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arXiv · 2202.10227

On the L$_\infty$ structure of Poisson gauge theory

O. Abla·V. G. Kupriyanov·M. Kurkov
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Abstract

The Poisson gauge theory is a semi-classical limit of full non-commutative gauge theory. In this work we construct an L$_\infty^{full}$ algebra which governs both the action of gauge symmetries and the dynamics of the Poisson gauge theory. We derive the minimal set of non-vanishing $\ell$-brackets and prove that they satisfy the corresponding homotopy relations. On the one hand, it provides new explicit non-trivial examples of L$_\infty$ algebras. On the other hand, it can be used as a starting point for bootstrapping the full non-commutative gauge theory. The first few brackets of such a theory are constructed explicitly in the text. In addition we show that the derivation properties of $\ell$-brackets on L$_\infty^{full}$ with respect to the truncated product on the exterior algebra are satisfied only for the canonical non-commutativity. In general, L$_\infty^{full}$ does not have a structure of P$_\infty$ algebra.

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O. Abla, V. G. Kupriyanov, M. Kurkov. 2022-02-21. On the L$_\infty$ structure of Poisson gauge theory. https://doi.org/10.1088/1751-8121%2Fac87df

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