Grigoriev M. Gauge PDE and AKSZ sigma models (abstract)

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Speaker: Maxim Grigoriev

Title: Gauge PDE and AKSZ sigma models

AKSZ sigma models were originally proposed to describe topological systems. In so doing the Batalin-Vilkovisky formulation of the system is encoded in the pair (target space and the source) of Q-manifolds. In fact, an AKSZ model with finite-dimensional target and space-time dimension higher than 1 is necessarily topological. It turns out that generic gauge PDE can be cast into the AKSZ sigma model whose target space is the BRST-extended equation manifold equipped with the BRST differential and the horizontal differential. This gives a rather flexible and powerful framework to study gauge PDE. I plan to discuss various applications of the framework including invariant gauge PDE, higher spin gauge theories and their holographic relations.

Slides: GriroievTrieste2018slides.pdf

Event: Local and Nonlocal Geometry of PDEs and Integrability, 8-12 October 2018, SISSA, Trieste, Italy.
The conference in honor of Joseph Krasil'shchik's 70th birthday.