
Geometries from field theoriesGeometries from field theories 
"/Aoki, Sinya/"Aoki, Sinya ,
"/Kikuchi, Kengo/"Kikuchi, Kengo ,
"/Onogi, Tetsuya/"Onogi, Tetsuya
2015
(
10
)
201510 , Oxford University Press (OUP)
ISSN:20503911
Description
We propose a method to define a d+1d+1dimensional geometry from a dddimensional quantum field theory in the 1/N1/N expansion. We first construct a d+1d+1dimensional field theory from the dddimensional one via the gradientflow equation, whose flow time tt represents the energy scale of the system such that t→0t→0 corresponds to the ultraviolet and t→∞t→∞ to the infrared. We then define the induced metric from d+1d+1dimensional field operators. We show that the metric defined in this way becomes classical in the largeNN limit, in the sense that quantum fluctuations of the metric are suppressed as 1/N1/N due to the largeNN factorization property. As a concrete example, we apply our method to the O(N)O(N) nonlinear σσ 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.
FullText
http://repository.kulib.kyotou.ac.jp/dspace/bitstream/2433/216696/1/ptep_ptv131.pdf