Gauge theory in deformed $$ \mathcal{N} $$ = (1, 1) superspace

We review the non-anticommutative Q-deformations of = (1, 1) supersymmetric theories in four-dimensional Euclidean harmonic superspace. These deformations preserve chirality and harmonic Grassmann analyticity. The associated field theories arise as a low-energy limit of string theory in specific backgrounds and generalize the Moyal-deformed supersymmetric field theories. A characteristic feature of the Q-deformed theories is the half-breaking of supersymmetry in the chiral sector of the Euclidean superspace. Our main focus is on the chiral singlet Q-deformation, which is distinguished by preserving the SO(4) ∼ Spin(4) “Lorentz” symmetry and the SU(2) R-symmetry. We present the superfield and component structures of the deformed = (1, 0) supersymmetric gauge theory as well as of hypermultiplets coupled to a gauge superfield: invariant actions, deformed transformation rules, and so on. We discuss quantum aspects of these models and prove their renormalizability in the Abelian case. For the charged hypermultiplet in an Abelian gauge superfield background we construct the deformed holomorphic effective action. The text was submitted by the authors in English.     

Quantum gravity,field theory and signatures of noncommutative spacetime

A pedagogical introduction to some of the main ideas and results of field theories on quantized spacetimes is presented, with emphasis on what such field theories may teach us about the problem of quantizing gravity. We examine to what extent noncommutative gauge theories may be regarded as gauge theories of gravity. UV/IR mixing is explained in detail and we describe its relations to renormalization, to gravitational dynamics, and to deformed dispersion relations in models of quantum spacetime of interest in string theory and in doubly special relativity. We also discuss some potential experimental probes of spacetime noncommutativity.     

Linear bosonic and fermionic quantum gauge theories on curved spacetimes

We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearised Yang-Mills theory and linearised general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, the centre and representations of this algebra, however, have to be analysed on a case-by-case basis. We discuss an example of a fermionic gauge field theory where the necessary conditions for the existence of Hilbert space representations are not met on any spacetime. On the other hand, we prove that these conditions are met for the Rarita-Schwinger gauge field in linearised pure $N=1$ supergravity on certain spacetimes, including asymptotically flat spacetimes and classes of spacetimes with compact Cauchy surfaces. We also present an explicit example of a supergravity background on which the Rarita-Schwinger gauge field can not be consistently quantized.     

A Brief Guide to Variations in Teleparallel Gauge Theories of Gravity and the Kaniel-Itin Model

Recently Kaniel and Itin proposed a gravitational model with the wave type equation as vacuum field equation, where denotes the coframe of spacetime. They found that the viable Yilmaz-Rosen metric is an exact solution of the tracefree part of their field equation. This model belongs to the teleparallelism class of gravitational gauge theories. Of decisive importance for the evaluation of the Kaniel-Itin model is the question whether the variation of the coframe commutes with the Hodge star. We find a master formula for this commutator and rectify some corresponding mistakes in the literature. Then we turn to a detailed discussion of the Kaniel-Itin model.     

Monopole and Coulomb Field as Duals within the Unifying Reissner-NordstrSm Geometry

We are going to prove that the Monopole and the Coulomb fields are duals within the unifying structure provided by the Reissner-Nordstrom spacetime. This is accomplished when noticing that in order to produce the tetrad that locally and covariantly diagonalizes the stress-energy tensor, both the Monopole and the Coulomb fields are necessary in the construction. Without any of them it would be impossible to express the tetrad vectors that locally and covariantly diagonalize the stress-energy tensor. Then, both electromagnetic fields are an integral part of the same structure, the Reissner-Nordstrom geometry.     

Cosmology from a gauge induced gravity

The main goal of the present work is to analyze the cosmological scenario of the induced gravity theory developed in previous works. Such a theory consists on a Yang–Mills theory in a four-dimensional Euclidian spacetime with \({ SO}(m,n)\) such that \(m+n=5\) and \(m\in \{0,1,2\}\) as its gauge group. This theory undergoes a dynamical gauge symmetry breaking via an Inönü–Wigner contraction in its infrared sector. As a consequence, the \({ SO}(m,n)\) algebra is deformed into a Lorentz algebra with the emergency of the local Lorentz symmetries and the gauge fields being identified with a vierbein and a spin connection. As a result, gravity is described as an effective Einstein–Cartan-like theory with ultraviolet correction terms and a propagating torsion field. We show that the cosmological model associated with this effective theory has three different regimes. In particular, the high curvature regime presents a de Sitter phase which tends towards a \(\Lambda \)CDM model. We argue that \({ SO}(m,n)\) induced gravities are promising effective theories to describe the early phase of the universe.     

