Bulk Criticality and Boundary Spectra in AdS from Matrix Product States

Abstract

We study interacting scalar quantum field theories in anti-de Sitter (AdS) space using a tensor-network approach based on matrix product states. We develop methods for extracting low-lying boundary spectra from global-AdS energy levels, probing bulk criticality through finite-size scaling in the AdS radius, and identifying conformal boundary conditions. Applying these methods to scalar ${\varphi }^4$ theory in ${\mathrm{AdS}}_2$, we compute the lowest non-trivial ${\mathbb{Z}}_2$-odd and even boundary scaling dimensions non-perturbatively. We then locate the bulk ${\mathbb{Z}}_2$ symmetry-breaking transition and extract critical exponents and central charge consistent with the 2D Ising universality class. At the critical point, we determine the low-lying boundary spectrum and use it to identify the ${\mathbb{Z}}_2$-preserving free/ordinary Ising conformal boundary condition, thereby characterising both the bulk and boundary universality classes.

Comments: 36 pages, 6 figures