376 research outputs found
Algebraic Renormalization of Supersymmetric Yang-Mills Chern-Simons Theory in the Wess-Zumino Gauge
We consider a N=2 supersymmetric Yang-Mills-Chern-Simons model, coupled to
matter, in the Wess-Zumino gauge. The theory is characterized by a superalgebra
which displays two kinds of obstructions to the closure on the translations:
field dependent gauge transformations, which give rise to an infinite algebra,
and equations of motion. The aim is to put the formalism in a closed form,
off-shell, without introducing auxiliary fields. In order to perform that, we
collect all the symmetries of the model into a unique nilpotent Slavnov-Taylor
operator. Furthermore, we prove the renormalizability of the model through the
analysis of the cohomology arising from the generalized Slavnov-Taylor
operator. In particular, we show that the model is free of anomaly.Comment: 17 pages, latex, no figures. Computation of the cohomology corrected.
Appendix adde
Quantization of the Jackiw-Teitelboim model
We study the phase space structure of the Jackiw-Teitelboim model in its
connection variables formulation where the gauge group of the field theory is
given by local SL(2,R) (or SU(2) for the Euclidean model), i.e. the de Sitter
group in two dimensions. In order to make the connection with two dimensional
gravity explicit, a partial gauge fixing of the de Sitter symmetry can be
introduced that reduces it to spacetime diffeomorphisms. This can be done in
different ways. Having no local physical degrees of freedom, the reduced phase
space of the model is finite dimensional. The simplicity of this gauge field
theory allows for studying different avenues for quantization, which may use
various (partial) gauge fixings. We show that reduction and quantization are
noncommuting operations: the representation of basic variables as operators in
a Hilbert space depend on the order chosen for the latter. Moreover, a
representation that is natural in one case may not even be available in the
other leading to inequivalent quantum theories.Comment: Published version, a short note (not present in the published
version) on the quantization of the null sector has been adde
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