Large N gauge theories and topological cigars

We analyze the conjectured duality between a class of double-scaling limits of a one-matrix model and the topological twist of non-critical superstring backgrounds that contain the N = 2 Kazama-Suzuki SL(2)/U(1) supercoset model. The untwisted backgrounds are holographically dual to double-scaled Little String Theories in four dimensions and to the large N double-scaling limit of certain supersymmetric gauge theories. The matrix model in question is the auxiliary Dijkgraaf-Vafa matrix model that encodes the F-terms of the above supersymmetric gauge theories. We evaluate matrix model loop functions with the goal of extracting information on the spectrum of operators in the dual non-critical bosonic string. The twisted coset at level one, the topological cigar, is known to be equivalent to the c = 1 non-critical string at selfdual radius and to the topological theory on a deformed conifold. In this case, we find that the matrix model double-scaling limit describes a subset of the full spectrum of the c = 1 theory at selfdual radius. In particular, it contains operators that do not satisfy the Seiberg bound.

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