Free □k scalar conformal field theory

@article{Brust2017FreeS,
title={Free □k scalar conformal field theory},
author={Christopher Brust and Kurt Hinterbichler},
journal={Journal of High Energy Physics},
year={2017},
volume={2017},
pages={1-52}
}
• Published 2017
• Physics
• Journal of High Energy Physics
A bstractWe consider the generalizations of the free U(N ) and O(N ) scalar conformal field theories to actions with higher powers of the Laplacian □k, in general dimension d. We study the spectra, Verma modules, anomalies and OPE of these theories. We argue that in certain d and k, the spectrum contains zero norm operators which are both primary and descendant, as well as extension operators which are neither primary nor descendant. In addition, we argue that in even dimensions d ≤ 2k, there… Expand
39 Citations

Figures and Tables from this paper

Weyl versus conformal invariance in quantum field theory
• Physics
• 2017
A bstractWe argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions d ≤ 10. We also studyExpand
AdS/CFT in Fractional Dimension and Higher-Spins at One Loop
• Physics
• 2017
Large-N, ϵ -expansion or the conformal bootstrap allow one to make sense of some of conformal field theories in non-integer dimension, which suggests that AdS/CFT may also extend to fractionalExpand
New conformal higher spin gravities in 3d
• Physics
• 2019
We propose a new class of conformal higher spin gravities in three dimensions, which extends the one by Pope and Townsend. The main new feature is that there are infinitely many examples of the newExpand
Partially massless higher-spin theory II: one-loop effective actions
• Physics
• 2016
We continue our study of a generalization of the D-dimensional linearized Vasiliev higher-spin equations to include a tower of partially massless (PM) fields. We compute one-loop effective actions byExpand
AdS/CFT in Fractional Dimension and Higher Spin Gravity at One Loop
• Physics
• 2017
Large-$N$, $\epsilon$-expansion or the conformal bootstrap allow one to make sense of some of conformal field theories in non-integer dimension, which suggests that AdS/CFT may also extend toExpand
Comments on Short Multiplets in Superconformal Algebras
The problem of classifying all short multiplets of superconformal algebras still seems to be an open question. A generic short multiplet is non-unitary, which nevertheless is of interest in variousExpand
The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points
• Physics
• 2017
A bstractWe describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure ofExpand
Remarks on BMS(3) invariant field theories: correlation functions and nonunitary CFTs
We study some generic aspects of CFTs with the BMS${}_3$ algebra defined as a chiral symmetry. These theories are realized through the isomorphism between the BMS${}_3$ and the $W(2,2)$ algebras. ForExpand
Character integral representation of zeta function in AdSd+1. Part II. Application to partially-massless higher-spin gravities
• Physics
• 2018
A bstractWe compute the one-loop free energies of the type-Aℓ and type-Bℓ higher-spin gravities in (d + 1)-dimensional anti-de Sitter (AdSd+1) spacetime. For large d and ℓ, these theories have aExpand
Multicritical scalar theories with higher-derivative kinetic terms: A perturbative RG approach with the $\epsilon$-expansion
• Physics
• 2018
We employ perturbative renormalization group and e-expansion to study multicritical single-scalar field theories with higher derivative kinetic terms of the form ϕ(-□)kϕ. We focus on those with aExpand

References

SHOWING 1-10 OF 95 REFERENCES
The free σCFTs
• Physics
• 2016
A bstractWe introduce the conformal field theories that describe the shadows of the lowest dimension composites made out of massless free scalars and fermions in d dimensions. We argue that theseExpand
Weyl versus conformal invariance in quantum field theory
• Physics
• 2017
A bstractWe argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions d ≤ 10. We also studyExpand
Critical Sp(N ) models in 6 − ϵ dimensions and higher spin dS/CFT
• Physics
• 2015
A bstractTheories of anti-commuting scalar fields are non-unitary, but they are of interest both in statistical mechanics and in studies of the higher spin de Sitter/Conformal Field TheoryExpand
Symplectic critical models in 6 + ϵ dimensions
Abstract We consider nontrivial critical models in d = 6 + ϵ spacetime dimensions with anticommuting scalars transforming under the symplectic group Sp ( N ) . These models are nonunitary, but theExpand
Recursion relations for conformal blocks
• Physics
• 2015
A bstractIn the context of conformal field theories in general space-time dimension, we find all the possible singularities of the conformal blocks as functions of the scaling dimension Δ of theExpand
ASYMPTOTIC FREEDOM IN EXTENDED CONFORMAL SUPERGRAVITIES
• Physics
• 1982
Abstract We present the calculation of the one-loop β-function in extended conformal supergravities. N = 1, 2, 3, theories (free or coupled to the Einstein supergravities) are found to theExpand
Higher spin realization of the DS/CFT correspondence
• Physics
• 2011
We conjecture that Vasiliev's theory of higher spin gravity in four-dimensional de Sitter space (dS) is holographically dual to a three-dimensional conformal field theory (CFT) living on theExpand
One-loop β-function in conformal supergravities
• Physics
• 1982
Abstract We present a detailed calculation of the one-loop β-function in N = 1 conformal supergravity. The conformal gravitino is found to give a negative contribution of the gravitational infinitiesExpand
Operator product expansion and conservation laws in non-relativistic conformal field theories
• Physics
• 2014
A bstractWe explore the consequences of conformal symmetry for the operator product expansions in nonrelativistic field theories. Similar to the relativistic case, the OPE coefficients of descendantsExpand
Hidden global conformal symmetry without Virasoro extension in theory of elasticity
The theory of elasticity (a.k.a. Riva-Cardy model) has been regarded as an example of scale invariant but not conformal field theories. We argue that in $d=2$ dimensions, the theory has hidden globalExpand