Five-dimensional gauge theory and compactification on a torus. (English) Zbl 1301.81132
Summary: We study five-dimensional minimally supersymmetric gauge theory compactified on a torus down to three dimensions, and its embedding into string/M-theory using geometric engineering. The moduli space on the Coulomb branch is hyperkähler equipped with a metric with modular transformation properties. We determine the one-loop corrections to the metric and show that they can be interpreted as worldsheet and D1-brane instantons in type IIB string theory. Furthermore, we analyze instanton corrections coming from the solitonic BPS magnetic string wrapped over the torus. In particular, we show how to compute the path-integral for the zero-modes from the partition function of the M5 brane, or, using a 2d/4d correspondence, from the partition function of \(N=4\) SYM theory on a Hirzebruch surface.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 83E15 | Kaluza-Klein and other higher-dimensional theories |
| 14M25 | Toric varieties, Newton polyhedra, Okounkov bodies |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 35C08 | Soliton solutions |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
| 53C26 | Hyper-Kähler and quaternionic Kähler geometry, “special” geometry |
| 81T18 | Feynman diagrams |
| 81S40 | Path integrals in quantum mechanics |
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