nLab permutation D-brane

1. 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.

2. Examples

For the Gepner model

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

(Enger-Recknagel-Roggenkamp 05)

3. 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)