Abstract
We propose a correspondence between two-dimensional (0, 4) sigma models with target space the moduli spaces of r monopoles, and four-dimensional \( \mathcal{N}=4 \), U(r) Yang-Mills theory on del Pezzo surfaces. In particular, the two- and four-dimensional BPS partition functions are argued to be equal. The correspondence relies on insights from five-dimensional supersymmetric gauge theory and its geometric engineering in M-theory, hence the name “5d/2d/4d correspondence”. We provide various tests of our proposal. The most stringent ones are for r = 1, for which we prove the equality of partition functions.
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Haghighat, B., Manschot, J. & Vandoren, S. A 5d/2d/4d correspondence. J. High Energ. Phys. 2013, 157 (2013). https://doi.org/10.1007/JHEP03(2013)157
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DOI: https://doi.org/10.1007/JHEP03(2013)157