Abstract: |
“Mysterious Duality” was discovered by Iqbal, Neitzke, and Vafa in a 2001 paper. They noticed that toroidal compactifications of M-theory lead to the same series of combinatorial objects as del Pezzo surfaces do, along with numerous mysterious coincidences: both toroidal compactifications and del Pezzo surfaces give rise to the exceptional series E_k; the U-duality group corresponds to the Weyl group W(E_k), arising also as a group of automorphisms of the del Pezzo surface; a collection of various M- and D-branes corresponds to a set of divisors; the brane tension is related to the “area” of the corresponding divisor, etc. The mystery is that it is not at all clear where this duality comes from: ideally, one wishes to reformulate M-theory and its compactifications in terms of del Pezzo surfaces, e.g., as string theory on them. In the talk, I will present another series of mathematical objects: certain versions of multiple loop spaces of the sphere S^4, which are, on the one hand, directly connected to M-theory and its combinatorics, and, on the hand, possess the same combinatorics as the del Pezzo surfaces. This is a report on an ongoing work with Hisham Sati. |