Can a non-symmetric metric mimic NCQFT in $e^ + e^- \to \gamma \gamma$?

In the non-symmetric gravitational theory (NGT) the space-time metric departs from the flat-space Minkowski form in such a way that it is no longer symmetric, i.e. . We find that in the most conservative such scenario coupled to quantum field theory, which we call minimally non-symmetric quantum field theory (MNQFT), there are experimentally measurable consequences similar to those from non-commutative quantum field theory (NCQFT). This can be expected from the Seiberg-Witten map which has recently been interpreted as equating gauge theories on non-commutative space-times with those in a field-dependent gravitational background. In particular, in scattering processes such as the pair annihilation , both theories make the same striking prediction that the azimuthal cross section oscillates in . However the predicted number of oscillations differs in the two theories: MNQFT predicts between one and four, whereas NCQFT has no such restriction.Received: 17 May 2004, Revised: 10 September 2004, Published online: 18 November 2004This work was supported by the Department of Physics at Tsinghua University and the Chinese Academy of Sciences.     

Superselection Sectors and General Covariance. I

This paper is devoted to the analysis of charged superselection sectors in the framework of the locally covariant quantum field theories. We shall analyze sharply localizable charges, and use net-cohomology of J.E. Roberts as a main tool. We show that to any 4-dimensional globally hyperbolic spacetime a unique, up to equivalence, symmetric tensor -category with conjugates (in case of finite statistics) is attached; to any embedding between different spacetimes, the corresponding categories can be embedded, contravariantly, in such a way that all the charged quantum numbers of sectors are preserved. This entails that to any spacetime is associated a unique gauge group, up to isomorphisms, and that to any embedding between two spacetimes there corresponds a group morphism between the related gauge groups. This form of covariance between sectors also brings to light the issue whether local and global sectors are the same. We conjecture this holds that at least on simply connected spacetimes. It is argued that the possible failure might be related to the presence of topological charges. Our analysis seems to describe theories which have a well defined short-distance asymptotic behaviour.     

algebras and field theory

We review and develop the general properties of algebras focusing on the gauge structure of the associated field theories. Motivated by the homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the structure of general gauge invariant perturbative field theories. We sketch such formulations for non‐abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full algebra for the interacting theory. The analysis suggests that algebras provide a classification of perturbative gauge invariant classical field theories.     

Quantum criticality and Yang–Mills gauge theory

We present a family of nonrelativistic Yang–Mills gauge theories in D+1$D+1$ dimensions whose free-field limit exhibits quantum critical behavior with gapless excitations and dynamical critical exponent z=2$z=2$. The ground state wavefunction is intimately related to the partition function of relativistic Yang–Mills in D   dimensions. The gauge couplings exhibit logarithmic scaling and asymptotic freedom in the upper critical spacetime dimension, equal to 4+1$4+1$. The theories can be deformed in the infrared by a relevant operator that restores Poincaré invariance as an accidental symmetry. In the large-N limit, our nonrelativistic gauge theories can be expected to have weakly curved gravity duals.     

Geometrical Lagrangian for a Supersymmetric Yang–Mills Theory on the Group Manifold

Perhaps one of the main features of Einstein's General Theory of Relativity is that spacetime is not flat itself but curved. Nowadays, however, many of the unifying theories like superstrings on even alternative gravity theories such as teleparalell geometric theories assume flat spacetime for their calculations. This article, an extended account of an earlier author's contribution, it is assumed a curved group manifold as a geometrical background from which a Lagrangian for a supersymmetric N=2, d=5 Yang–Mills – SYM, N=2, d=5 – is built up. The spacetime is a hypersurface embedded in this geometrical scenario, and the geometrical action here obtained can be readily coupled to the five-dimensional supergravity action. The essential idea that underlies this work has its roots in the Einstein–Cartan formulation of gravity and in the group manifold approach to gravity and supergravity theories. The group SYM, N=2, d=5, turns out to be the direct product of supergravity and a general gauge group .     

