Advances in Theoretical and Mathematical Physics

Volume 22 (2018)

Number 3

Caustics and Maxwell sets of world sheets in anti-de Sitter space

Pages: 759 – 802

DOI: http://dx.doi.org/10.4310/ATMP.2018.v22.n3.a5

Author

Shyuichi Izumiya (Department of Mathematics, Hokkaido University, Sapporo, Japan)

Abstract

A world sheet in anti-de Sitter space is a timelike submanifold consisting of a one-parameter family of spacelike submanifolds. We consider the family of lightlike hypersurfaces along spacelike submanifolds in the world sheet. The locus of the singularities of light-like hypersurfaces along spacelike submanifolds forms the caustic of the world sheet. This notion is originally introduced by Bousso and Randall in theoretical physics. In this paper we give a mathematical framework for the caustics of world sheets as an application of the theory of graph-like Legendrian unfoldings.

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