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High Energy Physics - Theory

arXiv:0710.2544 (hep-th)
[Submitted on 12 Oct 2007 (v1), last revised 19 Oct 2007 (this version, v2)]

Title:Chern class identities from tadpole matching in type IIB and F-theory

Authors:Paolo Aluffi (FSU), Mboyo Esole (KU Leuven)
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Abstract: In light of Sen's weak coupling limit of F-theory as a type IIB orientifold, the compatibility of the tadpole conditions leads to a non-trivial identity relating the Euler characteristics of an elliptically fibered Calabi-Yau fourfold and of certain related surfaces. We present the physical argument leading to the identity, and a mathematical derivation of a Chern class identity which confirms it, after taking into account singularities of the relevant loci. This identity of Chern classes holds in arbitrary dimension, and for varieties that are not necessarily Calabi-Yau. Singularities are essential in both the physics and the mathematics arguments: the tadpole relation may be interpreted as an identity involving stringy invariants of a singular hypersurface, and corrections for the presence of pinch-points. The mathematical discussion is streamlined by the use of Chern-Schwartz-MacPherson classes of singular varieties. We also show how the main identity may be obtained by applying `Verdier specialization' to suitable constructible functions.
Comments: 26 pages, 1 figure, references added, typos corrected
Subjects: High Energy Physics - Theory (hep-th); Algebraic Geometry (math.AG)
Report number: MPIM2007-126, FSU07-23, KUL-TF-07/22
Cite as: arXiv:0710.2544 [hep-th]
  (or arXiv:0710.2544v2 [hep-th] for this version)
  https://doi.org/10.48550/arXiv.0710.2544
Journal reference: J. High Energy Phys. 2009, no. 3, 032, 29 pp
Related DOI: https://doi.org/10.1088/1126-6708/2009/03/032

Submission history

From: Mboyo Esole [view email]
[v1] Fri, 12 Oct 2007 20:52:57 UTC (39 KB)
[v2] Fri, 19 Oct 2007 18:44:49 UTC (39 KB)
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