Grigory Tarnopolsky

AdS description of induced higher-spin gauge theory

A bstractWe study deformations of three-dimensional large N CFTs by double-trace operators constructed from spin s single-trace operators of dimension Δ. These theories possess UV fixed points, and we calculate the change of the 3-sphere free energy δF = FUV − FIR. To describe the UV fixed point using the dual AdS4 space we modify the boundary conditions on the spin s field in the bulk; this approach produces δF 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 QED3 (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 AdS4 with alternate boundary conditions on the spin s massless gauge field. We test this correspondence by calculating the leading term in δF for large N. We show that the coefficient of

Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity

\frac{1}{2}

On large N limit of symmetric traceless tensor models

log N in δF 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 AdSd+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 AdS3 we reproduce the well-known central charge c = −26 of the bc ghosts in 2-d gravity, as well as its higher- spin generalizations.

Generalized F-theorem and the ϵ expansion

A bstractWe continue our study of the AGT correspondence between instanton counting on

Spectra of Operators in Large

{{{{{\mathbb{C}}^2}}} \left/ {{{{\mathbb{Z}}_p}}} \right.}

N

and Conformal field theories with the symmetry algebra

Tensor Models

\mathcal{A}\left( {r,p} \right)

Bosonic tensor models at large

. In the cases r = 1, p = 2 and r = 2, p = 2 this algebra specialized to:

N

\mathcal{A}\left( {1,2} \right)=\mathcal{H}\oplus \widehat{\mathfrak{sl}}{(2)_1}

and small

and