Gauge Theory Models Research Articles

G2–instantons over asymptotically cylindrical manifolds

A concrete model for a 7-dimensional gauge theory under special holonomy is proposed, within the paradigm outlined by Donaldson and Thomas, over the asymptotically cylindrical G2-manifolds provided by Kovalev's noncompact version of the Calabi conjecture. One obtains a solution to the $G_2$-instanton equation from the associated Hermitian Yang-Mills problem, to which the methods of Simpson et al. are applied, subject to a crucial asymptotic stability assumption over the "boundary at infinity".

Model of fractionalization of Faraday lines in compact electrodynamics

Motivated by ideas of fractionalization and intrinsic topological order in bosonic models with short-range interactions, we consider similar phenomena in formal lattice gauge theory models. Specifically, we show that a compact quantum electrodynamics (CQED) can have, besides the familiar Coulomb and confined phases, additional unusual confined phases where excitations are quantum lines carrying fractions of the elementary unit of electric field strength. We construct a model that has $N$-tupled monopole condensation and realizes $1/N$ fractionalization of the quantum Faraday lines. This phase has another excitation which is a ${Z}_{N}$ quantum surface in spatial dimensions five and higher, but can be viewed as a quantum line or a quantum particle in four or three spatial dimensions, respectively. These excitations have statistical interactions with the fractionalized Faraday lines; for example, in three spatial dimensions, the particle excitation picks up a Berry phase of ${e}^{i2\ensuremath{\pi}/N}$ when going around the fractionalized Faraday line excitation. We demonstrate the existence of this phase by Monte Carlo simulations in (3+1) space-time dimensions.

Deconfinement transition as black hole formation by the condensation of QCD strings

We argue that the deconfinement transition of large-$N$ Yang-Mills theory is the condensation of very long and self-intersecting chromo-electric flux strings (QCD string), which is analogous to the formation of a black hole in string theory. We do this by using lattice gauge theory and matrix models. As evidence, we derive an analytic formula for the deconfinement temperature in the strong coupling limit and confirm it numerically. Dual gravity descriptions interpreted in this manner should make it possible to understand the details of the formation of black holes in terms of fundamental strings. We argue that very simple matrix models capture the essence of the formation of black holes.

Effective confining potentials for QCD

We observe that the linear potential used as a leading approximation for describing color confinement in the instant form of dynamics corresponds to a quadratic confining potential in the front form of dynamics. In particular, the instant-form potentials obtained from lattice gauge theory and string models of hadrons agree with the potentials determined from models using front-form dynamics and light-front holography, not only in their shape, but also in their numerical strength.

Stochastic volatility models at [formula omitted] as second class constrained Hamiltonian systems

The stochastic volatility models used in the financial world are characterized, in the continuous-time case, by a set of two coupled stochastic differential equations for the underlying asset price S and volatility σ. In addition, the correlations of the two Brownian movements that drive the stochastic dynamics are measured by the correlation parameter ρ(−1≤ρ≤1). This stochastic system is equivalent to the Fokker–Planck equation for the transition probability density of the random variables S and σ. Solutions for the transition probability density of the Heston stochastic volatility model (Heston, 1993) were explored in Dragulescu and Yakovenko (2002), where the fundamental quantities such as the transition density itself, depend on ρ in such a manner that these are divergent for the extreme limit ρ=±1. The same divergent behavior appears in Hagan et al. (2002), where the probability density of the SABR model was analyzed. In an option pricing context, the propagator of the bi-dimensional Black–Scholes equation was obtained in Lemmens et al. (2008) in terms of the path integrals, and in this case, the propagator diverges again for the extreme values ρ=±1. This paper shows that these similar divergent behaviors are due to a universal property of the stochastic volatility models in the continuum: all of them are second class constrained systems for the most extreme correlated limit ρ=±1. In this way, the stochastic dynamics of the ρ=±1 cases are different of the −1<ρ<1 case, and it cannot be obtained as a continuous limit from the ρ≠±1 regimen. This conclusion is achieved by considering the Fokker–Planck equation or the bi-dimensional Black–Scholes equation as a Euclidean quantum Schrödinger equation. Then, the analysis of the underlying classical mechanics of the quantum model, implies that stochastic volatility models at ρ=±1 correspond to a constrained system. To study the dynamics in an appropriate form, Dirac’s method for constrained systems (Dirac, 1958, 1967) must be employed, and Dirac’s analysis reveals that the constraints are second class. In order to obtain the transition probability density or the option price correctly, one must evaluate the propagator as a constrained Hamiltonian path-integral (Henneaux and Teitelboim, 1992), in a similar way to the high energy gauge theory models. In fact, for all stochastic volatility models, after integrating over momentum variables, one obtains an effective Euclidean Lagrangian path-integral over the volatility alone. The role of the second class constraints is determining the underlying asset price S completely in terms of volatility, so it plays no role in the path integral. In order to examine the effect of the constraints on the dynamics for both extreme limits, the probability density function is evaluated by using semi-classical arguments, in an analogous manner to that developed in Hagan et al. (2002), for the SABR model.

