The Small E[8] Instanton and the Kraft Procesi Transition

The Small E[8] Instanton and the Kraft Procesi Transition

###### String Theory Seminar

#### Amihay Hanany (Imperial College)

**Thursday, February 15, 2018 -4:00pm to 5:00pm**

One of the simplest (1,0) supersymmetric theories in six dimensions lives on the world volume of one M5 brane at a D type singularity C^2/D[k]. The low energy theory is given by an SQCD theory with Sp(k-4) gauge group, a precise number of 2k flavors which is anomaly free, and a scale which is set by the inverse gauge coupling. The Higgs branch at finite coupling H[f] is a closure of a nilpotent orbit of D[2k] and develops many more flat directions as the inverse gauge coupling is set to zero (violating a standard lore that wrongly claims the Higgs branch remains classical). The quaternionic dimension grows by 29 for any k and the Higgs branch stops being a closure of a nilpotent orbit for k>4, with an exception of k=4 where it becomes min[E[8]], the closure of the minimal nilpotent orbit of E[8], thus having a rare phenomenon of flavor symmetry enhancement in six dimensions. Geometrically, the natural inclusion of H[f] ⊂ H[∞] fits into the Brieskorn Slodowy theory of transverse slices, and the transverse slice is computed to be min[E[8]] for any k>3. This is identified with the well known small E[8] instanton transition where 1 tensor multiplet is traded with 29 hypermultiplets, thus giving a physical interpretation to the geometric theory. By the analogy with the classical case, we call this the Kraft Procesi transition.