String Theory Seminar
Thursday, February 15, 2018, 4:00pm, 298 Physics (Physics Faculty Lounge)
Amihay Hanany (Imperial College)
The Small E[8] Instanton and the Kraft Procesi Transition
Abstract:- 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.
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