Deformed boson-fermion correspondence, Q-bosons, and topological strings on the conifold

Abstract

We consider two different physical systems for which the basis of the Hilbert space can be parametrized by Young diagrams: free complex fermions and the phase model of strongly correlated bosons. Both systems have natural, well-known deformations parametrized by a parameter Q: the former one is related to the deformed boson-fermion correspondence introduced by N. Jing, while the latter is the so-called Q-boson, arising also in the context of quantum groups. These deformations are equivalent and can be realized in the same way in the algebra of Hall-Littlewood symmetric functions. Without a deformation, these reduce to Schur functions, which can be used to construct a generating function of plane partitions, reproducing a topological string partition function on $C^3$. We show that a deformation of both systems leads then to a deformed generating function, which reproduces topological string partition function of the conifold, with the deformation parameter Q identified with the size of $P^1$. Similarly, a deformation of the fermion one-point function results in the A-brane partition function on the conifold.

20 pages, 1 figure; version published in JHEP

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Cited by in corpus (14)

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• Universal Character, Phase Model and Topological Strings on ${\mathbb{C}}^3$
• Macdonald topological vertices and brane condensates
• An elliptic topological vertex
• Free fermions in classical and quantum integrable models
• Matrix models and stochastic growth in Donaldson-Thomas theory
• 3D Bosons, 3-Jack polynomials and affine Yangian of $\mathfrak{gl}(1)$
• $Q$-Boson model and relations with integrable hierarchies
• Geometry of the Ground State of Higgs Fields in Next-to-MSSM
• Fermionic gluing principle of the topological vertex
• On fermionic representation of the Gromov-Witten invariants of the resolved Conifold
• Algebraic formulas for the structure constants in symmetric functions