String solutions in $AdS_3\times S^3\times S^3\times S^1$ with $B$-field

TL;DR

This paper finds explicit string solutions in a complex ten-dimensional space with a nonzero B-field, expressing them through advanced special functions and calculating conserved quantities like energy and angular momentum.

Contribution

It introduces a new class of string solutions in $AdS_3\times S^3\times S^3\times S^1$ with B-field, using specific ansatz and special functions, and computes their conserved charges.

Findings

Solutions involve incomplete elliptic integrals and Lauricella hypergeometric functions.

Conserved charges such as energy, spin, and angular momenta are explicitly calculated.

The solutions describe strings moving in the full ten-dimensional background.

Abstract

We consider strings living in $AdS_3\times S^3\times S^3\times S^1$ with nonzero $B$-field. By using specific ansatz for the string embedding, we obtain a class of solutions corresponding to strings moving in the whole ten dimensional space-time. For the $AdS_3$ subspace, these solutions are given in terms of incomplete elliptic integrals. For the two three-spheres, they are expressed in terms of Lauricella hypergeometric functions of many variables. The conserved charges, i.e. the string energy, spin and angular momenta, are also found.