Lax pairs for deformed Minkowski spacetimes
High Energy Physics - Theory
2016-03-23 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We proceed to study Yang-Baxter deformations of 4D Minkowski spacetime based on a conformal embedding. We first revisit a Melvin background and argue a Lax pair by adopting a simple replacement law invented in 1509.00173. This argument enables us to deduce a general expression of Lax pair. Then the anticipated Lax pair is shown to work for arbitrary classical -matrices with Poinca\'e generators. As other examples, we present Lax pairs for pp-wave backgrounds, the Hashimoto-Sethi background, the Spradlin-Takayanagi-Volovich background.
Keywords
Cite
@article{arxiv.1512.00208,
title = {Lax pairs for deformed Minkowski spacetimes},
author = {Hideki Kyono and Jun-ichi Sakamoto and Kentaroh Yoshida},
journal= {arXiv preprint arXiv:1512.00208},
year = {2016}
}
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29 pages