Path integral action and exact renormalization group dualities for quantum systems in noncommutative plane

We employ the path integral approach developed in [29] to discuss the (generalized) harmonic oscillator in a noncommutative plane. The action for this system is derived in the coherent state basis with additional degrees of freedom. From this the action in the coherent state basis without any additional degrees of freedom is obtained. This gives the ground state spectrum of the system. We then employ the exact renormalization group approach to show that an equivalence can be constructed between this (noncommutative) system and a commutative system.Comment: 8 pages Latex, revisions made, equations corrected, To appear in Euro.Phys.Lett. arXiv admin note: text overlap with arXiv:1402.615

Analytic study of properties of holographic superconductors away from the probe limit

In this paper, based on the Sturm-Liouville eigenvalue approach, we analytically investigate the properties of holographic superconductors in the background of pure Einstein and Gauss-Bonnet gravity taking into account the backreaction of the spacetime. Higher value of the backreaction parameter results in a harder condensation to form in both cases. The analytical results obtained are found to be in good agreement with the existing numerical results.Comment: 9 pages Late