Spectral Covers, Integrality Conditions, and Heterotic/F-theory Duality

Journal of Singularities
volume 15 (2016), 1-13

Received: 13 October 2014. Received in revised form: 24 January 2016.

DOI: 10.5427/jsing.2016.15a

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Abstract:

In this work we review a systematic, algorithmic construction of dual heterotic/F-theory geometries corresponding to 4-dimensional, N=1 supersymmetric compactifications. We look in detail at an exotic class of well-defined Calabi-Yau fourfolds for which the standard formulation of the duality map appears to fail, leading to dual heterotic geometry which appears naively incompatible with the spectral cover construction of vector bundles. In the simplest class of examples the F-theory background consists of a generically singular elliptically fibered Calabi-Yau fourfold with E_7 symmetry. The vector bundles arising in the corresponding heterotic theory appear to violate an integrality condition of an SU(2) spectral cover. A possible resolution of this puzzle is explored by studying the most general form of the integrality condition. This leads to the geometric challenge of determining the Picard group of surfaces of general type. We take an important first step in this direction by computing the Hodge numbers of an explicit spectral surface and bounding the Picard number.

Keywords:

Heterotic string compactification, F-theory, 4-dimensional N=1 string dualities, algebraic geometry, surfaces of general type, Picard number

Author(s) information:

Lara B. Anderson
Department of Physics
Virginia Tech
Blacksburg, Virginia 24060
USA
email: lara.anderson@vt.edu