Noncommutative gauge theories on $ \mathbb{R}_{\theta}^2 $ as matrix models

Abstract We study a class of noncommutative gauge theory models on 2-dimensional Moyal space from the viewpoint of matrix models and explore some related properties. Expanding the action around symmetric vacua generates non local matrix models with polynomial interaction terms. For a particular vacuum, we can invert the kinetic operator which is related to a Jacobi operator. The resulting propagator can be expressed in terms of Chebyschev polynomials of second kind. We show that non vanishing correlations exist at large separations. General considerations on the kinetic operators stemming from the other class of symmetric vacua, indicate that only one class of symmetric vacua should lead to fast decaying propagators. The quantum stability of the vacuum is briefly discussed.

Constraint algebra in loop quantum gravity reloaded. II. Toy model of an Abelian gauge theory: Spatial diffeomorphisms

In A. Henderson, A. Laddha, and C. Tomlin, preceding article, [Phys. Rev. D 88, 044028 (2013)], we initiated an approach towards quantizing the Hamiltonian constraint in loop quantum gravity by requiring that it generates an anomaly-free representation of constraint algebra of -shell. We investigated this issue in the case of a toy model of a ($2+1$)-dimensional $\mathrm{U}(1{)}^{3}$ gauge theory, which can be thought of as a weak coupling limit of Euclidean three-dimensional gravity. However, in paper I, we only focused on the most nontrivial part of the constraint algebra that involves the commutator of two Hamiltonian constraints. In this paper we continue with our analysis and obtain a representation of full constraint algebra in a loop quantized framework. We show that there is a representation of the diffeomorphism group with respect to which the Hamiltonian constraint quantized in paper I is diffeomorphism covariant. Our work can be thought of as a potential first step towards resolving some longstanding issues with the Hamiltonian constraint in canonical loop quantum gravity.

Kaluza–Klein-type models of de Sitter and Poincaré gauge theories of gravity

We construct Kaluza–Klein-type models with a de Sitter or Minkowski bundle in the de Sitter or Poincaré gauge theory of gravity, respectively. A manifestly gauge-invariant formalism has been given. The gravitational dynamics is constructed by the geometry of the de Sitter or Minkowski bundle and a global section which plays an important role in the gauge-invariant formalism. Unlike the old Kaluza–Klein-type models of gauge theory of gravity, a suitable cosmological term can be obtained in the Lagrangian of our models and the models in the spin-current-free and torsion-free limit will come back to general relativity with a corresponding cosmological term. We also generalize the results to the case with a variable cosmological term.

AKSZ models of semistrict higher gauge theory

In the first part of this paper, we work out a perturbative Lagrangian formulation of semistrict higher gauge theory, that avoids the subtleties of the relationship between Lie 2-groups and algebras by relying exclusively on the structure semistrict Lie 2-algebra $ \mathfrak{v} $ and its automorphism 2-group $ \mathrm{Aut}\left( \mathfrak{v} \right) $ . Gauge transformations are defined and shown to form a strict 2-group depending on $ \mathfrak{v} $ . Fields are $ \mathfrak{v} $ -valued and their global behaviour is controlled by appropriate gauge transformation gluing data organized as a strict 2-groupoid. In the second part, using the BV quantization method in the AKSZ geometrical version, we write down a 3-dimensional semistrict higher BF gauge theory generalizing ordinary BF theory, carry out its gauge fixing and obtain as end result a semistrict higher topological gauge field theory of the Witten type. We also introduce a related 4-dimensional semistrict higher Chern-Simons gauge theory.

