String Seminar

M-theory on nodal Calabi-Yau 3-folds and torsion refined GV-invariants

by Dr Thorsten Schimannek (Utrecht University)

In this talk we will argue that the physics of M-theory and Type IIA strings on nodal CY 3-folds is essentially determined by the geometry of a small resolution, even if the latter is not Kähler.
We will demonstrate this explicitly in the context of nodal CY 3-folds that are double covers of P^3 with the ramification locus being a symmetric determinantal surface.
Using conifold transitions, we prove that in certain cases the exceptional curves in any small resolution are torsion while the same transitions imply that M-theory develops a discrete gauge symmetry.
We further argue that twisted circle compactifications of the 5d theory are dual to IIA compactifications on the nodal CY 3-fold with a flat but topologically non-trivial B-field.
Given knowledge of the A-model topological string free energies associated to all twists one can then extract the torsion refined GV-invariants.
In many cases GLSM techniques and/or mirror symmetry can be used to calculate these topological string free energies at least for low genera.