On the M2-Brane Index on Noncommutative Crepant Resolutions
arXiv:2111.01102 · doi:10.1007/s11005-022-01579-2
Abstract
On certain M-theory backgrounds which are a circle fibration over a smooth Calabi-Yau, the quantum theory of M2 branes can be studied in terms of the K-theoretic Donaldson-Thomas theory on the threefold. We extend this relation to noncommutative crepant resolutions. In this case the threefold develops a singularity and classical smooth geometry is replaced by the algebra of paths of a certain quiver. K-theoretic quantities on the quiver representation moduli space can be computed via toric localization and result in certain rational functions of the toric parameters. We discuss in particular the case of the conifold and certain orbifold singularities.
38 pages, two Mathematica notebooks are included with the paper; v2 typos corrected; v3 typos corrected, presentation improved, published version
References in corpus (8)
- Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
- Non-commutative Donaldson-Thomas theory and the conifold
- Crystal Melting and Toric Calabi-Yau Manifolds
- Wall crossing in local Calabi Yau manifolds
- Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
- Playing with the index of M-theory
- Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex
- On Framed Quivers, BPS Invariants and Defects