Abstract
We study the proposal that a (d+1)-dimensional induced metric is constructed from a d-dimensional field theory using gradient flow. Applying the idea to the O(N) ϕ4 model and normalizing the flow field, we have shown in the large N limit that the induced metric is finite and universal in the sense that it does not depend on the details of the flow equation and the original field theory except for the renormalized mass, which is the only relevant quantity in this limit. We have found that the induced metric describes Euclidean anti-de Sitter (AdS) space in both ultraviolet (UV) and infrared (IR) limits of the flow direction, where the radius of the AdS is bigger in the IR than in the UV.
Highlights
The anti-de Sitter/conformal field theory (AdS/CFT) correspondence [1] is a surprising but significant finding in field theories and string theories
We have introduced the
This shows that the divergence that appeared in the perturbation expansion disappears in the large N expansion where potentially divergent contributions are summed up to an exponential form
Summary
The anti-de Sitter/conformal field theory (AdS/CFT) correspondence [1] (or, more generally, the gravity/gauge theory correspondence) is a surprising but significant finding in field theories and string theories. In the example mentioned above, the threedimensional induced metric, constructed from a product of three-dimensional flow fields at the same point, is free from UV divergences in the large N limit. If the original twodimensional fields were used directly to define the two-dimensional metric, it would badly diverge These two special properties allow us to infer that (the VEV of) the induced metric describes a geometry. (The modified flow equation can avoid this divergence [13].) As shown later, the induced metric ĝμν in Eq (3) is free from such UV divergences in the large N limit. Showing that the induced metric ĝμν becomes classical in the large N limit, and quantum fluctuations are sub-leading and calculable in the large N expansion.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
