Standard Gauge Theory Research Articles

On the Lie-Algebraic Origin of Metric 3-Algebras

Since the pioneering work of Bagger–Lambert and Gustavsson, there has been a proliferation of three-dimensional superconformal Chern–Simons theories whose main ingredient is a metric 3-algebra. On the other hand, many of these theories have been shown to allow for a reformulation in terms of standard gauge theory coupled to matter, where the 3-algebra does not appear explicitly. In this paper we reconcile these two sets of results by pointing out the Lie-algebraic origin of some metric 3-algebras, including those which have already appeared in three-dimensional superconformal Chern–Simons theories. More precisely, we show that the real 3-algebras of Cherkis–Samann, which include the metric Lie 3-algebras as a special case, and the hermitian 3-algebras of Bagger–Lambert can be constructed from pairs consisting of a metric real Lie algebra and a faithful (real or complex, respectively) unitary representation. This construction generalises and we will see how to construct many kinds of metric 3-algebras from pairs consisting of a real metric Lie algebra and a faithful (real, complex or quaternionic) unitary representation. In the real case, these 3-algebras are precisely the Cherkis–Samann algebras, which are then completely characterised in terms of this data. In the complex and quaternionic cases, they constitute generalisations of the Bagger–Lambert hermitian 3-algebras and anti-Lie triple systems, respectively, which underlie N = 6 and N = 5 superconformal Chern–Simons theories, respectively. In the process we rederive the relation between certain types of complex 3-algebras and metric Lie superalgebras.

DYNAMICALLY BROKEN ANTI-DE SITTER ACTION FOR GRAVITY

Due to a suitable Higgs mechanism, a standard Anti-de Sitter gauge theory becomes spontaneously broken. The resulting Lorentz invariant gravitational action includes the Hilbert–Einstein term of ordinary Einstein–Cartan gravity with cosmological constant, plus contributions quadratic in curvature and torsion, and a scalar Higgs sector.

Generation of Cosmological Baryon Asymmetry – (B–L)-Genesis –

The advent of the standard gauge theory of particle physics is a story of remarkable suceess. Yet it is the view of most particle physicists that it is not the end for the quest of the ultimate microscopic world. Direct experimental hints for physics beyond the standard theory have recently been provided by the discovery of neutrino oscillation. On the theoretical side, there are many unsolved problems, one of which we will explain in this article.

HIGHER GAUGE THEORY AND GRAVITY IN 2+1 DIMENSIONS

Non-Abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher-dimensional (two-dimensional in the present context) connection forms, and as such, it has been successfully applied to the non-Abelian generalizations of the Yang–Mills theory and 2-form electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a fertile testing ground for many concepts related to classical and quantum gravity, and it is therefore only natural to investigate whether we can find an application of higher gauge theory in this latter context. In the present paper we investigate the possibility of applying the formalism of higher gauge theory to gravity in 2+1 dimensions, and we show that a nontrivial model of (2+1)-dimensional gravity coupled to scalar and tensorial matter fields — the ΣΦEA model — can be formulated as a higher gauge theory (as well as a standard gauge theory). Since the model has a very rich structure — it admits as solutions black-hole BTZ-like geometries, particle-like geometries as well as Robertson–Friedman–Walker cosmological-like expanding geometries — this opens a wide perspective for higher gauge theory to be tested and understood in a relevant gravitational context. Additionally, it offers the possibility of studying gravity in 2+1 dimensions coupled to matter in an entirely new framework.

D-branes at Singularities and String Phenomenology

In this lecture notes we give an introduction to some of the mathematical and physical concepts involved in constructing Standard Model-like gauge theories via D-branes at local singularities of Calabi-Yau manifolds.

Beyond standard gauge theory: Extended gauge and diffeomorphism symmetry and mass generation

The standard gauge theory for internal as well as space-time symmetries is revisited. Then we propose an extension of the gauge and diffeomorphism symmetry allowing for infinitely many (nonnull) Noether invariants parametrizing the field configurations. For internal groups, the inclusion of the gauge group parameters into the theory, as dynamical fields, permits a natural mass-generating mechanism for the gauge potentials without damaging gauge invariance. With regards the space-time symmetry, the new formalism helps to fix the actual Lagrangian for general relativity in the teleparallelism version.

Four-dimensional symplectic cobordisms containing three-handles

We construct four-dimensional symplectic cobordisms between contact three-manifolds generalizing an example of Eliashberg. One key feature is that any handlebody decomposition of one of these cobordisms must involve three-handles. The other key feature is that these cobordisms contain chains of symplectically embedded two-spheres of square zero. This, together with standard gauge theory, is used to show that any contact three-manifold of non-zero torsion (in the sense of Giroux) cannot be strongly symplectically fillable. John Etnyre pointed out to the author that the same argument together with compactness results for pseudo-holomorphic curves implies that any contact three-manifold of non-zero torsion satisfies the Weinstein conjecture. We also get examples of weakly symplectically fillable contact three-manifolds which are (strongly) symplectically cobordant to overtwisted contact three-manifolds, shedding new light on the structure of the set of contact three-manifolds equipped with the strong symplectic cobordism partial order.

