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

Higher Spins & Strings

It is natural to believe that the free symmetric product orbifold CFT is dual to the tensionless limit of string theory on AdS3 x S3 x T4. At this point in moduli space, string theory is expected to contain a Vasiliev higher spin theory as a subsector. We confirm this picture explicitly by showing that the large level limit of the N=4 cosets of arXiv:1305.4181, that are dual to a higher spin theory on AdS3, indeed describe a closed subsector of the symmetric product orbifold. Furthermore, we reorganise the full partition function of the symmetric product orbifold in terms of representations of the higher spin algebra (or rather its $W_{\infty}$ extension). In particular, the unbroken stringy symmetries of the tensionless limit are captured by a large chiral algebra which we can describe explicitly in terms of an infinite sum of $W_{\infty}$ representations, thereby exhibiting a vast extension of the conventional higher spin symmetry.Comment: 47 pages; ancillary file included; v2. typos corrected, minor changes in Sec.

Instantons and Non-renormalisation in AdS/CFT

The series of perturbative fluctuations around a multi-instanton contribution to a specific class of correlation functions of supercurrents in $\cal N=4$ supersymmetric SU(N) Yang-Mills theory is examined in the light of the AdS/CFT correspondence. Subject to certain plausible assumptions, we argue that a given term in the 1/N expansion in such a background receives only a finite number of perturbative corrections in the 't Hooft limit. Such instanton non-renormalisation theorems would explain, for example, the exact agreement of certain weak coupling Yang-Mills instanton calculations with the strong coupling predictions arising from D-instanton effects in string theory amplitudes. These non-renormalisation theorems essentially follow from the assumption of a well defined derivative $(\alpha^{\prime})$ expansion in the string theory dual of the Yang-Mills theory.Comment: 11 pages, harvmac, minor typo correcte