Abstract
We embed the large N Chern–Simons/topological string duality in ordinary superstrings. This corresponds to a large N duality between generalized gauge systems with N=1 supersymmetry in four dimensions and superstrings propagating on noncompact Calabi–Yau manifolds with certain fluxes turned on. We also show that in a particular limit of the N=1 gauge theory system, certain superpotential terms in the N=1 system (including deformations if spacetime is noncommutative) are captured to all orders in 1/N by the amplitudes of noncritical bosonic strings propagating on a circle with self-dual radius. We also consider D-brane/anti-D-brane system wrapped over vanishing cycles of compact Calabi–Yau manifolds and argue that at large N they induce a shift in the background to a topologically distinct Calabi–Yau, which we identify as the ground state system of the brane/anti-brane system.
Highlights
The idea that large N gauge theories should have a phase described by perturbative strings, set forth by ‘t Hooft [1], has been beautifully realized by various examples
The first example of this kind was found by Kontsevich [2], which relates the bosonic string theory coupled to certain matter ((1, 2) minimal model, which is equivalent to pure topological gravity formulated by Witten [3]), to a matrix integral with cubic interaction1
Another example of a string/large N duality was discovered in [9], where it was shown that large N limit of Chern-Simons gauge theory on S3 is equivalent to topological strings on a non-compact Calabi-Yau threefold which is a blow up of the conifold (given by O(−1)+O(−1) bundle over P1)
Summary
The idea that large N gauge theories should have a phase described by perturbative strings, set forth by ‘t Hooft [1], has been beautifully realized by various examples. In particular certain gauge theories at large N are equivalent to superstrings propagating on AdS backgrounds Another example of a string/large N duality was discovered in [9], where it was shown that large N limit of Chern-Simons gauge theory on S3 is equivalent to topological strings on a non-compact Calabi-Yau threefold which is a blow up of the conifold (given by O(−1)+O(−1) bundle over P1). The basic idea is to consider type IIA superstring propagating in the conifold background (which is symplectically the same as T ∗S3) in the presence of N D6 branes wrapped around S3 and filling the spacetime It has been known [13] that the topological string amplitudes for the internal theory on the non-compact Calabi-Yau compute superpotential terms on the left-over R4 worldvolume of the D6 brane. The same configuration of wrapped D-branes/antiD-branes considered in section 6 was studied in [20] in a different context
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