AdS description of induced higher-spin gauge theory

Abstract

We study deformations of three-dimensional large N CFTs by double-trace operators constructed from spin s single-trace operators of dimension Delta. These theories possess UV fixed points, and we calculate the change of the 3-sphere free energy delta F = F-UV - F-IR. To describe the UV fixed point using the dual AdS(4) space we modify the boundary conditions on the spin s field in the bulk; this approach produces delta F in agreement with the field theory calculations. If the spin s operator is a conserved current, then the fixed point is described by an induced parity invariant conformal spin s gauge theory. The low spin examples are QED(3) (s = 1) and the 3-d induced conformal gravity (s = 2). When the original CFT is that of N conformal complex scalar or fermion fields, the U(N) singlet sector of the induced 3-d gauge theory is dual to Vasiliev’s theory in AdS(4) with alternate boundary conditions on the spin s massless gauge field. We test this correspondence by calculating the leading term in delta F for large N. We show that the coefficient of 1/2 log N in delta F is equal to the number of spin s - 1 gauge parameters that act trivially on the spin s gauge field. We discuss generalizations of these results to 3-d gauge theories including Chern-Simons terms and to theories where s is half-integer. We also argue that the Weyl anomaly a-coefficients of conformal spin s theories in even dimensions d, such as that of the Weyl-squared gravity in d = 4, can be efficiently calculated using massless spin s fields in AdS(d+1) with alternate boundary conditions. Using this method we derive a simple formula for the Weyl anomaly a-coefficients of the d = 4 Fradkin-Tseytlin conformal higher-spin gauge fields. Similarly, using alternate boundary conditions in AdS(3) we reproduce the well-known central charge c = -26 of the be ghosts in 2-d gravity, as well as its higher-spin generalizations.