Abstract
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.
Highlights
Large N limits of U (N ) gauge theories have been a source of inspiration in physics, ever since ’t Hooft introduced the idea [1]
In particular the large N limit of gauge theories should be equivalent to some kind of closed string theory
The first contact this idea had with string theory was in the context of non-critical bosonic strings described by c ≤ 1 conformal field theories coupled to two-dimensional gravity
Summary
Large N limits of U (N ) gauge theories have been a source of inspiration in physics, ever since ’t Hooft introduced the idea [1]. Before taking this limit the matrix model would not have a string dual, whereas according to ’t Hooft’s general idea one would have expected it to have In one context this was remedied by a different kind of matrix model introduced by Kontsevich [4], where without taking a double scaling limit one finds an equivalence between a matrix model and non-critical string theory. The AdS/CFT correspondence [7] is in the same spirit as ’t Hooft’s original proposal in that one did not have to take a particular limit to obtain an equivalence Another example of such a strict large N duality is the relation between Chern-Simons gauge theory and A-model topological strings [8] where one does not have to take any particular limit for the equivalence to hold. We discuss the meaning of the double scaling limit from the viewpoint of type IIB superstrings
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