## October 22, 2002

I’m in Cambridge, MA, but I thought I’d mention a couple of papers of recent interest.

David Berenstein had a nice paper today in which he investigates a couple of gauge theories with quantum-deformed moduli spaces from the matrix-model approach of Dijkgraaf-Vafa. Probably the most interesting example is an SU(2) gauge theory with three adjoint chiral multiplets with superpotential

W = g ( Tr( XYZ+ZYX)–2Tr(X+Y+Z) )

This is the worldvolume gauge theory on a bulk probe brane near the C3/Z2 ×Z2 orbifold with discrete torsion.

Another intriguing (“intriguing” is all I’m about to commit to right now) paper appeared yesterday by Yonatan Zunger.

In the context of matrix theory, one can reproduce various D-brane configurations by letting the X’s of the matrix theory (at finite N, they are NxN matrices) in the infinite N limit turn into operators which act as derivations on some algebra, A.

Actually, even in empty flat space , we can consider X0 = d/dt + A0 as a tenth “X”, which acts as a derivation on the algebra A= C(R)×MN. In flat space, the rest of the X’s (acting by commutator, [X,.]) are “inner” derivations of this algebra. In matrix string theory, two derivations are “outer”, and eight are “inner”.

His general proposal is to consider an arbitrary algebra, A, with some number of inner and some number of outer derivations. This he proposes as a generalized D-brane configuration in the matrix realization. It is characterized by k (k >2) classes in the Hochschild Cohomology H1(A) (essentially, the number of X’s which are outer derivations), and a class in the algebraic K-theory K0(A), which gives the “charge” of the D-brane configuration.

Anyway, time to get myself some dinner. More later …

Posted by distler at October 22, 2002 6:22 PM

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