Playing with the index of M-theory
arXiv:2103.10271 · doi:10.1007/s00220-022-04479-7
Abstract
Motivated by M-theory, we study rank n K-theoretic Donaldson-Thomas theory on a toric threefold X. In the presence of compact four-cycles, we discuss how to include the contribution of D4-branes wrapping them. Combining this with a simple assumption on the (in)dependence on Coulomb moduli in the 7d theory, we show that the partition function factorizes and, when X is Calabi-Yau and it admits an ADE ruling, it reproduces the 5d master formula for the geometrically engineered theory on A(n-1) ALE space, thus extending the usual geometric engineering dictionary to n>1. We finally speculate about implications for instanton counting on Taub-NUT.
arXiv commentv2: expand section 2.3, add subsections 4.2.1 and 5.4.1, fix typos
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