AdS description of induced higher-spin gauge theory

By S. Giombi, I. Klebanov, Silviu S. Pufu, B. Safdi, G. Tarnopolsky. 2013

137 citations recorded by the source corpus.

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 $ \frac{1}{2} $ 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.

Subfields: Nuclear and High Energy Physics, Political Science and International Relations

View Paper: https://www.semanticscholar.org/paper/0160495a40e86287dd782a0e86ac03a68883a5df

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Citations in the corpus

Spinning AdS propagators (2014, methodology): “Our goal is to check computations done in [18] that can also be done by directly computing the difference between the short distance behaviour of spin J propagators of dimension ∆ and d − ∆.”
Moving the CFT into the bulk with TT¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ T\overline{T} $$\end{document} (2016, methodology): “It was suggested in [37] based on the Hubbard-Stratonovich presentation of the T T̄ deformed theory (4.”
One loop tests of higher spin AdS/CFT (2013, methodology): “the ∆+ = 2 boundary condition, a consistent prescription [34] to obtain the correct value for the alternate boundary condition ∆− = 1 is to analytically continue (2.”
Light-front higher-spin theories in flat space (2016, background): “In this regard, it is worth mentioning that there is a one-parameter family of boundary conditions [83]:”
Higher spins in AdS5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT (2014, unknown): “In the case when the 4d boundary is a sphere S4 this leads to an expression for the conformal anomaly a-coefficient of the 4d CHS field in terms of the properties of the AdS5 determinants [1].”
Notes on the complex Sachdev-Ye-Kitaev model (2019, methodology): “We note that this procedure is similar to that used to compute the influence of double trace operators on the free energy in the AdS/CFT correspondence [40–45].”