118862884
Supersymmetry algebra cohomology. I. Definition and general structure
This paper concerns standard supersymmetry algebras in diverse dimensions, involving bosonic translational generators and fermionic supersymmetry generators. A cohomology related to these supersymmetry algebras, termed supersymmetry algebra cohomology, and corresponding “primitive elements” are defined by means of a BRST (Becchi-Rouet-Stora-Tyutin)-type coboundary operator. A method to systematically compute this cohomology is outlined and illustrated by simple examples.
119057407
Extended antifield formalism
Abstract The antifield formalism is extended so as to incorporate the rigid symmetries of a given theory. To that end, it is necessary to introduce global ghosts not only for the given rigid symmetries, but also for all the higher order conservation laws, associated with conserved antisymmetric tensors j μ 1 3 μ k fulfilling ϖ μ 1 j μ 1 3 μ k 2~ 0. Otherwise, one may encounter obstructions of the type discussed in by the authors. These higher order conservation laws are shown to define additional rigid symmetries of the master equation and to form — together with the standard symmetries — an interesting algebraic structure. They lead furthermore to independent Ward identities which are derived in the standard manner, because the resulting master (“Zinn-Justin”) equation capturing both the gauge symmetries and the rigid symmetries of all orders takes a known form. Issues such as anomalies or consistent deformations of the action preserving some set of rigid symmetries can be also systematically analysed in this framework.
116908765
Gauge Covariant Algebras and Local BRST Cohomology
The formulation of the local BRST cohomology on infinite jet bundles and its relation and reduction to gauge covariant algebras are reviewed. As an illustration, we compute the local BRST cohomology for geodesic motion in (pseudo-) Riemannian manifolds and discuss briefly the result (symmetries, constants of the motion, consistent deformations).
117843456
All Solutions of the Wess-Zumino Consistency Conditions
For the case of a compact gauge group we list all solutions to the Wess-Zumino consistency equations which have to be satisfied by anomalies. We describe the main algebraic tools and theorems required for this complete classification. Our results answer the question whether in nonrenormalizable gauge theories there exist additional up-to-now unknown anomalies in the negative.
118395460
Nonpolynomial gauge invariant interactions of 1-form and 2-form gauge potentials
A four dimensional gauge theory with nonpolynomial but local interactions of 1-form and 2-form gauge potentials is constructed. The model is a nontrivial deformation of a free gauge theory with nonpolynomial dependence on the deformation parameter (= gauge coupling constant).
120563531
The gravitational anomalies
Abstract We determine all solutions to the consistency equations which have to be satisfied by anomalies in gravitational theories with a Poincare-invariant ground state.
119502016
Dispersion relations for the self-energy in noncommutative field theories
We study the IR/UV connection in non-commutative $\phi^{3}$ theory as well as in non-commutative QED from the point of view of the dispersion relation for the self-energy. We show that, although the imaginary part of the self-energy is well behaved as the parameter of non-commutativity vanishes, the real part becomes divergent as a consequence of the high energy behavior of the dispersion integral. Some other interesting features that arise from this analysis are also briefly discussed.
119440690
Thermal operator representation of finite temperature graphs. II
Using the mixed space representation (t,p{yields}) in the context of scalar field theories, we prove in a simple manner that the Feynman graphs at finite temperature are related to the corresponding zero temperature diagrams through a simple thermal operator, both in the imaginary time as well as in the real time formalisms. This result is generalized to the case when there is a nontrivial chemical potential present. Several interesting properties of the thermal operator are also discussed.
125687040
Finite temperature gluon self-energy in a class of general temporal gauges
118914118
General structure of the photon self-energy in noncommutative QED
We study the behavior of the photon two point function, in noncommutative QED, in a general covariant gauge and in arbitrary space-time dimensions. We show, to all orders, that the photon self-energy is transverse. Using an appropriate extension of the dimensional regularization method, we evaluate the one-loop corrections, which show that the theory is renormalizable. We also prove, to all orders, that the poles of the photon propagator are gauge independent and briefly discuss some other related aspects.
119534920
Factorization of finite temperature graphs in thermal QED
We extend our previous analysis of gauge and Dirac fields in the presence of a chemical potential. We consider an alternative thermal operator which relates in a simple way the Feynman graphs in QED at finite temperature and charge density to those at zero temperature but nonzero chemical potential. Several interesting features of such a factorization are discussed in the context of the thermal photon and fermion self-energies.