Thursday, March 30, 2006

Mithat Ünsal: deconstruction as twisting

Mithat Ünsal from Boston University spoke about his interesting work with David B. Kaplan, his collaborator. The talk was about deconstruction. As we explained in the past, the method of deconstruction allows you to define lattice-like models of gauge theories with supersymmetry in such a way that fine-tuning is no longer necessary or at least the amount of necessary fine-tuning is reduced.

In the continuum limit, one naturally obtains a larger amount of supersymmetry from a discretized starting point with a smaller amount of supersymmetry. From the field theory viewpoint, it is a consequence of some nice and non-generic discrete symmetries. For a string theorist, the main reason can be described as a combination of dualities and various limiting procedures.

If you deconstruct the N=4 gauge theory, only a subset of supersymmetries is preserved before taking the continuum limit. There exists another manipulation with the N=4 gauge theory that preserves a part of supersymmetry: namely topological twisting. Mithat argued that deconstruction and topological twists are closely related.

More concretely, he explained that the discrete symmetries that act on the "theory space" are not really discrete subgroups of the rotational (or Lorentz) symmetry group. Instead, they form a discrete subgroup of a diagonal SO(4) group that generates rotations of the Euclidean spacetime as well as SO(4) rotations inside the SO(6) R-symmetry group.

When you redefine your Euclideanized Lorentz symmetry to include the R-symmetry rotations, you effectively change the spins of the fields - just like in the case of topological twisting. The preserved supercharges are those that look like spin 0 operators after this field and symmetry redefinition.

Mithat also discussed other topics - such as a deformation that changes the U(k N^2) gauge group on one space to a U(k) gauge group on a higher-dimensional space by using some extra phases in the superpotential - phases analogous to the giant fuzzy moose but apparently different in details. (There should also be a link to a paper of Nick Dorey here but I am not sure which paper is the most relevant one.) See their previous available paper for more details and wait for a new one.

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