On the weak field approximation of the de Sitter gauge theory of gravity

The weak field approximation of a model of de Sitter gauge theory of gravity is studied in two cases. Without torsion and spin current, the model cannot give the right non-relativistic approximation unless the density is a constant. With small torsion, a satisfactory Newtonian approximation can be obtained.

Real forms of extended Kac–Moody symmetries and higher spin gauge theories

We consider the relation between higher spin gauge fields and real Kac–Moody Lie algebras. These algebras are obtained by double and triple extensions of real forms $${\mathfrak{g}_0}$$ of the finite-dimensional simple algebras $${\mathfrak{g}}$$ arising in dimensional reductions of gravity and supergravity theories. Besides providing an exhaustive list of all such algebras, together with their associated involutions and restricted root diagrams, we are able to prove general properties of their spectrum of generators with respect to a decomposition of the triple extension of $${\mathfrak{g}_0}$$ under its gravity subalgebra $${\mathfrak{gl}(D,\mathbb {R})}$$ . These results are then combined with known consistent models of higher spin gauge theory to prove that all but finitely many generators correspond to non-propagating fields and there are no higher spin fields contained in the Kac–Moody algebra.

Lattice quantum electrodynamics for graphene

The effects of gauge interactions in graphene have been analyzed up until now in terms of effective models of Dirac fermions. However, in several cases lattice effects play an important role and need to be taken consistently into account. In this paper, we introduce and analyze a lattice gauge theory model for graphene, which describes tight binding electrons hopping on the honeycomb lattice and interacting with a three-dimensional quantum U ( 1 ) gauge field. We perform an exact renormalization group analysis, which leads to a renormalized expansion that is finite at all orders. The flow of the effective parameters is controlled thanks to Ward identities and a careful analysis of the discrete lattice symmetry properties of the model. We show that the Fermi velocity increases up to the speed of light and Lorentz invariance spontaneously emerges in the infrared. The interaction produces critical exponents in the response functions; this removes the degeneracy present in the non interacting case and allows us to identify the dominant excitations. Finally, we add mass terms to the Hamiltonian and derive by a variational argument the correspondent gap equations, which have an anomalous non-BCS form, due to the non trivial effects of the interaction.

Chiral symmetry restoration in monolayer graphene induced by Kekulé distortion

We propose a chiral symmetry restoration mechanism in monolayer graphene, in analogy with the strongly coupled gauge theory. The chiral (sublattice) symmetry of graphene, which is spontaneously broken under the effectively strong Coulomb interaction, is restored by introducing the Kekule-patterned lattice distortion externally. Such a phase transition is investigated analytically by the lattice gauge theory model with the original honeycomb lattice structure. We discuss the relation between the chiral phase transition and the spectral gap amplitude.

The model for self-dual chiral bosons as a Hodge theory

We consider (1+1) dimensional theory for a single self-dual chiral boson as a classical model for gauge theory. Using the Batalin–Fradkin–Vilkovisky (BFV) technique, the nilpotent BRST and anti-BRST symmetry transformations for this theory have been studied. In this model other forms of nilpotent symmetry transformations like co-BRST and anti-co-BRST, which leave the gauge-fixing part of the action invariant, are also explored. We show that the nilpotent charges for these symmetry transformations satisfy the algebra of the de Rham cohomological operators in differential geometry. The Hodge decomposition theorem on compact manifold is also studied in the context of conserved charges.

