טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentOvdat Omrie
SubjectLinear Response in 4D Spatially Modulated Phases
DepartmentDepartment of Physics
Supervisor Professor Amos Yarom


Abstract

The AdS/CFT correspondence provides a dictionary that relates classic asymptotically anti de-Sitter (AdS) gravitational systems and CFT. Using this dictionary one can evaluate physical quantities in the CFT side such as n-point correlators from the near AdS boundary behavior of fields in the gravity side. The fields on the gravity side are determined through the solutions of the Einstein equations and prescribed boundary conditions. Of special interest are many body quantum states described at equilibrium by thermodynamic quantities such as temperature, chemical potential entropy and free energy. The gravity dual of these states are asymptotically AdS black holes. It is possible that under the same boundary conditions there will be more than one possible black hole solution. In this case, the interpretation is that the different solutions correspond to different possible phases and the more stable phase will be the one that has the least free energy. When the lowest free energy is shared by two different phases a phase transition occurs. In this thesis we are interested in a setup where at high temperature there is a homogenous and isotropic phase and under some critical temperature the system undergoes a second order phase transition and a spatially modulated phase emerges. The phase transition is accompanied by a spontaneous breaking of translational symmetry in one of the spatial directions. The gravity dual of these phases are spatially modulated black holes often called 'striped'. In this thesis we analytically find 5 dimensional striped black hole solutions in a probe approximation and near the phase transition. We then compute the response of the spatially modulated background to time dependent electric field and metric perturbations. In particular, we obtain the conductivity tensor in the low frequency limit and the counterpart of the shear viscosity to entropy density ratio in the new phase.