MG12 - Talk detail
 

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Abstract

Localization of Matter in Braneworlds with Broken Lorentz Invariance

We consider deformations of Randall-Sundrum model with broken Lorentz invariance in the bulk. First we consider static setup and prove a theorem that no smooth solution of Einstein equations exist given a matter satisfying the null energy condition (NEC). Then we consider a family of solutions of Einstein equations with broken Lorentz invariance in the bulk and study field fluctuations in these backgrounds. We conclude that localization properties of perturbations depend on asymptotic behavior of the metric tensor. Many known braneworld models can be embedded into our model. In the end we elaborate on time dependent solutions and discuss cosmological manifestations of the deformations we introduced.

Quantum Deformations of the One-Dimensional Hubbard Model

The centrally extended superalgebra psu(2|2)xR^3 was shown to play an important role for the integrable structures of the one-dimensional Hubbard model and of the planar AdS/CFT correspondence. Here we consider its quantum deformation U_q(psu(2|2)xR^3) and derive the fundamental R-matrix. From the latter we deduce an integrable spin chain Hamiltonian with three independent parameters and the corresponding Bethe equations to describe the spectrum on periodic chains. We relate our Hamiltonian to a two-parametric Hamiltonian proposed by Alcaraz and Bariev which can be considered a quantum deformation of the one-dimensional Hubbard model.

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