Abstract
We generalize noncommutative gauge theory using Nambu–Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg–Witten map. We construct a covariant Nambu–Poisson gauge theory action, give its first order expansion in the Nambu–Poisson tensor and relate it to a Nambu–Poisson matrix model.
Highlights
We introduce a higher analogue of noncommutative pure gauge theory
We develop the theory at a semiclassical level, briefly commenting on the issue of quantization at the end
The paper is organized as follows: After discussing conventions in Sec. 2, we introduce in Sec. 3 covariant coordinates, which transform nontrivially with respect to gauge transformations parametrized by a (p − 1)form, the gauge transformation being described in terms of a (p + 1)-bracket arising from a background Nambu-Poisson (p + 1)-tensor
Summary
We introduce a higher analogue of noncommutative (abelian) pure gauge theory. The paper is organized as follows: After discussing conventions in Sec. 2, we introduce in Sec. 3 covariant coordinates, which transform nontrivially with respect to gauge transformations parametrized by a (p − 1)form, the gauge transformation being described in terms of a (p + 1)-bracket arising from a background Nambu-Poisson (p + 1)-tensor. A satisfactory description of Nambu-Poisson noncommutative gauge theory beyond the semiclassical level will require a suitable analogue of Kontsevich’s formality, solving in particular the deformation quantization problem for an arbitrary Nambu-Poisson structure
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