Gauged Wess–Zumino model in noncommutative Minkowski superspace

We develop a gauged Wess–Zumino model in noncommutative Minkowski superspace. This is the natural extension of the work of Carlson and Nazaryan, which extended N=1∕2 supersymmetry written over deformed Euclidean superspace to Minkowski superspace. We investigate the coupling of the vector and chiral superfields. Noncommutativity is implemented by replacing products with star products. Although, in general, our star product is nonassociative, we prove that it is associative to the first order in the deformation parameter C. We show that our model reproduces the N=1∕2 theory in the appropriate limit, namely when the deformation parameters C¯α̇β̇=0. Essentially, we find the N=1∕2 theory and a conjugate copy. As in the N=1∕2 theory, a reparametrization of the gauge parameter, vector superfield, and chiral superfield are necessary to write standard C-independent gauge theory. However, our choice of parametrization differs from that used in the N=1∕2 supersymmetry, which leads to some unexpected new terms.

Vortices, infrared effects and Lorentz invariance violation

The Yang–Mills theory with non-commutative fields is constructed following Hamiltonian and Lagrangian methods. This modification of the standard Yang–Mills theory produces spatially localized solutions very similar to those of the standard non-Abelian gauge theories. This modification of the Yang–Mills theory contain in addition to the standard contribution, the term θμεμνρλ(AνFρλ+23AνAρAλ) where θμ is a given space-like constant vector with canonical dimension of energy. The Aμ field rescaling and the choice θμ=(0,0,0,θ), suggest the equivalence between the Yang–Mills–Chern–Simons theory in 2+1 dimensions and QCD in 3+1 dimensions in the heavy fermionic excitations limit. Thus, the Yang–Mills–Chern–Simons theory in 2+1 dimensions could be a codified way to QCD with only heavy quarks. The classical solutions of the modified Yang–Mills theory for the SU(2) gauge group are explicitly studied.

ON q - SU(3) GLOBAL GAUGE THEORY

We study the replacement of SU(3) by SU q(3) in standard gauge theories. At the level of a global theory there is a physically sensible SU q(3) formalism with measurable differences from the SU (3) theory.

On low rank classical groups in string theory, gauge theory and matrix models

We consider N=1 supersymmetric U( N), SO( N), and Sp( N) gauge theories, with two-index tensor matter and added tree-level superpotential, for general breaking patterns of the gauge group. By considering the string theory realization and geometric transitions, we clarify when glueball superfields should be included and extremized, or rather set to zero; this issue arises for unbroken group factors of low rank. The string theory results, which are equivalent to those of the matrix model, refer to a particular UV completion of the gauge theory, which could differ from conventional gauge theory results by residual instanton effects. Often, however, these effects exhibit miraculous cancellations, and the string theory or matrix model results end up agreeing with standard gauge theory. In particular, these string theory considerations explain and remove some apparent discrepancies between gauge theories and matrix models in the literature.

Spinons in more than one dimension: Resonance valence bond state stabilized by frustration

For two spatially anisotropic, SU(2)-invariant models of frustrated magnets in arbitrary space dimension we present a non-perturbative proof of the existence of neutral spin-1/2 excitations (spinons). In one model the frustration is static and based on fine tuning of the coupling constants, whereas in the other it is dynamic and does not require adjusting of the model parameters. For both models we derive a low-energy effective action which does not contain any constraints. Though our models admit the standard gauge theory treatment, we follow an alternative approach based on Abelian and non-Abelian bosonization. We prove the existence of propagating spin-1/2 excitations (spinons) and consider in detail certain exactly solvable limits. A qualitative discussion of the most general case is also presented.

Lectures on Supergravity

The text is an essentially self-contained introduction to four-dimensional N = 1 supergravity, including its couplings to super Yang-Mills and chiral matter multiplets, for readers with basic knowledge of standard gauge theories and general relativity. Emphasis is put on showing how supergravity fits in the general framework of gauge theories and how it can be derived from a tensor calculus for gauge theories of a standard form.

Probing neutral gauge boson self-interactions in ZZ production at hadron colliders

A detailed analysis of ZZ production at the upgraded Fermilab Tevatron and the CERN Large Hadron Collider is presented for general ZZZ and ZZ\gamma couplings. Deviations from the Standard Model gauge theory structure for each of these can be parameterized in terms of two form factors which are severely restricted by unitarity at high energy. Achievable limits on these couplings are shown to be a dramatic improvement over the limits currently obtained by e^+e^- experiments.

