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.
Highlights
Five-dimensional N = 1 supersymmetric gauge theories play an important role in our understanding of supersymmetric gauge theories in general
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
A geometric description of twisted circle compactifications of 6d N = (1, 0) SCFTs has been analysed with the aim to fully characterise the resulting 5d theory
Summary
Equation (3.75) shows the 5d frame where f1 and e1 have been exchanged and the resulting intersection matrix is the Cartan matrix of the 5d gauge group In all cases we study in this paper, the geometric prepotential we obtain by taking the cube of the Kähler form agrees precisely with the expectation from the corresponding 5d N = 1 QFTs. When discussing fibre-base dual theories, we only present results for one specific 5d duality frame. In the following paragraphs we see how to obtain the prepotential (2.1) from various viewpoints ranging from a parent 6d SCFT to a geometric realisation in terms of intersecting complex rational surfaces
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