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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.
A warped resolved conifold background of type IIB theory, constructed in hep-th/0701064, is dual to the supersymmetric $SU(N)times SU(N)$ gauge theory with a vacuum expectation value (VEV) for one of the bifundamental chiral superfields. This VEV bre
The warped deformed conifold background of type IIB theory is dual to the cascading $SU(M(p+1))times SU(Mp)$ gauge theory. We show that this background realizes the (super-)Goldstone mechanism where the U(1) baryon number symmetry is broken by expect
When a quantum field theory possesses topological excitations in a phase with spontaneously broken symmetry, these are created by operators which are non-local with respect to the order parameter. Due to non-locality, such disorder operators have non
We obtain the spectrum of glueball masses for the N=1 non-conformal cascade theory whose supergravity dual was recently constructed by Klebanov and Strassler. The glueball masses are calculated by solving the supergravity equations of motion for the
We described the $q$-deformed phase space. The $q$-deformed Hamilton eqations of motion are derived and discussed. Some simple models are considered.