nLab defect brane

Idea

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

• a cosmic string in 4-dimensional Yang-Mills theory,

• a super 1-brane in 4d,

• a super 2-brane in 5d,

• a super 3-brane in 6d,

• 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.

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.

Related concepts

• vortex string

• black brane

• exotic brane

• domain wall

• monopole

References

Branes of codimension $\leq 2$ are called non-standard branes in:

• Eric A. Bergshoeff, Fabio Riccioni, Solitonic branes and wrapping rules, Phys. Part. Nuclei 43 (2012) 557–561 [doi:10.1134/S106377961205005X]

See also:

• Claudia de Rham, The Effective Field Theory of Codimension-two Branes, JHEP 0801:060 (2008) [arXiv:0707.0884, doi:10.1088/1126-6708/2008/01/060]

The term “defect brane” was introduced in:

• Eric Bergshoeff, Tomas Ortin, Fabio Riccioni, Defect Branes, Nuclear Physics B 856 2 (2012) 210-227 [arXiv:1109.4484, doi:10.1016/j.nuclphysb.2011.10.037]

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

• Jan de Boer, Masaki Shigemori, Exotic Branes in String Theory, Physics Reports 532 (2013) 65-118 (arXiv:1209.6056, doi:j.physrep.2013.07.003)

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:

• Tetsuji Kimura, Defect $(p,q)$ Five-branes, Nucl. Phys. B 893 (2015) 1-20 [arXiv:1410.8403, doi:10.1016/j.nuclphysb.2015.01.023]

• Tetsuji Kimura, Shin Sasaki, Kenta Shiozawa, On Geometries and Monodromies for Branes of Codimension Two [arXiv:2312.03358]

Discussion of codimension-2 defects in the M5-brane worldvolume, hence defect branes in little string theory (cf. 3-brane in 6d):

• Hironori Mori, Yuji Sugimoto, around Fig. 9 in: Surface Operators from M-strings, Phys. Rev. D 95, 026001 (2017) [arXiv:1608.02849, doi:10.1103/PhysRevD.95.026001]

• 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)

• Pietro Capuozzo, John Estes, Brandon Robinson, Benjamin Suzzoni, Holographic Weyl Anomalies for 4d Defects in 6d SCFTs [arXiv:2310.17447]

and in relation to quantum Seiberg-Witten curves of class S-theories:

• Jin Chen, Babak Haghighat, Hee-Cheol Kim, Marcus Sperling, around Fig. 1 & Fig. 2 in: Elliptic Quantum Curves of Class $\mathcal{S}_k$, J. High Energ. Phys. 2021 28 (2021) [arXiv:2008.05155, doi:10.1007/JHEP03(2021)028]

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:

• Liang Kong, Yin Tian, Zhi-Hao Zhang, Section 2.2 of: Defects in the 3-dimensional toric code model form a braided fusion 2-category, J. High Energ. Phys. 2020, 78 (2020) (arXiv:2009.06564, doi:10.1007/JHEP12(2020)078)

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:

• Hisham Sati, Urs Schreiber, Anyonic defect branes in TED-K-theory, Reviews in Mathematical Physics 35 06 (2023) 2350009 [arXiv:2203.11838, doi:10.1142/S0129055X23500095]

On defect branes in D=4 N=4 SYM via AdS/CFT:

• Hongliang Jiang, Arkady A. Tseytlin, On co-dimension 2 defect anomalies in $\mathcal{N}=4$ SYM and $(2,0)$ theory via brane probes in AdS/CFT [arXiv:2402.07881]