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

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