nLab s-rule




In string theory, specifically for intersecting D-brane models, what has come to be known as the s-rule is the conjecture that the configuration of Dp-D(p+2)-brane bound states with the Dp-branes stretching from the D(p+2)-branes to NS5-branes, can be supersymmetric only if at most one Dpp-brane ends on any one D(p+2)(p+2)-brane (Hanany-Witten 97).


D3-D5 brane intersections

For D3-D5 brane intersections:

Hanay-Witten 97

D4-D6 brane intersections

For D4-D6 brane intersections:

graphics grabbed from Fazzi 17

D6-D8 brane intersections

For D6-D8 brane intersections:

graphics grabbed from Gaiotto-Tomasiello 14

graphics grabbed from Fazzi 17

graphics grabbed from GKSTY 02

brane intersections/bound states/wrapped branes/polarized branes

S-duality\,bound states:



The s-rule is attributed to

which considers D3-D5 brane intersections, speaks of “s-configurations” as those with more than one D3-brane ending on any D5-brane and gives plausibility arguments that these s-configurations are not supersymmetric.


Relation to the Pauli exclusion principle:

See also

For D2-D4 brane intersections:

  • Minoru Eto, Youichi Isozumi, Muneto Nitta, Keisuke Ohashi, Kazutoshi Ohta, Norisuke Sakai, Section 3 of: D-brane Construction for Non-Abelian Walls, Phys. Rev. D71 (2005) 125006 (arXiv:hep-th/0412024)

For D3-D5 brane intersections:

  • Constantin Bachas, Michael Green, Adam Schwimmer, Section 2.3 of: (8,0)(8,0) Quantum mechanics and symmetry enhancement in type I’ superstrings, JHEP 9801 :006, 1998 (arXiv:hep-th/9712086)

  • Akikazu Hashimoto, Peter Ouyang, Masahito Yamazaki, Section 3.6 of: Boundaries and Defects of N=4 SYM with 4 Supercharges, Part II: Brane Constructions and 3d N=2 Field Theories, JHEP 1410 : 108, 2014 (arXiv:1406.5501)

  • Federico Carta, Hirotaka Hayashi, Hilbert series and mixed branches of T[SU(N)]T[SU(N)] theory, JHEP 02 (2017) 037 (arXiv:1609.08034)

For D4-D6 brane intersections:

For D6-D8 brane intersections:

Review includes:

Last revised on December 4, 2019 at 11:07:07. See the history of this page for a list of all contributions to it.