M-theory, type IIA superstrings, and elliptic cohomology

Kříž, Igor; Sati, Hisham

doi:10.4310/atmp.2004.v8.n2.a3

Cited by 45 publications

(173 citation statements)

References 51 publications

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“…Many variations of constructions originating from such objects can be made, leading to slightly different elliptic cohomology theories. We do not have a definitive answer as to which theory to use (a similar difficulty was encountered in [24]). In algebraic topology, this difficulty is circumvented by observing certain common features of elliptic cohomology theories, and considering them therefore, in a way, all at once.…”

Section: Elliptic Cohomologymentioning

confidence: 97%

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Type IIB string theory, S-duality, and generalized cohomology

Kříž

Sati

2005

Nuclear Physics B

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In the presence of background Neveu-Schwarz flux, the description of the Ramond-Ramond fields of type IIB string theory using twisted K-theory is not compatible with S-duality. We argue that other possible variants of twisted K-theory would still not resolve this issue. We propose instead a connection of S-duality with elliptic cohomology, and a possible T-duality relation of this to a previous proposal for IIA theory, and higher-dimensional limits. In the process, we obtain some other results which may be interesting on their own. In particular, we prove a conjecture of Witten that the 11-dimensional spin cobordism group vanishes on K(Z, 6), which eliminates a potential new θ-angle in type IIB string theory.

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Section: Elliptic Cohomologymentioning

confidence: 97%

“…This is a unification of the IIA elliptic cohomology partition function correction of [24] and the IIB K 1 -partition function construction of [12].…”

Section: Introductionmentioning

confidence: 94%

Type IIB string theory, S-duality, and generalized cohomology

Kříž

Sati

2005

Nuclear Physics B

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“…The first stage would give the general contribution from the "loop sector." This connects nicely to [12,14], where one of the ways of justifying the appearance of elliptic cohomology was to propose the source of this looping as being the Dirac operators coupled to the loop bundles. The second stage is obtained if one further wants to get the Fourier modes.…”

Section: The Eta Invariant Of the Horizontal Dirac Operatormentioning

confidence: 99%

“…It then seems reasonable to assume that the resulting group will be the finite-dimensional part, i.e., the Lie group E 8 , after truncating the Fourier modes coming from the loops. 12 Corresponding to the symmetry breaking…”

Section: The Higgs Field and The Reduction Of The Le 8 To Ementioning

confidence: 99%

“…We start by embedding the M2-brane in 11-dimensional spacetime Y 11 . The understanding of the topology of both theories requires the extension to a "coboundary", namely the membrane to a bounding four-manifold X 4 and M-theory to a bounding twelve-manifold Z 12 . Of course one cannot just pull back an index, 5 but we can assume that the vector bundles on Z 12 get pulled back to X 4 .…”

Section: The Four Form As An Indexmentioning

confidence: 99%

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$E_8$ Gauge Theory and Gerbes in String T

Sati¹

2010

Advances in Theoretical and Mathematical Physics

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The reduction of the E 8 gauge theory to ten dimensions leads to a loop group, which in relation to twisted K-theory has a Dixmier-Douady class identified with the Neveu-Schwarz H-field. We give an interpretation of the degree two part of the eta form by comparing the adiabatic limit of the eta invariant with the one loop term in type IIA. More generally, starting with a G-bundle, the comparison for manifolds with String structure identifies G with E 8 and the representation as the adjoint, due to an interesting appearance of the dual Coxeter number. This makes possible a description in terms of a generalized Wess-Zumino-Witten model at the critical level. We also discuss the relation to the index gerbe, the possibility of obtaining such bundles from loop space, and the symmetry breaking to finite-dimensional bundles. We discuss the implications of this and we give several proposals.e-print archive: http://lanl.arXiv.org/abs/hep-th/0608190 400 HISHAM SATI

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L ∞-Algebra Connections and Applications to String- and Chern-Simons n-Transport

Sati

Schreiber

Stasheff

2009

Quantum Field Theory

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221

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We give a generalization of the notion of a Cartan-Ehresmann connection from Lie algebras to L∞algebras and use it to study the obstruction theory of lifts through higher String-like extensions of Lie algebras. We find (generalized) Chern-Simons and BF-theory functionals this way and describe aspects of their parallel transport and quantization.It is known that over a D-brane the Kalb-Ramond background field of the string restricts to a 2bundle with connection (a gerbe) which can be seen as the obstruction to lifting the P U (H)-bundle on the D-brane to a U (H)-bundle. We discuss how this phenomenon generalizes from the ordinary central extension U (1) → U (H) → P U (H) to higher categorical central extensions, like the String-extension BU (1) → String(G) → G. Here the obstruction to the lift is a 3-bundle with connection (a 2-gerbe): the Chern-Simons 3-bundle classified by the first Pontrjagin class. For G = Spin(n) this obstructs the existence of a String-structure. We discuss how to describe this obstruction problem in terms of Lie n-algebras and their corresponding categorified Cartan-Ehresmann connections. Generalizations even beyond String-extensions are then straightforward. For G = Spin(n) the next step is "Fivebrane structures" whose existence is obstructed by certain generalized Chern-Simons 7-bundles classified by the second Pontrjagin class.

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M-theory, type IIA superstrings, and elliptic cohomology

Cited by 45 publications

References 51 publications

Type IIB string theory, S-duality, and generalized cohomology

Type IIB string theory, S-duality, and generalized cohomology

$E_8$ Gauge Theory and Gerbes in String T

L ∞-Algebra Connections and Applications to String- and Chern-Simons n-Transport

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