Quantum Critical Dynamics from Black Holes

Abstract

This is a short introduction to applications of the holographic correspondence, written primarily for condensed matter theorists. It will become a chapter of the book "Understanding Quantum Phase Transitions," edited by Lincoln D. Carr (Taylor & Francis, Boca Raton, 2010).

Figures (7)

• Figure 1: The extra spatial dimension of the gravitational dual represents the renormalisation group flow of the quantum field theory.
• Figure 2: A source $J$ for an operator ${\mathcal{O}}$ in the QFT corresponds to a boundary condition $\delta \phi_{(0)}$ for the bulk field $\phi$ dual to ${\mathcal{O}}$. Solving the bulk equations of motion for $\phi$ allows computation of the expectation value $\langle {\mathcal{O}} \rangle$ due to the source $J$.
• Figure 3: The strongly coupled QFT at finite temperature is dual to classical gravity in a black hole spacetime.
• Figure 4: The strongly coupled QFT at finite temperature and finite charge density is dual to classical gravity in a charged black hole spacetime.
• Figure 5: Zero momentum quasinormal poles of charged bosons at temperature $T/\mu = 0.075$. The operators ${\mathcal{O}}$ have scaling dimension $\Delta=3$ in 2+1 dimensions and charges $q=0$ (left plot) and $q=2$ (right plot).