From E_8 to F via T

TL;DR

This paper explores how T-duality and F-theory naturally emerge from the E_8 gauge bundle perspective in M-theory, linking various dualities and topological features through bundle constructions and compactifications.

Contribution

It introduces a novel framework connecting E_8 bundles with T-duality and F-theory, providing new insights into their geometric and topological origins in M-theory.

Findings

Reproduces T-duality between NS5-branes and KK-monopoles

Derives F-theory monodromy from bundle constructions

Confirms Romans mass as a central extension of LE_8

Abstract

We argue that T-duality and F-theory appear automatically in the E_8 gauge bundle perspective of M-theory. The 11-dimensional supergravity four-form determines an E_8 bundle. If we compactify on a two-torus, this data specifies an LLE_8 bundle where LG is a centrally-extended loopgroup of G. If one of the circles of the torus is smaller than sqrt(alpha') then it is also smaller than a nontrivial circle S in the LLE_8 fiber and so a dimensional reduction on the total space of the bundle is not valid. We conjecture that S is the circle on which the T-dual type IIB theory is compactified, with the aforementioned torus playing the role of the F-theory torus. As tests we reproduce the T-dualities between NS5-branes and KK-monopoles, as well as D6 and D7-branes where we find the desired F-theory monodromy. Using Hull's proposal for massive IIA, this realization of T-duality allows us to confirm that the Romans mass is the central extension of our LE_8. In addition this construction immediately reproduces the conjectured formula for global topology change from T-duality with H-flux.