nLab
(p,q)5-brane

Contents

Context

String theory

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Gravity

Quantum field theory

Higher spin geometry

Elliptic cohomology

Contents

Idea

In type IIB string theory there are bound states of D5-branes with NS5-branes. The bound state of pp \in \mathbb{Z} D5-branes with qq \in\mathbb{Z} NS5-branes is then called a (p,q)(p,q)-fivebrane or similar.

As pp and qq varies the species of (p,q)(p,q)5-branes form the lattice 2\mathbb{Z}^2 and are naturally action acted on by the S-duality group SL(2,Z).

Properties

(p,q)(p,q)-Brane webs

Label local coordinate functions x ax^a on 10d Minkowski spacetime 9,1\mathbb{R}^{9,1} by 012345567890123455'6789 and write v a x av_a \coloneqq \partial_{x^a} for the corresponding vector field

Consider a (1,0)(1,0)5-brane (a D5-brane) along the multivector field v 0v 1v 2v 3v 4v 5v_0 v_1 v_2 v_3 v_4 v_5 and a (0,1)(0,1)5-brane (an NS-brane) along v 0v 1v 2v 3v 4v 5v_0 v_1 v_2 v_3 v_4 v_{5'}

a=a =00112233445555'66778899
D5
NS5

Charge conservation implies that at the brane intersection of the two a (1,1)(1,1)5-brane emerges stretched diagonally along v 5+v gv_5 + v_{g'}, i.e. along the multivector field v 0v 1v 2v 3v 4(v 5+v 5)v_0 v_1 v_2 v_3 v_4 (v_5 + v_{5'})

Aharony-Hanany 97, Sec. 3

The worldvolume-quantum field theory at the brane intersection point is a geometric engineering of D=5 N=1 SYM .

The T-dual perspective are D4/NS5-brane webs (Witten 97).

The result of connecting several such brane intersections are called (p,q)(p,q)-5brane webs (Aharony-Hanany-Krol 97).

brane intersections/bound states/wrapped branes

S-duality\,bound states:

intersecting\,M-branes:

from M-branes to F-branes: superstrings, D-branes and NS5-branes

M-theory on S A 1×S B 1S^1_A \times S^1_B-elliptic fibrationKK-compactification on S A 1S^1_Atype IIA string theoryT-dual KK-compactification on S B 1S^1_Btype IIB string theorygeometrize the axio-dilatonF-theory on elliptically fibered-K3 fibrationduality between F-theory and heterotic string theoryheterotic string theory on elliptic fibration
M2-brane wrapping S A 1S_A^1double dimensional reduction \mapstotype IIA superstring\mapstotype IIB superstring\mapsto\mapstoheterotic superstring
M2-brane wrapping S B 1S_B^1\mapstoD2-brane\mapstoD1-brane\mapsto
M2-brane wrapping pp times around S A 1S_A^1 and qq times around S B 1S_B^1\mapstopp strings and qq D2-branes\mapsto(p,q)-string\mapsto
M5-brane wrapping S A 1S_A^1double dimensional reduction \mapstoD4-brane\mapstoD5-brane\mapsto
M5-brane wrapping S B 1S_B^1\mapstoNS5-brane\mapstoNS5-brane\mapsto\mapstoNS5-brane
M5-brane wrapping pp times around S A 1S_A^1 and qq times around S B 1S_B^1\mapstopp D4-brane and qq NS5-branes\mapsto(p,q)5-brane\mapsto
M5-brane wrapping S A 1×S B 1S_A^1 \times S_B^1\mapsto\mapstoD3-brane\mapsto
KK-monopole/A-type ADE singularity (degeneration locus of S A 1S^1_A-circle fibration, Sen limit of S A 1×S B 1S^1_A \times S^1_B elliptic fibration)\mapstoD6-brane\mapstoD7-branes\mapstoA-type nodal curve cycle degeneration locus of elliptic fibration ADE 2Cycle (Sen 97, section 2)SU-gauge enhancement
KK-monopole orientifold/D-type ADE singularity\mapstoD6-brane with O6-planes\mapstoD7-branes with O7-planes\mapstoD-type nodal curve cycle degeneration locus of elliptic fibration ADE 2Cycle (Sen 97, section 3)SO-gauge enhancement
exceptional ADE-singularity\mapsto\mapsto\mapstoexceptional ADE-singularity of elliptic fibration\mapstoE6-, E7-, E8-gauge enhancement

(e.g. Johnson 97, Blumenhagen 10)

References

The original articles are:

The T-dual perspective are D4/NS5-brane webs:

Further intersection with orientifolds:

  • Amihay Hanany, Alberto Zaffaroni, Issues on Orientifolds: On the brane construction of gauge theories with SO(2n)SO(2n) global symmetry, JHEP 9907 (1999) 009 (arXiv:hep-th/9903242)

  • Hirotaka Hayashi, Sung-Soo Kim, Kimyeong Lee, Masato Taki, Futoshi Yagi, More on 5d descriptions of 6d SCFTs, JHEP10 (2016) 126 (arXiv:1512.08239)

  • Gabi Zafrir, Brane webs in the presence of an O5 O5^--plane and 4d class S theories of type D, JHEP07 (2016) 035 (arXiv:1602.00130)

  • Taro Kimura, Rui-Dong Zhu, Section 2 and 3 of Web Construction of ABCDEFG and Affine Quiver Gauge Theories (arXiv:1907.02382)

Last revised on November 11, 2019 at 13:42:26. See the history of this page for a list of all contributions to it.