Pure and Applied Mathematics Quarterly

Volume 18 (2022)

Number 4

Special issue celebrating the work of Herb Clemens

Guest Editor: Ron Donagi

Dimensional reduction of B-fields in F-theory

Pages: 1621 – 1660

DOI: https://dx.doi.org/10.4310/PAMQ.2022.v18.n4.a10


Sheldon Katz (Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Il., U.S.A.)

Washington Taylor (Center for Theoretical Physics, Department of Physics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)


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.

The work of S.K. is partially supported by NSF grant DMS-1802242.

The work of W.T. is supported by DOE grant DE-SC00012567.

Received 9 November 2021

Received revised 18 April 2022

Accepted 13 May 2022

Published 25 October 2022