Dimensional Reduction of B-Fields in F-theory

TL;DR

This paper explores the dimensional reduction of B-fields in F-theory using advanced mathematical tools like perverse sheaves and the Decomposition Theorem, providing new insights consistent with established physics results.

Contribution

It introduces a conjectured mathematical framework for normalizable B-fields in F-theory and demonstrates its consistency with known physical and mathematical principles.

Findings

New descriptions of normalizable B-fields in F-theory

Use of the Decomposition Theorem to facilitate computations

Conjecture of a physical framework for B-fields

Abstract

We describe the dimensional reduction of the IIB B-fields in F-theory using a conjectured description of normalizable B-fields in terms of perverse sheaves. Computations are facilitated using the Decomposition Theorem. Many of our descriptions are new, and all our results are all consistent with known results in physics. We also conjecture a physical framework for normalizable B-fields and show consistency with mathematics. We dedicate this paper to Herb Clemens, in admiration for his myriad fundamental contributions to complex algebraic geometry, together with his more recent interest in F-theory in physics. This paper deals with three of Herb's interests: Hodge theory, topology of algebraic varieties, and F-theory, and so is a fitting way for us to express our appreciation for his contributions over a period of more than five decades.