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

Kříž, Igor; Sati, Hisham

doi:10.1016/j.nuclphysb.2005.02.016

Cited by 30 publications

(79 citation statements)

References 45 publications

(127 reference statements)

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“…The above bundle description, however, gives an alternative point of view where the NSNS fields seem to be the fields twisted by (part of) the RR fields. Furthermore, this provides some further justification -at least morally -for the proposal in [13] for treating the NSNS field H 3 and the RR field F 3 , in type IIB string theory, democratically, that is, untwist the NSNS twist and view both fields as untwisted elements of elliptic cohomology. In the current context, it is even more because the twist is done by the RR field F 4 , representing the E 8 bundle, and what is being twisted is the NSNS field H 3 , representing the LE 8 -bundle.…”

Section: Twist Versus Twisted Based Versus Unbasedmentioning

confidence: 95%

“…At the level of representations, the Higgs field will then take values in the corresponding Ωe 8 bundle. 13 From the point of view of the gauge theory on the S 1 fiber the space of gauge orbits is the classifying space BG 0 = A/G 0 , i.e., the quotient of the space of connections A by the based gauge transformations G 0 . The group of gauge transformations is just ΩE 8 and so the space of equivalence classes is just E 8 .…”

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

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: Twist Versus Twisted Based Versus Unbasedmentioning

confidence: 95%

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

confidence: 99%

$E_8$ Gauge Theory and Gerbes in String T

Sati¹

2010

Advances in Theoretical and Mathematical Physics

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“…In the twisted case [7], i.e. 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.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, an S-duality covariant approach to describe the fields of type IIB string theory was proposed in [2,3]. In studying modularity in [3], the elliptic curve of elliptic cohomology was given another interpretation, namely as corresponding to the fiber of F-theory over type IIB string theory.…”

Section: Introductionmentioning

confidence: 99%

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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“…In [39] this was studied starting from the conjecture in [4], proven in [19], that in the absence of D3-brane charge…”

Section: Open Questionsmentioning

confidence: 99%

Flux compactifications on projective spaces and the $S$-duality puzzle

Bouwknegt

Evslin

Jurčo

et al. 2006

Advances in Theoretical and Mathematical Physics

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We derive a formula for D3-brane charge on a compact spacetime, which includes torsion corrections to the tadpole cancellation condition. We use this to classify D-branes and Ramond-Ramond fluxes in type II string theory on RP 3 × RP 2k+1 × S 6−2k with torsion H-flux and to demonstrate the conjectured T -duality to S 3 × S 2k+1 × S 6−2k with no flux. When k = 1, H = 0 and so the K-theory that classifies fluxes is twisted. When k = 2, the square of the H-flux yields an S-dual FreedWitten anomaly, which is canceled by a D3-brane insertion that ruins the dual K-theory flux classification. When k = 3, the cube of H is nontrivial and so the D3 insertion may itself be inconsistent and the compactification unphysical. Along the way we provide a physical interpretation for the Atiyah-Hirzebruch spectral sequence in terms of the boundaries of branes within branes.

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

Cited by 30 publications

References 45 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

Flux compactifications on projective spaces and the $S$-duality puzzle

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