The Elliptic curves in gauge theory, string theory, and cohomology
arXiv:hep-th/0511087 · doi:10.1088/1126-6708/2006/03/096
Abstract
Elliptic curves play a natural and important role in elliptic cohomology. In earlier work with I. Kriz, thes elliptic curves were interpreted physically in two ways: as corresponding to the intersection of M2 and M5 in the context of (the reduction of M-theory to) type IIA and as the elliptic fiber leading to F-theory for type IIB. In this paper we elaborate on the physical setting for various generalized cohomology theories, including elliptic cohomology, and we note that the above two seemingly unrelated descriptions can be unified using Sen's picture of the orientifold limit of F-theory compactification on K3, which unifies the Seiberg-Witten curve with the F-theory curve, and through which we naturally explain the constancy of the modulus that emerges from elliptic cohomology. This also clarifies the orbifolding performed in the previous work and justifies the appearance of the w_4 condition in the elliptic refinement of the mod 2 part of the partition function. We comment on the cohomology theory needed for the case when the modular parameter varies in the base of the elliptic fibration.
arXiv comment23 pages, typos corrected, minor clarifications
References in corpus (42)
- Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
- Dirichlet-Branes and Ramond-Ramond Charges
- Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
- String Theory Dynamics In Various Dimensions
- Evidence for F-Theory
- Bound States Of Strings And -Branes
- Solutions Of Four-Dimensional Field Theories Via M Theory
- Evidence for Heterotic - Type I String Duality
- Consistency Conditions for Orientifolds and D-Manifolds
- Open P-Branes
- Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics
- Phase Transitions In M-Theory And F-Theory
- F-theory and Orientifolds
- Simple Singularities and N=2 Supersymmetric Yang-Mills Theory
- On Flux Quantization In M-Theory And The Effective Action
- The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory
- D-branes from M-branes
- Self-Dual Strings and N=2 Supersymmetric Field Theory
- Some Relationships Between Dualities in String Theory
- F-Theory at Constant Coupling
- Probing F-theory With Branes
- Black and super p-branes in diverse dimensions
- Self-Duality, Ramond-Ramond Fields, and K-Theory
- Orientifold Limit of F-theory Vacua
- On the Monodromies of N=2 Supersymmetric Yang-Mills Theory with Gauge Group SO(2n)
- Ten Dimensional Heterotic String as a Soliton
- The Moduli Space and Monodromies of N=2 Supersymmetric \(SO(2r+1) \) Yang-Mills Theory
- BPS Quantization of the Five-Brane
- String-String Duality in Ten Dimensions
- A Hiker's Guide to K3 - Aspects of N=(4,4) Superconformal Field Theory with central charge c=6
- Some Relations between Twisted K-theory and E8 Gauge Theory
- On Ramond-Ramond fields and K-theory
- Type IIB String Theory, S-Duality, and Generalized Cohomology
- Type II string theory and modularity
- Duality symmetry and the form fields of M-theory
- The Seiberg-Witten Differential From M-Theory
- Orientifold Limit of F-theory Vacua
- Triples, Fluxes, and Strings
- Flux Quantization and the M-Theoretic Characters
- M-theory and Characteristic Classes
- SUSY vs E8 Gauge Theory in 11 Dimensions
- TASI Lectures on Compatification and Duality