TY - JOUR

T1 - Exact renormalization group and higher-spin holography

AU - Leigh, Robert G.

AU - Parrikar, Onkar

AU - Weiss, Alexander B.

N1 - Publisher Copyright:
© 2015 American Physical Society.

PY - 2015/1/6

Y1 - 2015/1/6

N2 - In this paper, we revisit scalar field theories in d space-time dimensions possessing U(N) global symmetry. Following our recent work [1], we consider the generating function of correlation functions of all U(N)-invariant, single-trace operators at the free-fixed point. The exact renormalization group equations are cast as Hamilton equations of radial evolution in a model space-time of one higher dimension, in this case AdSd+1. The geometry associated with the renormalization group equations is seen to emerge naturally out of the infinite jet bundle corresponding to the field theory and suggests their interpretation as higher-spin equations of motion. While the higher-spin equations we obtain are remarkably simple, they are nonlocal in an essential way. Nevertheless, solving these bulk equations of motion in terms of a boundary source, we derive the on-shell action and demonstrate that it correctly encodes all of the correlation functions of the field theory, written as "Witten diagrams." Since the model space-time has the isometries of the fixed point, it is possible to construct new higher-spin theories defined in terms of geometric structures over other model space-times. We illustrate this by explicitly constructing the higher-spin renormalization group equations corresponding to the z=2 nonrelativistic free field theory in D spatial dimensions. In this case, the model space-time is the Schrödinger space-time, SchrD+3.

AB - In this paper, we revisit scalar field theories in d space-time dimensions possessing U(N) global symmetry. Following our recent work [1], we consider the generating function of correlation functions of all U(N)-invariant, single-trace operators at the free-fixed point. The exact renormalization group equations are cast as Hamilton equations of radial evolution in a model space-time of one higher dimension, in this case AdSd+1. The geometry associated with the renormalization group equations is seen to emerge naturally out of the infinite jet bundle corresponding to the field theory and suggests their interpretation as higher-spin equations of motion. While the higher-spin equations we obtain are remarkably simple, they are nonlocal in an essential way. Nevertheless, solving these bulk equations of motion in terms of a boundary source, we derive the on-shell action and demonstrate that it correctly encodes all of the correlation functions of the field theory, written as "Witten diagrams." Since the model space-time has the isometries of the fixed point, it is possible to construct new higher-spin theories defined in terms of geometric structures over other model space-times. We illustrate this by explicitly constructing the higher-spin renormalization group equations corresponding to the z=2 nonrelativistic free field theory in D spatial dimensions. In this case, the model space-time is the Schrödinger space-time, SchrD+3.

UR - http://www.scopus.com/inward/record.url?scp=84921278056&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84921278056&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.91.026002

DO - 10.1103/PhysRevD.91.026002

M3 - Article

AN - SCOPUS:84921278056

VL - 91

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 2

M1 - 026002

ER -