Fibre-base duality of 5d KK theories

TL;DR

This paper explores the geometric duality in 5d KK theories derived from 6d superconformal theories, revealing a fibre-base duality that exchanges 6d and 5d perspectives through Calabi-Yau geometries.

Contribution

It introduces a novel geometric interpretation of fibre-base duality in local Calabi-Yau 3-folds, explicitly incorporating gauge couplings and mass parameters for accurate prepotential parametrization.

Findings

Fibre-base duality relates 6d and 5d theories via swapping base and fibre curves.

The duality is realized by exchanging surfaces with zero self-intersection.

Results unify geometric and field-theoretic descriptions of KK theories.

Abstract

We study circle compactifications of 6d superconformal field theories giving rise to 5d rank 1 and rank 2 Kaluza-Klein theories. We realise the resulting theories as M-theory compactifications on local Calabi-Yau 3-folds and match the prepotentials from geometry and field theory. One novelty in our approach is that we include explicit dependence on bare gauge couplings and mass parameters in the description which in turn leads to an accurate parametrisation of the prepotential including all parameters of the field theory. We find that the resulting geometries admit "fibre-base" duality which relates their six-dimensional origin with the purely five-dimensional quantum field theory interpretation. The fibre-base duality is realised simply by swapping base and fibre curves of compact surfaces in the local Calabi-Yau which can be viewed as the total space of the anti-canonical bundle over such surfaces. Our results show that such swappings precisely occur for surfaces with a zero self-intersection of the base curve and result in an exchange of the 6d and 5d pictures.