39 research outputs found
A Vector Supersymmetry Killing the Infrared Singularity of Gauge Theories in Noncommutative Space
We show that the "topological BF-type" term introduced by Slavnov in order to
cure the infrared divergences of gauge theories in noncommutative space can be
characterized as the consequence of a new symmetry. This symmetry is a
supersymmetry, generated by vector charges, of the same type as the one
encountered in Chern-Simons or BF topological theories.Comment: 9 pages, LaTex. Work presented by O. Piguet at the Fifth
International Conference on Mathematical Methods in Physics, 24 - 28 April
2006, Rio de Janeiro, Brazi
On the symmetries of BF models and their relation with gravity
The perturbative finiteness of various topological models (e.g. BF models)
has its origin in an extra symmetry of the gauge-fixed action, the so-called
vector supersymmetry. Since an invariance of this type also exists for gravity
and since gravity is closely related to certain BF models, vector supersymmetry
should also be useful for tackling various aspects of quantum gravity. With
this motivation and goal in mind, we first extend vector supersymmetry of BF
models to generic manifolds by incorporating it into the BRST symmetry within
the Batalin-Vilkovisky framework. Thereafter, we address the relationship
between gravity and BF models, in particular for three-dimensional space-time.Comment: 29 page
A Vector Supersymmetry in Noncommutative U(1) Gauge Theory with the Slavnov Term
We consider noncommutative U(1) gauge theory with the additional term,
involving a scalar field lambda, introduced by Slavnov in order to cure the
infrared problem. we show that this theory, with an appropriate space-like
axial gauge-fixing, wxhibits a linear vector supersymmetry similar to the one
present in the 2-dimensional BF model. This vector supersymmetry implies that
all loop corrections are independent of the -vertex and thereby
explains why Slavnov found a finite model for the same gauge-fixing.Comment: 18 pages, 3 figures; v2 Acknowledgments adde
d=2, N=2 Superconformal Symmetries and Models
We discuss the following aspects of two-dimensional N=2 supersymmetric
theories defined on compact super Riemann surfaces: parametrization of (2,0)
and (2,2) superconformal structures in terms of Beltrami coefficients and
formulation of superconformal models on such surfaces (invariant actions,
anomalies and compensating actions, Ward identities).Comment: 43 pages, late
Observables in Topological Theories: A Superspace Formulation
Observables of topological Yang-Mills theory were defined by Witten as the
classes of an equivariant cohomology. We propose to define them alternatively
as the BRST cohomology classes of a superspace version of the theory, where
BRST invariance is associated to super Yang-Mills invariance. We provide and
discuss the general solution of this cohomology.Comment: Prepared for International Conference on Renormalization Group and
Anomalies in Gravity and Cosmology (IRGA 2003), Ouro Preto, MG, Brazil, 17-23
Mar 200
Observables in Topological Yang-Mills Theories
Using topological Yang-Mills theory as example, we discuss the definition and
determination of observables in topological field theories (of Witten-type)
within the superspace formulation proposed by Horne. This approach to the
equivariant cohomology leads to a set of bi-descent equations involving the
BRST and supersymmetry operators as well as the exterior derivative. This
allows us to determine superspace expressions for all observables, and thereby
to recover the Donaldson-Witten polynomials when choosing a Wess-Zumino-type
gauge.Comment: 39 pages, Late
Symmetries and observables in topological gravity
After a brief review of topological gravity, we present a superspace approach
to this theory. This formulation allows us to recover in a natural manner
various known results and to gain some insight into the precise relationship
between different approaches to topological gravity. Though the main focus of
our work is on the vielbein formalism, we also discuss the metric approach and
its relationship with the former formalism.Comment: 34 pages; a few explanations added in subsection 2.2.1, published
version of pape
Translation-invariant models for non-commutative gauge fields
Motivated by the recent construction of a translation-invariant
renormalizable non-commutative model for a scalar field (see arXiv:0802.0791
[math-ph]), we introduce models for non-commutative U(1) gauge fields along the
same lines. More precisely, we include some extra terms into the action with
the aim of getting rid of the UV/IR mixing.Comment: 9 page