Holographic anomalous conductivities and the chiral magnetic effect

We calculate anomaly induced conductivities from a holographic gauge theory model using Kubo formulas, making a clear conceptual distinction between thermodynamic state variables such as chemical potentials and external background fields. This allows us to pinpoint ambiguities in previous holographic calculations of the chiral magnetic conductivity. We also calculate the corresponding anomalous current three-point functions in special kinematic regimes. We compare the holographic results to weak coupling calculations using both dimensional regularization and cutoff regularization. In order to reproduce the weak coupling results it is necessary to allow for singular holographic gauge field configurations when a chiral chemical potential is introduced for a chiral charge defined through a gauge invariant but non-conserved chiral density. We argue that this is appropriate for actually addressing charge separation due to the chiral magnetic effect.

A New Solution with Torsion in Model of dS Gauge Theory of Gravity

A new static de Sitter solution with torsion in the model of de Sitter gauge theory of gravity is obtained. The torsion only contains O(3)-symmetric tensor part according to irreducible decomposition. Some properties of the new solution are discussed.

Lattice gauge theory model for graphene

The effects of the electromagnetic (em) electron-electron interactions in half-filled graphene are investigated in terms of a lattice gauge theory model. By using exact renormalization group methods and lattice Ward identities, we show that the em interactions amplify the responses to the excitonic pairings associated to a Kekul\'e distortion and to a charge-density wave. The effect of the electronic repulsion on the Peierls-Kekul\'e instability, usually neglected, is evaluated by deriving an exact non BCS gap equation, from which we find evidence that strong em interactions among electrons facilitate the spontaneous distortion of the lattice and the opening of a gap.

Fate of the false monopoles: Induced vacuum decay

We study a gauge theory model where there is an intermediate symmetry breaking to a meta- stable vacuum that breaks a simple gauge group to a U (1) factor. Such models admit the existence of meta-stable magnetic monopoles, which we dub false monopoles. We prove the existence of these monopoles in the thin wall approximation. We determine the instantons for the collective coordinate that corresponds to the radius of the monopole wall and we calculate the semi-classical tunneling rate for the decay of these monopoles. The monopole decay consequently triggers the decay of the false vacuum. As the monopole mass is increased, we find an enhanced rate of decay of the false vacuum relative to the celebrated homogeneous tunneling rate due to Coleman [1].

De Sitter spacetimes with torsion in the model of de Sitter gauge theory of gravity

In the model of the de Sitter gauge theory of gravity, the empty homogenous and isotropic spacetimes with constant curvature scalar and nonvanishing homogenous and isotropic torsion must have de Sitter metrics. The static de Sitter spacetime with static, $O(3)$-symmetric, vector torsion is the only spherically symmetric, vacuum solution with the metric of the form ${g}_{\ensuremath{\mu}\ensuremath{\nu}}=\mathrm{diag}({A}^{2}(r),\ensuremath{-}{B}^{2}(r),\ensuremath{-}{r}^{2},\ensuremath{-}{r}^{2}{sin}^{2}\ensuremath{\theta})$. The expressions of the torsion for different de Sitter spacetimes are presented. They are different from one to another. The properties of different de Sitter spacetimes with torsion are also studied.

Renormalization, duality, and phase transitions in two- and three-dimensional quantum dimer models

We derive an extended lattice gauge theory type action for quantum dimer models and relate it to the height representations of these systems. We examine the system in two and three dimensions and analyze the phase structure in terms of effective theories and duality arguments. For the two-dimensional case we derive the effective potential both at zero and finite temperature. The zero-temperature theory at the Rokhsar-Kivelson (RK) point has a critical point related to the self-dual point of a class of ${Z}_{N}$ models in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. Two phase transitions featuring a fixed line are shown to appear in the phase diagram, one at zero temperature and at the RK point and another one at finite temperature above the RK point. The latter will be shown to correspond to a Kosterlitz-Thouless (KT) phase transition, while the former will be governed by a KT-like universality class, i.e., sharing many features with a KT transition but actually corresponding to a different universality class. On the other hand, we show that at the RK point no phase transition happens at finite temperature. For the three-dimensional case we derive the corresponding dual gauge theory model at the RK point. We show in this case that at zero temperature a first-order phase transition occurs, while at finite temperatures both first- and second-order phase transitions are possible, depending on the relative values of the couplings involved.