic higher spin gauge theory: symmetry algebra and linearized constraints

We construct the minimal bosonic higher spin extension of the 7D AdS algebra SO(6,2), which we call hs(8 ∗) . The generators, which have spin s=1,3,5,… , are realized as monomials in Grassmann even spinor oscillators. Irreducibility, in the form of tracelessness, is achieved by modding out an infinite-dimensional ideal containing the traces. In this a key role is played by the tree bilinear traces which form an SU(2) K algebra. We show that gauging of hs(8 ∗) yields a spectrum of physical fields with spin s=0,2,4,… which make up a UIR of hs(8 ∗) isomorphic to the symmetric tensor product of two 6D scalar doubletons. The scalar doubleton is the unique SU(2) K invariant 6D doubleton. The spin s⩾2 sector comes from an hs(8 ∗) -valued one-form which also contains the auxiliary gauge fields required for writing the curvature constraints in covariant form. The physical spin s=0 field arises in a separate zero-form in a ‘quasi-adjoint’ representation of hs(8 ∗) . This zero-form also contains the spin s⩾2 Weyl tensors, i.e., the curvatures which are non-vanishing on-shell. We suggest that the hs(8 ∗) gauge theory describes the minimal bosonic, massless truncation of M-theory on AdS 7× S 4 in an unbroken phase where the holographic dual is given by N free (2,0) tensor multiplets for large N.

Dynamical fermions with fat links

We present and test a new method for simulating dynamical fermions with fat links. Our construction is based on the introduction of auxiliary but dynamical gauge fields and works with any fermionic action and can be combined with any fermionic updating. In our simulation we use an over-relaxation step which makes it effective. For four flavors of staggered fermions first results indicate that flavor symmetry at a lattice spacing a~0.2 fm is restored to a few percent. With the standard action this amount of flavor symmetry restoration is achieved at a~0.07 fm. We estimate that the overall computational cost is reduced by at least a factor 10.