Babak Haghighat, Jan Manschot, Stefan Vandoren
We propose a correspondence between two-dimensional $(0,4)$ sigma models with target space the moduli spaces of $r$ monopoles, and four-dimensional $\cN=4$, $U(r)$ 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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http://arxiv.org/abs/1211.0513
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