Matrix Models and Gravitational Corrections

We provide evidence of the relation between supersymmetric gauge theories and matrix models beyond the planar limit. We compute gravitational R^2 couplings in gauge theories perturbatively, by summing genus one matrix model diagrams. These diagrams give the leading 1/N^2 corrections in the large N limit of the matrix model and can be related to twist field correlators in a collective conformal field theory. In the case of softly broken SU(N) N=2 super Yang-Mills theories, we find that these exact solutions of the matrix models agree with results obtained by topological field theory methods.Comment: 18 pages, 1 figure. References added and minor correction

Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory

We derive the analog of the large $N$ Gross-Taylor holomorphic string expansion for the refinement of $q$-deformed $U(N)$ Yang-Mills theory on a compact oriented Riemann surface. The derivation combines Schur-Weyl duality for quantum groups with the Etingof-Kirillov theory of generalized quantum characters which are related to Macdonald polynomials. In the unrefined limit we reproduce the chiral expansion of $q$-deformed Yang-Mills theory derived by de Haro, Ramgoolam and Torrielli. In the classical limit $q=1$, the expansion defines a new $\beta$-deformation of Hurwitz theory wherein the refined partition function is a generating function for certain parameterized Euler characters, which reduce in the unrefined limit $\beta=1$ to the orbifold Euler characteristics of Hurwitz spaces of holomorphic maps. We discuss the geometrical meaning of our expansions in relation to quantum spectral curves and $\beta$-ensembles of matrix models arising in refined topological string theory.Comment: 45 pages; v2: References adde

Massive Vacua of N=1* Theory and S-duality from Matrix Models

In this note we show how Dijkgraaf and Vafa's hypothesis relating the exact superpotential of an N=1 theory to a matrix model can be used to describe all the massive vacua of the N=1*, or mass deformed N=4, theory including the Higgs vacuum. The matrix model computation of the superpotential for each massive vacuum independently yields a modular function of the associated effective coupling in that vacuum which agrees with previously derived results up to a vacuum-independent additive constant. The results in the different massive vacua can be related by the action of SL(2,Z) on the N=4 coupling, thus providing evidence for modular invariance of the underlying N=4 theory.Comment: 9 pages, JHEP.cl

Open G2 Strings

We consider an open string version of the topological twist previously proposed for sigma-models with G2 target spaces. We determine the cohomology of open strings states and relate these to geometric deformations of calibrated submanifolds and to flat or anti-self-dual connections on such submanifolds. On associative three-cycles we show that the worldvolume theory is a gauge-fixed Chern-Simons theory coupled to normal deformations of the cycle. For coassociative four-cycles we find a functional that extremizes on anti-self-dual gauge fields. A brane wrapping the whole G2 induces a seven-dimensional associative Chern-Simons theory on the manifold. This theory has already been proposed by Donaldson and Thomas as the higher-dimensional generalization of real Chern-Simons theory. When the G2 manifold has the structure of a Calabi-Yau times a circle, these theories reduce to a combination of the open A-model on special Lagrangians and the open B+\bar{B}-model on holomorphic submanifolds. We also comment on possible applications of our results.Comment: 55 pages, no figure

N=1* vacua, Fuzzy Spheres and Integrable Systems

We calculate the exact eigenvalues of the adjoint scalar fields in the massive vacua of N=1* SUSY Yang-Mills with gauge group SU(N). This provides a field theory prediction for the distribution of D3 brane charge in the AdS dual. We verify the proposal of Polchinski and Strassler that the D3-brane's lie on a fuzzy sphere in the supergravity limit and determine the corrections to this distribution due to worldsheet and quantum effects. The calculation also provides several new results concerning the equilibrium configurations of the N-body Calogero-Moser Hamiltonian.Comment: 20 page

On topological F-theory

We consider the construction of a topological version of F-theory on a particular Spin(7) 8-manifold which is a Calabi-Yau 3-fold times a 2-torus. We write an action for this theory in eight dimensions and reduce it to lower dimensions using Hitchin's gradient flow method. A symmetry of the eight-dimensional theory which follows from modular transformations of the torus induces duality transformations of the variables of the topological A- and B-models. We also consider target space form actions in the presence of background fluxes in six dimensions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49157/2/jhep052005021.pd

A Six Dimensional View on Twistors

We study the twistor formulation of the classical N=4 super Yang-Mills theory on the quadric submanifold of CP(3|3) X CP(3|3). We reformulate the twistor equations in six dimension, where the superconformal symmetry is manifest, and find a connection to complexified AdS5.Comment: 15 pages, 3 figure