The Holographic Geometry of the Renormalization Group and Higher Spin Symmetries

Understand

We consider the Wilson-Polchinski exact renormalization group applied to the generating functional of single-trace operators at a free-fixed point in $d=2+1$ dimensions.

• By exploiting the rich symmetry structure of free field theory, we study the geometric nature of the RG equations and the associated Ward identities.
• The geometry, as expected, is holographic, with $AdS$ spacetime emerging correspondent with RG fixed points.
• The field theory construction gives us a particular vector bundle over the $d+1$-dimensional RG mapping space, called a jet bundle, whose structure group arises from the linear orthogonal bi-local transformations of the bare fields in the path integral.