Topological Strings and Integrable Hierarchies

@article{Aganagic2006TopologicalSA,
title={Topological Strings and Integrable Hierarchies},
author={Mina Aganagic and Robbert Dijkgraaf and Albrecht Klemm and Marcos Mari{\~n}o and Cumrun Vafa},
journal={Communications in Mathematical Physics},
year={2006},
volume={261},
pages={451-516}
}
• Published 9 December 2003
• Mathematics
• Communications in Mathematical Physics
We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using -algebra symmetries which encode 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…
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References

SHOWING 1-10 OF 70 REFERENCES

Topological strings and Nekrasov's formulas

• Mathematics, Physics
• 2003
We apply the method of geometric transition and compute all genus topological closed string amplitudes compactified on local F0 by making use of the Chern-Simons gauge theory. We find an exact

Topological $\sigma$-Models and Large-$N$ Matrix Integral

• Mathematics
• 1995
In this paper we describe in some detail the representation of the topological CP1 model in terms of a matrix integral which we have introduced in a previous article. We first discuss the integrable

The Topological Vertex

• Mathematics, Physics
• 2005
We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact toric Calabi-Yau threefolds. The topology of a given Feynman diagram encodes the

Quantum Calabi-Yau and Classical Crystals

• Mathematics
• 2003
We propose a new duality involving topological strings in the limit of the large string coupling constant. The dual is described in terms of a classical statistical mechanical model of crystal

Intersection theory, integrable hierarchies and topological field theory

The last two years have seen the emergence of a beautiful new subject in mathematical physics. It manages to combine a most exotic range of disciplines: two-dimensional quantum field theory,