Phase transition of a vector operator in AdS-CFT

Abstract

In this thesis, we studied a vector operator in finite density system through AdS-CFT correspondence. By numerically solving the wave equations of the corresponding vector field in a AdS-RN black hole background geometry, we found poles of the retarded Green's functions in momentum space, which indicate possible instabilities. We found that existence of such poles depends a parameter r,, which indicates possible phase transitions when we adjust K through some critical values. Interestingly, we also found that depending on the conformal dimension of the operator, the transitions in transverse and longitudinal directions may behave in the same way, or in the opposite way.