We show that B-model topological strings on local Calabi-Yau threefolds are large N duals of matrix models, which in the planar limit naturally give rise to special geometry.These matrix models directly compute F-terms in an associated N = 1 supersymmetric gauge theory, obtained by deforming N = 2 theories by a superpotential term that can be directly identified with the potential of the matrix model. Moreover by tuning some of the parameters of the geometry in a double scaling limit we recover (p, q) conformal minimal models coupled to 2d gravity, thereby relating non-critical string theories to type II superstrings on Calabi-Yau backgrounds.
Via compactification on a circle, the matrix model of M-theory proposed by Banks et al suggests a concrete identification between the large N limit of two-dimensional N = 8 supersymmetric Yang-Mills theory and type IIA string theory. In this paper we collect evidence that supports this identification. We explicitly identify the perturbative string states and their interactions, and describe the appearance of D-particle and D-membrane states. * Here we work in string units α ′ = 1. A derivation of (1) from matrix theory and a discussion of our normalizations is given in the appendix.
We consider the topological B-model on local Calabi-Yau geometries. We show
how one can solve for the amplitudes by using W-algebra symmetries which
encodes the symmetries of holomorphic diffeomorphisms of the Calabi-Yau. In the
highly effective fermionic/brane formulation this leads to a free fermion
description of the amplitudes. Furthermore we argue that topological strings on
Calabi-Yau geometries provide a unifying picture connecting non-critical
(super)strings, integrable hierarchies, and various matrix models. In
particular we show how the ordinary matrix model, the double scaling limit of
matrix models, and Kontsevich-like matrix model are all related and arise from
studying branes in specific local Calabi-Yau three-folds. We also show how
A-model topological string on P^1 and local toric threefolds (and in particular
the topological vertex) can be realized and solved as B-model topological
string amplitudes on a Calabi-Yau manifold.Comment: 82 pages, harvmac, 1 figur
We present a microscopic index formula for the degeneracy of dyons in four-dimensional N = 4 string theory. This counting formula is manifestly symmetric under the duality group, and its asymptotic growth reproduces the macroscopic Bekenstein-Hawking entropy. We give a derivation of this result in terms of the type II five-brane compactified on K3, by assuming that its fluctuations are described by a closed string theory on its world-volume. We find that the degeneracies are given in terms of the denominator of a generalized super Kac-Moody algebra. We also discuss the correspondence of this result with the counting of D-brane states.where the 'contour' integral over σ is from 0 to 1 and η(σ) is the Dedekind η-function.The conjectured electric-magnetic SL(2, Z)-duality predicts that there should also exist a solitonic version of the heterotic string that carries pure magnetic charge q m ∈ Γ 22,6 , and thus that a similar formula counts the pure magnetically charged 1/2 BPS states. The generic dyonic states, however, preserve only 1/4 of the supersymmetries and are more * Here and in the subsequent we omit a factor of 16, and therefore count the number of 1/2 BPS multiplets rather than individual states.
In this note we prove an identity that equates the elliptic genus partition
function of a supersymmetric sigma model on the N-fold symmetric product
$M^N/S_N$ of a manifold M to the partition function of a second quantized
string theory on the space $M \times S^1$. The generating function of these
elliptic genera is shown to be (almost) an automorphic form for O(3,2,Z). In
the context of D-brane dynamics, this result gives a precise computation of the
free energy of a gas of D-strings inside a higher-dimensional brane.Comment: 17 pages, latex, 1 figure, to appear in Commun. Math. Phy
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