Dijkgraaf-Vafa theory as large-N reduction

We construct a large-N twisted reduced model of the four-dimensional super Yang-Mills theory coupled to one adjoint matter. We first consider a non-commutative version of the four-dimensional superspace, and then give the mapping rule between matrices and functions on this space explicitly. The supersymmetry is realized as a part of the internal $U(\infty)$ gauge symmetry in this reduced model. Our reduced model can be compared with the Dijkgraaf-Vafa theory that claims the low-energy glueball superpotential of the original gauge theory is governed by a simple one-matrix model. We show that their claim can be regarded as the large-N reduction in the sense that the one-matrix model they proposed can be identified with our reduced model. The map between matrices and functions enables us to make direct identities between the free energies and correlators of the gauge theory and the matrix model. As a by-product, we can give a natural explanation for the unconventional treatment of the one-matrix model in the Dijkgraaf-Vafa theory where eigenvalues lie around the top of the potential.Comment: 34 pages, LaTeX, to appear in Nucl. Phys.

Design and Synthesis of Novel Lamellarin D Analogues Targeting Topoisomerase I

ナノダイナミクス国際シンポジウム 平成22年1月21日(木) 於長崎大学Nagasaki Symposium on Nano-Dynamics 2010 (NSND2010), January 21, 2010, Nagasaki University, Nagasaki, Japan, Invited Lectur

Efficient Total Syntheses of Heterocyclic Marine Alkaloids, Lamellarins

Nagasaki Symposium on Nano-Dynamics 2008 (NSND2008) 平成20年1月29日(火)於長崎大学 Poster Presentatio

Super Yang-Mills Theory from a Supermatrix Model

It is known that Yang-Mills theories on non-commutative space can be derived from large-N reduced models. Gauge fields in non-commutative Yang-Mills theories can be described as fluctuations of matrices expanded about an appropriate classical solution of the reduced models. We investigate a generalization of this procedure in superfield formalism. We show that we can construct a supermatrix model such that D=4 $\N=1$ super Yang-Mills theory can be derived from it. In addition, we can couple matter supermatrices to this supermatrix model and also construct models corresponding to $\N=2$ and $\N=4$ super Yang-Mills theories. In these investigations, we need to introduce a new non-anti-commutative superspace, and we investigate the definition of field theories on this space.Comment: 24 pages, published versio

Direct derivation of the Veneziano-Yankielowicz superpotential from matrix model

We derive the Veneziano-Yankielowicz superpotential directly from the matrix model by fixing the measure precisely. The essential requirement here is that the effective superpotential of the matrix model corresponding to the ${\cal N}=4$ supersymmetric Yang-Mills theory vanishes except for the tree gauge kinetic term. Thus we clarify the reason why the matrix model reproduces the Veneziano-Yankielowicz superpotential correctly in the Dijkgraaf-Vafa theory.Comment: 13 pages, to appear in Phys. Lett.

Non-planar Diagrams and Non-commutative Superspace in Dijkgraaf-Vafa theory

We consider the field theory on non-commutative superspace and non-commutative spacetime that arises on D-branes in Type II superstring theory with a constant self-dual graviphoton and NS-NS $B$ field background. $\N=1$ supersymmetric field theories on this non-commutative space (such theories are called $\N=1/2$ supersymmetric theories.) can be reduced to supermatrix models as in hep-th/0303210 \cite{KKM}. We take an appropriate commutative limit in these theories and show that holomorphic quantities in commutative field theories are equivalent to reduced models, including non-planar diagrams to which the graviphoton contributes. This is a new derivation of Dijkgraaf-Vafa theory including non-planar diagrams.Comment: 15 pages, 1 figure, the version to appear in Phys. Lett.

Supersymmetric large-N reduced model with multiple matter

We showed in hep-th/0303210 that the Dijkgraaf-Vafa theory can be regarded as large-N reduction in the case of $\mathcal{N}=1$ supersymmetric U(N) gauge theories, with single adjoint matter. We generalize this to gauge theories with gauge groups being the products of some unitary groups coupled to bifundamental or fundamental matter. We show that some large-N reduced models of these theories are supermatrix models, whose free energy is equivalent to the prepotentials of the original gauge theories. The supermatrix model in our approach should be taken in the Veneziano limit $N_c,N_f \to \infty$ with $N_f/N_c$ fixed.Comment: 24 pages, LaTeX. to appear in Nucl. Phys.