Yang-Mills interaction from boundary vector model

We construct a non-Abelian spin-1 gauge theory with a cubic interaction in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msub> <a:mrow> <a:mi>AdS</a:mi> </a:mrow> <a:mrow> <a:mn>4</a:mn> </a:mrow> </a:msub> </a:mrow> </a:math> from the exact renormalization group (ERG) flow of a conformal field theory (CFT) in three dimensions. The latter is the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mi>U</c:mi> <c:mi>S</c:mi> <c:mi>p</c:mi> </c:mrow> <c:mo stretchy="false">(</c:mo> <c:mn>2</c:mn> <c:mi>N</c:mi> <c:mo stretchy="false">)</c:mo> </c:math> singlet sector of the free field theory of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mn>2</g:mn> <g:mi>N</g:mi> </g:math> massless complex scalars. The quadratic and cubic terms in the bulk action are those of a gauge fixed version of a (local) gauge invariant action. By construction, this bulk action is the evolution operator for the ERG equation of the boundary theory and thus is guaranteed to reproduce the correct boundary correlators using the usual AdS/CFT prescription. This work expands on the program initiated by one of the authors [A holographic form for Wilson’s RG, ].