Flux quantization and the M-theoretic characters

Sati, Hisham

doi:10.1016/j.nuclphysb.2005.09.008

Cited by 22 publications

(30 citation statements)

References 22 publications

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“…This means that the index gerbe would come from G 4 written as an index, and having the same expression (4.12) without the integral. Alternatively, if one uses the putative index formula in [15,16] then G 4 would have a shift coming from A 4 leading to G 4 -λ/24. It is interesting that requiring this to be an integral class implies that λ is divisible by 24, a condition for orientability with respect to topological modular forms (TMF).…”

Section: The Quantization Conditionsmentioning

confidence: 99%

“…It is interesting that requiring this to be an integral class implies that λ is divisible by 24, a condition for orientability with respect to topological modular forms (TMF). Note that this uses the definition in [15,16] for the zeroth component of the character to be one, which in comparison can be seen to indicate the abelian nature of G 4 .…”

Section: The Quantization Conditionsmentioning

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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Section: The Quantization Conditionsmentioning

confidence: 99%

Section: The Quantization Conditionsmentioning

confidence: 99%

$E_8$ Gauge Theory and Gerbes in String T

Sati¹

2010

Advances in Theoretical and Mathematical Physics

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“…Among the generalized cohomology theories in which we are interested and which have appeared in the study of type II string theories [1,2,3] -and to some extent also in M-theory [8,9,10] -are the theories in the so-called chromatic tower of spectra, 2 i.e. the ones that descend from complex cobordism theories.…”

Section: Interpreting the "Generalized" In Generalized Cohomologymentioning

confidence: 99%

“…in the presence of the NSNS field H 3 , the twisted K-theoretic description is discussed in [7] for type IIA, and an S-duality covariant description for type IIB using generalized cohomology refinements was proposed in [2]. For M-theory, in [8,9,10], a higher degree analog of K-theory was proposed. In both string theory and M-theory, several generalized cohomology theories were considered, including the theory of topological modular forms, TMF [11].…”

Section: Introductionmentioning

confidence: 99%

“…For example, for Z[t], one has a i (t) ∈ Z[t], and y 2 + a 1 (t)xy + a 3 (t)y = x 3 + a 2 (t)x 2 + a 4 (t)x + a 6 (t), (3.5) giving an elliptic curve E over Z[t]. 9 The question of whether the resulting 'discrete' varieties correspond in reality to some discrete versions of spacetime seems to be a much deeper question that goes far beyond the scope of this paper.…”

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

Sati

2006

J. High Energy Phys.

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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 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 Ftheory 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

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The Rational Higher Structure of M‐theory

Fiorenza

Sati

Schreiber

2019

Fortschritte der Physik

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We review how core structures of string/M‐theory emerge as higher structures in super homotopy theory; namely from systematic analysis of the brane bouquet of universal invariant higher central extensions growing out of the superpoint. Since super homotopy theory is immensely rich, to start with we consider this in the rational/infinitesimal approximation which ignores torsion‐subgroups in brane charges and focuses on tangent spaces of super space‐time. Already at this level, super homotopy theory discovers all super p‐brane species, their intersection laws, their M/IIA‐, T‐ and S‐duality relations, their black brane avatars at ADE‐singularities, including their instanton contributions, and, last not least, Dirac charge quantization: for the D‐branes it recovers twisted K‐theory, rationally, but for the M‐branes it gives cohomotopy cohomology theory. We close with an outlook on the lift of these results beyond the rational/infinitesimal approximation to a candidate formalization of microscopic M‐theory in super homotopy theory.

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Flux quantization and the M-theoretic characters

Cited by 22 publications

References 22 publications

$E_8$ Gauge Theory and Gerbes in String T

$E_8$ Gauge Theory and Gerbes in String T

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

The Rational Higher Structure of M‐theory

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