Classifying A-field and B-field configurations in the presence of D-branes

Bonora, L.; Ruffino, Fabio Ferrari; Savelli, Raffaele

doi:10.1088/1126-6708/2008/12/078

Cited by 7 publications

(12 citation statements)

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“…In particular, the natural map H n dR (X) → H n crn (X), obtained by thinking of a form as a current, is a canonical isomorphism. To realize an isomorphism between H n (X, R) and H n dR (X) we can use iteratively the Poincaré lemma, as explained in [2]. For all of these three groups we can consider the compactly-supported version, which we call respectively H n dR,cpt (X), H n crn,cpt (X) and H n cpt (X, R).…”

Section: Jhep11(2009)012mentioning

confidence: 99%

“…Such an integral is actually the holonomy of the line bundle over the curve γ, and in a general background the field strength F can be topologically non-trivial, so A is locally defined and has gauge transformations. The problem is that, as explained in [2], holonomy is a well-defined function on closed curves, while it is a section of a line bundle over the space of open curves. However, at classical level, when we minimize the action we do it for curves connecting two fixed points (they can be at infinity, in case the bundle extends to the closure S).…”

Section: Definition Of the Actionmentioning

confidence: 99%

“…For a brief review about the holonomy of gerbes we refer to [2] chap. 3 and references therein: that discussion can be immediately generalized to p-gerbes, considering triangulations of dimension p + 1 instead of 2.…”

Section: Jhep11(2009)012mentioning

confidence: 99%

“…If we want to define the holonomy as a number, we must give boundary conditions at infinity, but since the forms C p+1 are defined only locally and only up to gauge transformations, it is not immediately clear how to impose boundary conditions on them at infinity. We refer to [2] chap. 4 for a discussion aboutČech hypercohomology and trivializations of gerbes.…”

Section: Holonomy and Boundary Conditionsmentioning

confidence: 99%

“…For example, for R 1,3 × X such a compactification is D 4 ×X for D 4 the 4-disc, so that the boundary is S 4 ×X. Generalizing the explanation in [2] to p-gerbes we can define the holonomy of a p-gerbe G p on S along a (p + 1)-submanifold with boundary. This holonomy is not a function, it is a section of a line bundle over the space of maps from open (p + 1)-manifolds to S. In particular, if we fix a (p + 1)-manifold Σ and we endow the space Maps(Σ, S) with a suitable topology, the holonomy of G p is a section of a line bundle over Maps(Σ, S).…”

Section: Holonomy and Boundary Conditionsmentioning

confidence: 99%

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Demonstration of Secondary Electron Detection using Monolithic Multi-Channel Electron Detector

Tanimoto

Pickard

Kenney

et al. 2008

jjap

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In this paper we discuss some topics on the geometry of type II superstring backgrounds with D-branes, in particular on the geometrical meaning of the D-brane charge, the Ramond-Ramond fields and the Wess-Zumino action. We see that, depending on the behaviour of the D-brane on the four non-compact space-time directions, we need different notions of homology and cohomology to discuss the associated fields and charge: we give a mathematical definition of such notions and show their physical applications. We then discuss the problem of corretly defining Wess-Zumino action using the theory of p-gerbes. Finally, we recall the so-called * -problem and make some brief remarks about it. Conclusions and perspectives 24A p-Gerbes 24 B Hodge- * with Minkowskian signature 25 C Direct sum and direct product 26 JHEP11(2009)012of homology and cohomology in the same way it is used for electromagnetism, so that the theory of D-branes becomes actually a generalized version of electromagnetism with higher dimensional sources. In particular, one considers D-branes as sources for violation of Bianchi identity for the Ramond-Ramond fields, so that a Dp-brane charge is the analogue of the magnetic charge for the associated Ramond-Ramond field G 8−p and of the electric charge for its Hodge-dual G p+2 , assuming the democratic formulation of supergravity. Moreover, the Wess-Zumino action, i.e. the minimal coupling of a Dp-brane to the Ramond-Ramond potential C p+1 , is the analogue of the Wilson line for a charged particle moving in a background electromagnetic field. In order to describe D-brane charges, we can consider D-branes which cover part or all of the non-compact space directions. In this case, the brane cannot be seen as an ordinary homology cycle since, by definition of homology, all cycles have compact support. Thus, in order to correctly describe a theory of electromagnetism with non-compact sources, we are forced to consider a different version of homology, called Borel-Moore homology, which takes into account also non-compact cycles. We will also introduce some modified versions of Borel-Moore homology, in order to describe the possible kinds of D-branes. Moreover, we deal with the problem of giving a correct definition of Wess-Zumino action. The potential C p+1 is a connection on a p-gerbe, so that we briefly recall the theory of gerbes with connection, using the language ofČech hypercohomology, in order to explain the meaning of the integral and, if necessary, of its conditions at infinity.As is well known, this picture is affected by some problems: in particular, magnetic charge is quantized by Dirac quantization condition, and this implies that both a Ramond-Ramond field and its Hodge-dual are quantized, while in general Hodge duality does not preserve quantization. In particular, in type IIB theory the field G 5 is self-dual, being a D3-brane both electric and magnetic charge with respect to it: but there is not a good lagrangian description of a theory with a source which is at the same time magnetic and electric, an...

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Section: Jhep11(2009)012mentioning

confidence: 99%

Section: Definition Of the Actionmentioning

confidence: 99%

Section: Jhep11(2009)012mentioning

confidence: 99%

Section: Holonomy and Boundary Conditionsmentioning

confidence: 99%

Section: Holonomy and Boundary Conditionsmentioning

confidence: 99%

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Demonstration of Secondary Electron Detection using Monolithic Multi-Channel Electron Detector

Tanimoto

Pickard

Kenney

et al. 2008

jjap

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On flux quantization in F-theory

Collinucci

Savelli

2012

J. High Energ. Phys.

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131

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We study the problem of four-form flux quantization in F-theory compactifications. We prove that for smooth, elliptically fibered Calabi-Yau fourfolds with a Weierstrass representation, the flux is always integrally quantized. This implies that any possible half-integral quantization effects must come from 7-branes, i.e. from singularities of the fourfold.We subsequently analyze the quantization rule on explicit fourfolds with Sp(N) singularities, and connect our findings via Sen's limit to IIB string theory. Via direct computations we find that the four-form is half-integrally quantized whenever the corresponding 7-brane stacks wrap non-spin complex surfaces, in accordance with the perturbative Freed-Witten anomaly. Our calculations on the fourfolds are done via toric techniques, whereas in IIB we rely on Sen's tachyon condensation picture to treat bound states of branes. Finally, we give general formulae for the curvature-and flux-induced D3 tadpoles for general fourfolds with Sp(N) singularities.

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