A defect brane (Bershoeff-Ortin-Riccioni 11) is a brane of codimension 2; such as, for example
a cosmic string in 4-dimensional Yang-Mills theory,
a D7-brane in 10d type IIB string theory.
In string theory, defect branes with U-duality-group monodromy have been argued to be identified with “exotic branes” deBoer & Shigemori 2012, p. 12.
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.
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:
Hironori Mori, Yuji Sugimoto, Surface Operators from M-strings, Phys. Rev. D 95, 026001 (2017) (arXiv:1608.02849)
Hironori Mori, M-theory Perspectives on Codimension-2 Defects (spire:1519095, pdf)
Nathan Haouzi, Christian Schmid, Little String Origin of Surface Defects, J. High Energ. Phys. 2017, 82 (2017) (arXiv:1608.07279, doi:10.1007/JHEP05(2017)082)
and in D=5 supergravity:
Minkyu Park, Masaki Shigemori, Codimension-2 Solutions in Five-Dimensional Supergravity, JHEP 1510 (2015) 011 (arXiv:1505.05169)
Masaki Shigemori, Interpolating between multi-center microstate geometries, JHEP 09 (2021) 010 (arXiv:2105.11639)
On defect strings in 4d TQFT satisfying braid group- and more generally loop braid group-statistics:
in 4d BF theory:
John Baez, Derek Wise, Alissa Crans, Exotic Statistics for Strings in 4d BF Theory, Adv. Theor. Math. Phys. 11:707-749, 2007 (arXiv:gr-qc/0603085)
Alex Bullivant, João Faria Martins, Paul Martin, Representations of the Loop Braid Group and Aharonov-Bohm like effects in discrete (3+1)-dimensional higher gauge theory, Advances in Theoretical and Mathematical Physics Volume 23 (2019) Number 7 (arXiv:1807.09551)
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.