Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-08-18
JHEP0810:104,2008
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, 1 figure; version published in JHEP
Scientific paper
10.1088/1126-6708/2008/10/104
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.
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