nLab (p,q)-string

Contents

under construction

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 II string theory: a bound state of pp-F1-branes and qq D1-branes.

Under S-duality the modular group SL 2()SL_2(\mathbb{Z}) acts on these (p,q)(p,q)-tuples and mixes the F1F1- and the D1D1-brane states.

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)

brane intersections/bound states/wrapped branes/polarized branes

S-duality\,bound states:

intersecting\,M-branes:

References

  • Igor Bandos, Superembedding Approach and S-Duality. A unified description of superstring and super-D1-brane, Nucl.Phys.B599:197-227,2001 (arXiv:hep-th/0008249)

Last revised on November 11, 2019 at 18:43:47. See the history of this page for a list of all contributions to it.