A vector supersymmetry in noncommutative U(1) gauge theory with the Slavnov term

Abstract

We consider noncommutative U (1) gauge theory with the additional term, involving a scalar field λ, introduced by Slavnov in order to cure the infrared problem. We show that this theory, with an appropriate space-like axial gauge-fixing, exhibits 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 λAA-vertex and thereby explains why Slavnov found a finite model for the same gaugefixing.

Gauge Theories on Deformed Spaces

“…Furthermore, it was shown [71,72] that the Slavnov term may be identified with a topological term similar to the BF models [165,166,167,168], e.g. :…”

“…With these choices the Slavnov term, together with the gauge fixing terms, have the form of a 2-dimensional topological BF model (cf. [71] and references therein). This action is invariant under the BRST transformations…”

“…Notice that the algebra involving s, δ i ,δ i and the (x 1 , x 2 )-plane translation generator ∂ i closes on-shell (cf. [71]). (The reader not interested in the technical details of deriving the total action and related Ward identities, may proceed directly to their consequences on page 21.)…”

“…Additional constraints are introduced for pure gauge theory. This approach has been explored in detail and developed further in [70,71,72].…”

One-loop calculations for a translation invariant non-commutative gauge model

“…1 In fact, there are also two other candidates on the market, but these either reduce the degrees of freedom [9,10] or break translation invariance and have difficulties with non-trivial vacuum configurations [11,12,13] (although the latter problem might be solved [14]). 2 Notice that from Eqn.…”