F-theory and linear sigma models

Abstract

We present an explicit method for translating between the linear sigma model and the spectral cover description of SU(r) stable bundles over an elliptically fibered Calabi-Yau manifold. We use this to investigate the 4-dimensional duality between (0,2) heterotic and F-theory compactifications. We indirectly find that much interesting heterotic information must be contained in the `spectral bundle' and in its dual description as a gauge theory on multiple F-theory 7-branes. A by-product of these efforts is a method for analyzing semistability and the splitting type of vector bundles over an elliptic curve given as the sheaf cohomology of a monad.Comment: 40 pages, no figures; minor cosmetic reorganization of section 4; reference [6] update

Duality in heterotic vacua with four supercharges

“…In this appendix we present some of the technical details connected to the dimensional reduction of the 11-dimensional supergravity Lagrangian (22) on Calabi-Yau fourfolds. Starting from the Ansatz (27) one considers infinitesimally small deformations of the metric, (29) and (30), which preserve the Calabi-Yau condition. These metric deformations correspond to variations of the Kähler class and the complex structure of the Calabi-Yau metric.…”

“…R (8) ab (ĝ + δg) = 0. Solving these equations shows that the metric deformations can (to lowest order) be expanded like in (29) and (30) [67]. The expansions are sufficient as we are only interested in the leading terms of the Kaluza-Klein reduced Lagrangian.…”

The heterotic string, the tangent bundle and derived categories

“…At present the analysis of moduli for the heterotic string on a Calabi-Yau threefold and of its duality with F-theory is a technically formidable subject, although some progress has been made (see, for example, [4][5][6][7][8][9]). In this paper we will tackle the simpler question concerning the E 8 × E 8 heterotic string compactified on the tangent bundle of a K3 surface.…”

Calabi-Yau Fourfold Compactifications in String Theory

“…@a p ¼ 0. 59 A similar construction can be made for p-forms. Let us recall that a p-form on M is a totally skew symmetric covariant tensor field of rank p, see (A.5).…”

“…and eliminating the fields F A m via their equations of motion. The result is In order to find the Kähler potential for the scalars in (47) one introduces the coordinates (58), (59). With this redefinition the derivatives (34) take the form…”