Towards a diagrammatic derivation of the Veneziano-Yankielowicz-Taylor superpotential

We show how it is possible to integrate out chiral matter fields in N=1 supersymmetric theories and in this way derive in a simple diagrammatic way the $N_f S \log S - S \log \det X$ part of the Veneziano-Yankielowicz-Taylor superpotential.Comment: 8 pages, 2 figure

Topological B-Model and \hat{c}=1 Fermionic Strings

We construct topological B-model descriptions of \hat{c}=1 strings, and corresponding Dijkgraaf-Vafa type matrix models and quiver gauge theories.Comment: 6 pages, Contribution to the 37th International Symposium Ahrenshoop on the Theory of Elementary Particle

Konishi Anomalies and N=1 Curves

We present a brief summary of exact results on the non-perturbative effective superpotential of N=1 supersymmetric gauge theories based on generalized Konishi anomaly equations. In particular we consider theories with classical gauge groups and chiral matter in two-index tensor representations. All these theories can be embedded into theories with unitary gauge group and adjoint matter. This embedding can be used to derive expressions for the exact non-perturbative superpotential in terms of the 1/N expansion of the free energy of the related matrix models.Comment: 6 pages, contribution to the proceedings of the 37th International Symposium Ahrenshoop on the Theory of Elementary Particles; v2: References adde

Quantum parameter space in super Yang-Mills, II

In [1] (hep-th/0211069), the author has discussed the quantum parameter space of the N=1 super Yang-Mills theory with one adjoint Higgs field Phi, tree-level superpotential W_tree = m (Phi^2)/2 + g (Phi^3)/3$, and gauge group U(Nc). In particular, full details were worked out for U(2) and U(3). By discussing higher rank gauge groups like U(4), for which the classical parameter space has a large number of disconnected components, we show that the phenomena discussed in [1] are generic. It turns out that the quantum space is connected. The classical components are related in the quantum theory either through standard singularities with massless monopoles or by branch cuts without going through any singularity. The branching points associated with the branch cuts correspond to new strong coupling singularities, which are not associated with vanishing cycles in the geometry, and at which glueballs can become massless. The transitions discussed recently by Cachazo, Seiberg and Witten are special instances of those phenomena.Comment: 12 pages including 2 large figure

The Mathematics of Fivebranes

Fivebranes are non-perturbative objects in string theory that generalize two-dimensional conformal field theory and relate such diverse subjects as moduli spaces of vector bundles on surfaces, automorphic forms, elliptic genera, the geometry of Calabi-Yau threefolds, and generalized Kac-Moody algebras.Comment: 10 pages, 2 figures, Lecture at ICM'9

Derivation of the Konishi anomaly relation from Dijkgraaf-Vafa with (Bi-)fundamental matters

We explicitly write down the Feynman rules following the work of Dijkfraaf, Vafa and collaborators for N=1 super Yang-Mills having products of SU groups as the gauge group and matter chiral superfields in adjoint, fundamental, and bi-fundamental representations without baryonic perturbations. As an application of this, we show expectation values calculated by these methods satisfy the Konishi anomaly relation.Comment: 6 pages, no figures. v2: A few arguments improved, conclusion not change

Exact superpotentials in N=1 theories with flavor and their matrix model formulation

In this note we investigate the effective superpotential of an N=1 SU(N_c) gauge theory with one adjoint chiral multiplet and N_f fundamental chiral multiplets. We propose a matrix model prescription in which only matrix model diagrams with less than two boundaries contribute to the gauge theory effective superpotential. This prescription reproduces exactly the known gauge theory physics for all N_f and $N_c$. For N_f < N_c this is given by the Affleck-Dine-Seiberg superpotential. For N_f > N_c we present arguments leading to the conclusion that the dynamics of these theories is also reproduced by the matrix model.Comment: 12 pages, Latex; v2: Typos, references, presentation improve

More Superstrings from Supergravity

The four six-dimensional ``little string'' theories are all described in the infinite momentum frame (IMF) as matrix theories by non-trivial 1+1 dimensional infra-red fixed points. We characterize these fixed points using supergravity. Starting from the matrix theory definition of M5-branes, we derive an associated dual supergravity description of the fixed point theories, arising as the near horizon geometry of certain brane configurations. These supergravity solutions are all smooth, and involve three dimensional Anti-de Sitter space AdS_3. They therefore provide a complete description of the fixed point theories, and hence the IMF little string theories, if the AdS/CFT correspondence holds.Comment: 17 pages, harvmac.tex; epsf.tex for two decorative figures (References added.

Konishi anomaly and N=1 effective superpotentials from matrix models

We discuss the restrictions imposed by the Konishi anomaly on the matrix model approach to the calculation of the effective superpotentials in N=1 SUSY gauge theories with different matter content. It is shown that they correspond to the anomaly deformed Virasoro $L_0$ constraints .Comment: Latex, 8 pages, misprint and the normalization of the condensate in the elliptic model are correcte

Seiberg Duality in Matrix Models II

In this paper we continue the investigation, within the context of the Dijkgraaf-Vafa Programme, of Seiberg duality in matrix models as initiated in hep-th/0211202, by allowing degenerate mass deformations. In this case, there are some massless fields which remain and the theory has a moduli space. With this illustrative example, we propose a general methodology for performing the relevant matrix model integrations and addressing the corresponding field theories which have non-trivial IR behaviour, and which may or may not have tree-level superpotentials.Comment: 11 pages, comments adde