Spectral branes

TL;DR

This paper introduces spectral branes (S-branes) in string theory, exploring their properties, boundary conditions, and dualities, including their relation to D-branes and open strings, with implications for non-commutative geometry.

Contribution

It presents the concept of spectral branes with non-local spectral boundary conditions and analyzes their properties, dualities, and relation to D-branes in string theory.

Findings

S-branes can be commutative or non-commutative depending on boundary conditions.

T-duality maps S-branes to other S-branes.

Duality transformations relate S-branes to D-branes and open strings.

Abstract

We study the objects (called spectral branes or S-branes) which are obtained by imposing non-local spectral boundary conditions at the boundary of the world sheet of the bosonic string. They possess many nice properties which make them an ideal test ground for the string theory methods. Depending on a particular choice of the boundary operator S-branes may be commutative or non-commutative. We demonstrate that projection of the B-field on the brane directions (i.e. on the components which actually influence the boundary conditions) is done with the help of the chirality operator. We show that the T-duality transformation maps an S-brane to another S-brane. At the expense of introducing non-local interactions in the bulk we construct also a duality transformation between S-branes and D-branes or open strings.