Enlarged Geometries of Gauge Bundles

The geometrical picture of gauge theories must be enlarged when a gauge potentialceases to behave like a connection, as it does in electroweak interactions. Whenthe gauge group has dimension four, the vector space isomorphism betweenspacetime and the gauge algebra is realized by a tetrad-like field. The objectmeasuring the deviation from a strict bundle structure has the formal behaviorof a spacetime connection, of which the deformed gauge field strength is thetorsion. A generalized derivative emerges in terms of which the two Bianchiidentities are formally recovered. Effects of gravitational type turn up. Thedynamical equations obtained correspond to a broken gauge model on acurved spacetime.     

Nonlinear gauge realization of spacetime symmetries including translations

We present a general scheme for the nonlinear gauge realizations of spacetime groups on coset spaces of the groups considered. In order to show the relevance of the method for the rigorous treatment of the translations in gravitational gauge theories, we apply it in particular to the affine group. This is an illustration of the family of spacetime symmetries having the form of a semidirect productH T, whereH is the stability subgroup andT are the translations. The translational component of the connection behaves like a true tensor underH when coset realizations are involved.     

Consistent Dyson summation of Higgs propagators in non-linear parameterizations revisited

As we demonstrate in a process independent way, in a non-linear parameterization of the scalar sector of the standard model the Dyson summation of the Higgs self-energy can be performed without violating the Ward identities. This implies also the Goldstone boson equivalence theorem, in the limited range of its validity in effective field theories. This proves an earlier conjecture of Valencia and Willenbrock. Furthermore, the full Higgs propagator is independent of the gauge parameters. These results are consistent with the extension of the gauge flip formalism for the construction of gauge invariant classes of Feynman diagrams to loop diagrams. In a non-linear parameterization of a 2-Higgs doublet model, the consistent Dyson summation is possible for all neutral Higgs bosons, but not for the charged scalars. Explicit examples of the equivalence theorem are discussed both in the minimal standard model and a 2-Higgs doublet model.Received: 24 August 2004, Revised: 14 October 2004, Published online: 26 November 2004PACS: 11.15.Ex, 12.15.-y, 14.80.Cp, 11.15.Bt     

Noncommutative gauge fields coupled to noncommutative gravity

We present a noncommutative (NC) version of the action for vielbein gravity coupled to gauge fields. Noncommutativity is encoded in a twisted $\star $ -product between forms, with a set of commuting background vector fields defining the (abelian) twist. A first order action for the gauge fields avoids the use of the Hodge dual. The NC action is invariant under diffeomorphisms and $\star $ -gauge transformations. The Seiberg–Witten map, adapted to our geometric setting and generalized for an arbitrary abelian twist, allows to re-express the NC action in terms of classical fields: the result is a deformed action, invariant under diffeomorphisms and usual gauge transformations. This deformed action is a particular higher derivative extension of the Einstein-Hilbert action coupled to Yang-Mills fields, and to the background vector fields defining the twist. Here noncommutativity of the original NC action dictates the precise form of this extension. We explicitly compute the first order correction in the NC parameter of the deformed action, and find that it is proportional to cubic products of the gauge field strength and to the symmetric anomaly tensor $D_{IJK}$ .     

Renormalization group approach to lattice gauge field theories

We study four-dimensional pure gauge field theories by the renormalization group approach. The analysis is restricted to small field approximation. In this region we construct a sequence of localized effective actions by cluster expansions in one step renormalization transformations. We construct also -functions and we define a coupling constant renormalization by a recursive system of renormalization group equations.     

Self-consistent normal ordering of gauge field theories

Mean field theories with a real action of unconstrained fields can be self-consistently normal ordered. This leads to a considerable improvement over standard mean-field theory. This concept is applied to lattice gauge theories. We construct first an appropriate real action mean-field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean-field theory are derived.Invited talk presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

Spin-gap phase in the extended t — J chain

We study the one-dimensional deformed model in terms of the continuum field theories. We found that at low doping concentration and far away from the phase separation regime, there are two phases: the Luttinger liquid and the Luther-Emery liquid, depending on or , where . Moreover, the singlet superconducting correlations are dominant in the Luther-Emery liquid.Received: 12 October 2003, Published online: 19 February 2004PACS: 71.10.Fd Lattice fermion models - 71.10.Hf Non-Fermi-liquid ground states - 74.20.Mn Non-conventional mechanisms