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The elliptic curves in gauge theory, string theory, and cohomology

Sati, Hisham

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Elliptic curves play a natural and important role in elliptic cohomology. In earlier work with I. Kriz, these 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...[Show more]

dc.contributor.authorSati, Hisham
dc.date.accessioned2015-12-07T22:49:19Z
dc.identifier.issn1029-8479
dc.identifier.urihttp://hdl.handle.net/1885/26704
dc.description.abstractElliptic curves play a natural and important role in elliptic cohomology. In earlier work with I. Kriz, these 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 w4 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.
dc.publisherInstitute of Physics Publishing
dc.sourceJournal of High Energy Physics
dc.subjectKeywords: Duality in Gauge Field Theories; F-Theory; String Duality
dc.titleThe elliptic curves in gauge theory, string theory, and cohomology
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolumeJHEP 0603 (2006) 096
dc.date.issued2006
local.identifier.absfor010502 - Integrable Systems (Classical and Quantum)
local.identifier.ariespublicationu4441299xPUB46
local.type.statusPublished Version
local.contributor.affiliationSati, Hisham, College of Physical and Mathematical Sciences, ANU
local.description.embargo2037-12-31
local.identifier.doi10.1088/1126-6708/2006/03/096
dc.date.updated2015-12-07T12:07:34Z
local.identifier.scopusID2-s2.0-33645694586
CollectionsANU Research Publications

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