BPS states in Matrix Strings

Matrix string theory (or more generally U-Duality) requires Super Yang-Mills theory to reflect a stringy degeneracy of BPS short multiplets. These are found as supersymmetric states in the Yang-Mills carrying (fractionated) momentum, or in some cases, instanton number. Their energies also agree with those expected from M(atrix) theory. A nice parallel also emerges in the relevant cases, between momentum and instanton number, (both integral as well as fractional) providing evidence for a recent conjecture relating the two.Comment: Harvmac, 14 pages (big

N=1{\cal N}=1 Theories and a Geometric Master Field

We study the large $N$ limit of the class of U(N) {\CN}=1 SUSY gauge theories with an adjoint scalar and a superpotential $W(\P)$. In each of the vacua of the quantum theory, the expectation values \laTr$\Phi^p$\ra are determined by a master matrix $\Phi_0$ with eigenvalue distribution \rho_{GT}(\l). \rho_{GT}(\l) is quite distinct from the eigenvalue distribution \rho_{MM}(\l) of the corresponding large $N$ matrix model proposed by Dijkgraaf and Vafa. Nevertheless, it has a simple form on the auxiliary Riemann surface of the matrix model. Thus the underlying geometry of the matrix model leads to a definite prescription for computing \rho_{GT}(\l), knowing \rho_{MM}(\l).Comment: 16 pages; v2. Further elaboration in Sec. 5 on the relation between gauge and matrix eigenvalue distributions, v3: Minor change

Free Field Theory as a String Theory?

An approach to systematically implement open-closed string duality for free large $N$ gauge theories is summarised. We show how the relevant closed string moduli space emerges from a reorganisation of the Feynman diagrams contributing to free field correlators. We also indicate why the resulting integrand on moduli space has the right features to be that of a string theory on $AdS$.Comment: 10 pages, 1 figure, Contribution to Strings 2004 (Paris) proceeding