English

Non-associative star products and quantization of non-geometric backgrounds in string and M-theory

High Energy Physics - Theory 2018-05-03 v2 Mathematical Physics math.MP

Abstract

We review two known in the literature exemples of non-associative star products. The first one is the phase space star product representing quantization of non-geometric RR-flux background in closed string theory. The second is the octonionic star product which provides the quantization of the quasi-Poisson algebra isomorphic to the Malcev algebra of imaginary octonions. We discuss in details the construction, properties and physical applications of these star products. In particular, we consider the quantization of non-geometric M-theory background. Based on these two exemples we formulate the minimal set of physically motivated conditions for the definition of non-associative deformation quantization.

Keywords

Cite

@article{arxiv.1804.10161,
  title  = {Non-associative star products and quantization of non-geometric backgrounds in string and M-theory},
  author = {Vladislav G. Kupriyanov},
  journal= {arXiv preprint arXiv:1804.10161},
  year   = {2018}
}

Comments

v2; references added. Talk given at the Workshop on Testing Fundamental Physics Principles, Corfu Summer Institute on Elementary Particle Physics and Gravity, September 2-28, 2017, Corfu, Greece