DERIVATION OF THE LEHNERT FIELD EQUATIONS FROM GAUGE THEORY IN VACUUM: SPACE CHARGE AND CURRENT

It is shown that the Lehnert field equations in vacuum, with concomitant space charge and current, can be derived straightforwardly from standard gauge theory applied in vacuum, using the concept of covariant derivative and Feynman's universal influence. The Lehnert and Proca field equations are shown to be inter-related through the well-known de Broglie theorem, in which the photon mass can be interpreted as finite. These ideas go some way towards addressing the inconsistency inherent in Maxwell's famous displacement current, which has no concomitant vacuum space charge.

Gauge theory based upon solvable Lie algebras

It has been demonstrated that mathematically consistent Yang-Mills gauge theories can be constructed on the basis of a class of general Lie algebras called quasiclassical, which contains reductive as well as a class of solvable Lie algebras. However, if we require that these theories should be ghost-free, then only the standard gauge theories based upon compact Lie algebras are allowed. Nevertheless, these solvable gauge theories may be relevant for some integrable models based upon the zero-curvature condition.

D-theory: field theory via dimensional reduction of discrete variables

A new non-perturbative approach to quantum field theory — D-theory — is proposed, in which continuous classical fields are replaced by discrete quantized variables which undergo dimensional reduction. The 2-d classical O((3) model emerges from the (2 + 1)-d quantum Heisenberg model formulated in terms of quantum spins. Dimensional reduction is demonstrated explicity by simulating correlation lengths up to 350,000 lattice spacings using a loop cluster algorithm. In the framework of D-theory, gauge theories are formulated in terms of quantum links — the gauge analogs of quantum spins. Quantum links are parallel transporter matrices whose elements are non-commuting operators. They can be expressed as bilinears of anticommuting fermion constituents. In quantum link models dimensional reduction to four dimensions occurs, due to the presence of a 5-d Coulomb phase, whose existence is confirmed by detailed simulations using standard lattice gauge theory. Using Shamir's variant of Kaplan's fermion proposal, in quantum link QCD quarks appear as edge states of a 5-d slab. This naturally protects their chiral symmetries without fine-tuning. The first efficient cluster algorithm for a gauge theory with a continuous gauge group is formulated for the U(1) quantum link model. Improved estimators for Wilson loops are constructed, and dimensional reduction to ordinary lattice QED is verified numerically.

Tensor-tensor model of gravity

The main problem with the standard gauge theory of the Poincaré group realized as a subgroup of GL(5, R) is that fields, whose physical sense is unclear, appear in connection with the non-Lorentz symmetries. Here, the Poincaré fields are treated as new Yang-Mills-type tensor fields and gravity is treated as a Higgs-Goldstone field. In this case, the effective metric tensor for matter is a hybrid of two tensor fields. In the linear approximation, the massive translation gauge field gives the Yukawa-type correction to the Newtonian potential. Also, corrections to the standard Einstein post-Newtonian formulas for light deflection and radar echo delay are obtained. A spherically symmetric solution to the equations of translation gauge fields is also found. The translation gauge field leads to the existence of a singular surface, which is impenetrable to matter and can prevent gravitational collapse of a large body, inside the Schwarzschild sphere.

Edge states and entropy of two-dimensional black holes

In several recent publications Carlip, as well as Balachandran, Chandar, and Momen, has proposed a statistical-mechanical interpretation for black hole entropy in terms of ``would-be gauge'' degrees of freedom that become dynamical on the boundary to spacetime. After critically discussing several routes for deriving a boundary action, we examine their hypothesis in the context of generic 2D dilaton gravity. We first calculate the corresponding statistical-mechanical entropy of black holes in $1+1$ de Sitter gravity, which has a gauge theory formulation as a BF theory. Then we generalize the method to dilaton gravity theories that do not have a (standard) gauge theory formulation. This is facilitated greatly by the Poisson \ensuremath{\sigma}-model formulation of these theories. It turns out that the phase space of the boundary particles coincides precisely with a symplectic leaf of the Poisson manifold that enters as target space of the \ensuremath{\sigma} model. Despite this qualitatively appealing picture, the quantitative results are discouraging: In most of the cases, the symplectic leaves are noncompact and the number of microstates yields a meaningless infinity. In those cases where the particle phase space is compact---such as, e.g., in the Euclidean de Sitter theory---the edge state degeneracy is finite, but generically it is far too small to account for the semiclassical Bekenstein-Hawking entropy.

Gauge theories induced by bosons in the fundamental representation

A lattice theory of scalar bosons in the fundamental representation of the gauge group $SU(N_c)$ and of the global symmetry group $SU(N_f)$ is shown to induce a standard gauge theory only at large $N_f$. The system is in a deconfined phase at strong scalar self-coupling and any finite $N_f$. The requirement of convergence of the effective gauge action imposes a lower limit on the scalar mass.