Holographic description of quantum field theory

Abstract

We propose that general D-dimensional quantum field theories are dual to (D+1)-dimensional local quantum theories which in general include objects with spin two or higher. Using a general prescription, we construct a (D+1)-dimensional theory which is holographically dual to the D-dimensional O(N) vector model. From the holographic theory, the phase transition and critical properties of the model in dimensions D>2 are described.

Figures (1)

• Figure 1: Saddle point configuration of $J_{3a}(z)$ (a) in the disordered phase and (b) in the ordered phase. Although the action is quadratic in $J_{3a}$ in the bulk, the boundary action drives the phase transition. When ${\cal J}_2$ is sufficiently negative, a Mexican-hat potential at the boundary drags $J_{3a}(z)$ away from $J_{3a}(z)=0$ in the bulk. At the critical point, $J_{3a}$ at the IR boundary $z=\infty$ is more or less free to fluctuate, generating algebraic correlations between fields inserted at the UV boundary $z=0$.