# The vertex on a strip

@article{Iqbal2004TheVO, title={The vertex on a strip}, author={Amer Iqbal and Amir-Kian Kashani-Poor}, journal={Advances in Theoretical and Mathematical Physics}, year={2004}, volume={10}, pages={317-343} }

We demonstrate that for a broad class of local Calabi-Yau geometries built around a string of IP{sup 1}s--those whose toric diagrams are given by triangulations of a strip--we can derive simple rules, based on the topological vertex, for obtaining expressions for the topological string partition function in which the sums over Young tableaux have been performed. By allowing non-trivial tableaux on the external legs of the corresponding web diagrams, these strips can be used as building blocks…

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## References

SHOWING 1-10 OF 19 REFERENCES

### Symmetric functions and Hall polynomials

- Mathematics
- 1979

I. Symmetric functions II. Hall polynomials III. HallLittlewood symmetric functions IV. The characters of GLn over a finite field V. The Hecke ring of GLn over a finite field VI. Symmetric functions…

### 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…

### SU(N) Geometries and Topological String Amplitudes

- Mathematics, Physics
- 2003

It has been conjectured recently that the field theory limit of the topological string partition functions, including all higher genus contributions, for the family of CY3folds giving rise to N = 2…

### Introduction to Toric Varieties.

- Mathematics
- 1993

Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic…

### Seiberg-Witten prepotential from instanton counting

- Geology
- 2002

Direct evaluation of the Seiberg-Witten prepotential is accomplished following the localization programme suggested in [1]. Our results agree with all low-instanton calculations available in the…

### Geometric transitions and open string instantons

- Physics
- 2002

We investigate the physical and mathematical structure of a new class of geometric transitions proposed by Aganagic and Vafa. The distinctive aspect of these transitions is the presence of open…

### A mathematical theory of the topological vertex

- Mathematics
- 2004

We have developed a mathematical theory of the topological vertex--a theory that was original proposed by M. Aganagic, A. Klemm, M. Marino, and C. Vafa in hep-th/0305132 on effectively computing…

### All Loop Topological String Amplitudes from Chern-Simons Theory

- Mathematics
- 2004

We demonstrate the equivalence of all loop closed topological string amplitudes on toric local Calabi-Yau threefolds with computations of certain knot invariants for Chern-Simons theory. We use this…

### Geometric transitions, del Pezzo surfaces and open string instantons

- Mathematics
- 2002

Department of Mathematics, University of Pennsylvania,Philadelphia, PA 19104-6395, USAemail: grassi@math.upenn.eduWe continue the study of a class of geometric transitions proposed by Aganagicand…

### On the Gauge Theory/Geometry Correspondence

- Mathematics
- 1998

The 't Hooft expansion of SU(N) Chern-Simons theory on $S^3$ is proposed to be exactly dual to the topological closed string theory on the $S^2$ blow up of the conifold geometry. The $B$-field on the…