Geometries from field theories
Abstract
We propose a method to define a d+1dimensional geometry from a ddimensional quantum field theory in the 1/N expansion. We first construct a d+1dimensional field theory from the ddimensional one via the gradientflow equation, whose flow time t represents the energy scale of the system such that trArr 0 corresponds to the ultraviolet and trArr infty to the infrared. We then define the induced metric from d+1dimensional field operators. We show that the metric defined in this way becomes classical in the largeN limit, in the sense that quantum fluctuations of the metric are suppressed as 1/N due to the largeN factorization property. As a concrete example, we apply our method to the O(N) nonlinear σ model in two dimensions. We calculate the 3D induced metric, which is shown to describe an antide Sitter space in the massless limit. Finally, we discuss several open issues for future studies.
 Publication:

Progress of Theoretical and Experimental Physics
 Pub Date:
 October 2015
 DOI:
 10.1093/ptep/ptv131
 arXiv:
 arXiv:1505.00131
 Bibcode:
 2015PTEP.2015J1B01A
 Keywords:

 B30;
 B34;
 B35;
 B37;
 B39;
 High Energy Physics  Theory;
 High Energy Physics  Lattice
 EPrint:
 9 pages, the title has been changed, and some contents have also been modified. This version is accepted for a publication in PTEP