Contents

Contents

Idea

A defect brane (Bershoeff-Ortin-Riccioni 11) is a brane of codimension 2; such as, for example

In string theory, defect branes with U-duality-group monodromy have been argued to be identified with “exotic branesdeBoer & Shigemori 2012, p. 12.

Properties

Relation to anyons

An anyon is traditionally realized as a point-particle/defect in 2+1-dimensional spacetime, hence as a codimension-2 “0-brane” (see the references here). This suggests that general codimension-2 defect branes may serve as string-theoretic models for anyons. This general observation is briefly mentioned in deBoer & Shigemori 2012, p. 65 and further developed in SS22.

Concrete implementation of anyonic defect strings in 4d TQFT is discussed in Baez, Wise & Crans 2006, Bullivant, Martins & Martin 2018 Kong, Tian & Zhang 2020, Sec. 2.2. More generally, circle-shaped defect strings are going to satisfy loop braid group-statistics, which subsumes braid group-statistics but is richer still.

References

The term “defect brane” was introduced in:

Identification of codimension-2 defect branes with U-duality-group monodromy as exotic branes:

See also:

• Allan Bayntun, C.P. Burgess, Leo van Nierop, Codimension-2 Brane-Bulk Matching: Examples from Six and Ten Dimensions, New J. Phys. 12:075015, 2010 (arXiv:0912.3039)

• Takashi Okada, Yuho Sakatani, Defect branes as Alice strings, JHEP 1503 (2015) 131 (arXiv:1411.1043, doi:10.1007/JHEP03(2015)131)

• Yosuke Imamura, Hirotaka Kato, Codimension-2 brane solutions of maximal supergravities in 9, 8, and 7 dimensions, Prog. Theor. Exp. Phys. (2018) (arXiv:1711.03242, doi:10.1093/ptep/pty045)

Discussion of defect (p,q)5-branes:

Discussion of codimension-2 defects in the M5-brane worldvolume, hence defect branes in little string theory:

and in D=5 supergravity:

On defect strings in 4d TQFT satisfying braid group- and more generally loop braid group-statistics:

in 4d BF theory:

and in the 3d toric code-4d TQFT:

Incorporation of defect branes into the K-theory classification of D-brane charge by understanding the hypergeometric construction of KZ solutions as happening in twisted equivariant differential K-theory:

Last revised on May 28, 2022 at 15:08:17. See the history of this page for a list of all contributions to it.