On Flux Quantization in F-Theory II: Unitary and Symplectic Gauge Groups

TL;DR

This paper investigates the quantization conditions of G-flux in F-theory compactifications with unitary and symplectic gauge groups, revealing a half-integer shift linked to non-spin branes and exploring its relation to type IIB flux quantization.

Contribution

It explicitly constructs four-cycles for flux period calculations and uncovers a universal half-integer shift in flux quantization for certain gauge groups, except SU(3).

Findings

Half-integer flux shift occurs for non-spin 7-branes.

The shift applies to all unitary and symplectic groups except SU(3).

Analysis includes cases with additional U(1) flavor groups.

Abstract

We study the quantization of the M-theory G-flux on elliptically fibered Calabi-Yau fourfolds with singularities giving rise to unitary and symplectic gauge groups. We seek and find its relation to the Freed-Witten quantization of worldvolume fluxes on 7-branes in type IIB orientifold compactifications on Calabi-Yau threefolds. By explicitly constructing the appropriate four-cycles on which to calculate the periods of the second Chern class of the fourfolds, we find that there is a half-integral shift in the quantization of G-flux whenever the corresponding dual 7-brane is wrapped on a non-spin submanifold. This correspondence of quantizations holds for all unitary and symplectic gauge groups, except for SU(3), which behaves mysteriously. We also perform our analysis in the case where, in addition to the aforementioned gauge groups, there is also a 'flavor' U(1)-gauge group.