In gauge/gravity correspondence, the Einstein-scalar theory is dual to quantum field theories minimally deformed by a scalar operator. In this seminar, we will present a new first order formalism in studying the Einstein-scalar theory. (arXiv:1401.0888 and arXiv:1410.1091)
This first order formalism is based on the assumptions of holographic RG flows. After the renormalization procedure, we will derive the renormalized effective action as a functional of running couplings using a set of new conserved quantities. Then we will apply our formalism to holographic Yang-Mills theory. Our results confirm early speculation of the glueball effective potential from conformal anomaly.
In the last part, we will discuss how to generalize our formalism to finite temperature and its connection to the fluid/gravity correspondence. In the meantime, a comparison will be made between our first-order formalism and the Hamilton-Jacobi approach. The difficulties of obtaining finite temperature solutions in the Hamilton-Jacobi approach will be explained as well.
