Geometry from Matrices via D-branes

In this paper, we give a map from matrices to a commutative geometry from a bound state of a D2-brane and N D0-branes. For this, tachyons in auxiliary unstable D-brane system describing the bound state play crucial roles. We found the map obtained in this way coincides with the recent proposals. We also consider the map from the geometry to matrices in a large N limit and argue that the map is a matrix regularization of geometry.Comment: 15 pages, corrected typos, comments added, minor correction

A Nonperturbative Proof of Dijkgraaf-Vafa Conjecture

In this note we exactly compute the gaugino condensation of an arbitrary four dimensional N=1 supersymmetric gauge theory in confining phase, using the localization technique. This result gives a nonperturbative proof of the Dijkgraaf-Vafa conjecture.Comment: 12 pages, references adde

The Non-Abelian Born-Infeld Action and Noncommutative gauge theory

In this paper we explicitly show the equivalence between the non-Abelian Born-Infeld action, which was proposed by Tseytlin as an effective action on several D-branes, and its noncommutative counterpart for slowly varying fields. This confirms the equivalence between the two descriptions of the D-branes using an ordinary gauge theory with a constant B field background and a noncommutative gauge theory, claimed by Seiberg and Witten. We also construct the general forms of the 2 n-derivative terms for non-Abelian gauge fields which are consistent with the equivalence in the approximation of neglecting (2 n+2)-derivative terms.Comment: 18 pages, LaTeX, no figures. minor corrections, version to appear in JHE

AdS/CFT Correspondence in Operator Formalism

In this paper we study the AdS/CFT correspondence in the operator formalism without assuming the GKPW relation. We explicitly show that the low energy spectrum of the large N limit of CFT, which is realized by a strong coupling gauge theory, is identical to the spectrum of the free gravitational theory in the global AdS spacetime under some assumptions which are expected to be valid. Thus, two theories are equivalent for the low energy region under the assumptions. Using this equivalence, the bulk local field is constructed and the GKPW relation is derived.Comment: 26 pages, references adde

Hyperbolic 3-manifolds and Cluster Algebras

We advocate the use of cluster algebras and their y-variables in the study of hyperbolic 3-manifolds. We study hyperbolic structures on the mapping tori of pseudo-Anosov mapping classes of punctured surfaces, and show that cluster y-variables naturally give the solutions of the edge-gluing conditions of ideal tetrahedra. We also comment on the completeness of hyperbolic structures.Comment: v2: 26 pages, 17 figure