Rigid limit for hypermultiplets and five-dimensional gauge theories

Abstract

We study the rigid limit of a class of hypermultiplet moduli spaces appearing in Calabi-Yau compactifications of type IIB string theory, which is induced by a local limit of the Calabi-Yau. We show that the resulting hyperkahler manifold is obtained by performing a hyperkahler quotient of the Swann bundle over the moduli space, along the isometries arising in the limit. Physically, this manifold appears as the target space of the non-linear sigma model obtained by compactification of a five-dimensional gauge theory on a torus. This allows to compute dyonic and stringy instantons of the gauge theory from the known results on D-instantons in string theory. Besides, we formulate a simple condition on the existence of a non-trivial local limit in terms of intersection numbers of the Calabi-Yau, and find an explicit form for the hypermultiplet metric including corrections from all mutually non-local D-instantons, which can be of independent interest.

38+18+5 pages, 2 figures, fixed misprints in v2

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• Euclidean D-branes in Type IIB string theory on Calabi-Yau threefolds
• Exploring 5d BPS Spectra with Exponential Networks
• S-duality and refined BPS indices
• Black holes and higher depth mock modular forms
• Hypermultiplet metric and NS5-instantons
• Generalized Toric Polygons, T-branes, and 5d SCFTs
• All partial breakings in $\mathcal{N}=2$ supergravity with a single hypermultiplet
• Mock modularity at work, or black holes in a forest
• S-duality and the universal isometries of q-map spaces