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}
}
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

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

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

Matrix models, topological strings, and supersymmetric gauge theories

On geometry and matrix models

The Topological Vertex

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

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

Topological strings in d < 1

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,
...