nLab permutation D-brane

Idea

In string theory a permutation D-brane (Recknagel 02) is a D-brane inhabiting the diagonal of a Cartesian product space $X$ such that as boundary states for open strings these enforce that left/right worldsheet-fields are glued along some permutation of these factors.

Examples

For the Gepner model

All the known rational boundary states for Gepner models can be regarded as permutation branes.

(Enger-Recknagel-Roggenkamp 05)

References

Basic

The concept was introduced and studied in boundary conformal field theory in

• Andreas Recknagel, Permutation Branes, JHEP 0304 (2003) 041 (arXiv:hep-th/0208119)

• Andreas Recknagel, On permutation branes, Fortsch. Phys. 51 (2003) 824

A brief textbook account is in

• Andreas Recknagel, Volker Schomerus, section 4.A.4 in Boundary Conformal Field Theory and the Worldsheet Approach to D-branes, Cambridge 2013 (spire:1308990)

Further developments include

• Ilka Brunner, Matthias Gaberdiel, Matrix factorisations and permutation branes, JHEP 0507:012, 2005 (arXiv:hep-th/0503207)

• Håkon Enger, Andreas Recknagel, Daniel Roggenkamp, Permutation branes and linear matrix factorisations, JHEP0601:087, 2006 (arXiv:hep-th/0508053)

• Gor Sarkissian, Generalised Permutation Branes on a product of cosets $G_{k_1}/H \times G_{k_2}/H$, Nucl.Phys.B747:423-435, 2006 (arXiv:hep-th/0601061)

• Stefan Fredenhagen, Matthias Gaberdiel, Generalised $N=2$ permutation branes, JHEP0611:041, 2006 (arXiv:hep-th/0607095)

The case for orientifolds is discussed in

• Ilka Brunner, Vladimir Mitev, Permutation Orientifolds, JHEP 0705:078, 2007 (arXiv:hep-th/0612108)

• Kazuo Hosomichi, Permutation Orientifolds of Gepner Models, JHEP 0701:081, 2007 (arXiv:hep-th/0612109)

Relation to fractional branes

Relation to fractional branes:

• Bobby Ezhuthachan, Suresh Govindarajan, T. Jayaraman, A quantum McKay correspondence for fractional 2p-branes on LG orbifolds, JHEP 0508 (2005) 050 (arXiv:hep-th/0504164)

Generalised permutation branes

• Stefan Fredenhagen, Thomas Quella, Generalised permutation branes, JHEP0511:004, 2005 (arXiv:hep-th/0509153)

  It might surprise that despite all the progress that has been made in understanding branes on group manifolds, there are usually not enough D-branes known to explain the whole charge group predicted by (twisted) K-theory.

• Stefan Fredenhagen, Cosimo Restuccia, DBI analysis of generalised permutation branes, JHEP 1001:065, 2010 (arXiv:0908.1049)