Generalised Permutation Branes on a product of cosets $G_{k_1}/H\times G_{k_2}/H$

TL;DR

This paper explores the construction of non-factorizable permutation branes on product cosets, revealing a rich variety of solutions that generalize known permutation branes when the levels differ.

Contribution

It extends the theory of permutation branes to non-factorizable cases on product cosets, providing new classes of branes for differing levels.

Findings

Existence of diverse non-factorizable branes for $k_1 eq k_2$

Reduction to standard permutation branes when $k_1 = k_2$

Restoration of permutation symmetry in the equal-level case

Abstract

We study the modifications of the generalized permutation branes defined in hep-th/0509153, which are required to give rise to the non-factorizable branes on a product of cosets $G_{k_1}/H\times G_{k_2}/H$. We find that for $k_1\neq k_2$ there exists big variety of branes, which reduce to the usual permutation branes, when $k_1=k_2$ and the permutation symmetry is restored.