A note on CFT correlators in three dimensions

In this paper we continue and improve the analysis of the effective actions obtained by integrating out a scalar and a fermion field coupled to external symmetric sources, started in the previous paper. The first subject we study is the geometrization of the results obtained there, that is we express them in terms of covariant Jacobi tensors. The second subject concerns the treatment of tadpoles and seagull terms in order to implement off-shell covariance in the initial model. The last and by far largest part of the paper is a repository of results concerning all two point correlators (including mixed ones) of symmetric currents of any spin up to 5 and in any dimensions between 3 and 6. In the massless case we also provide formulas for any spin in any dimension.

Section: Jhep01(2018)080mentioning

confidence: 99%

One-loop effective actions and higher spins. Part II

Bonora¹,

Cvitan²,

Prester³

et al. 2018

“…In particular, we will determine all the three-point functions involving two fermion fields ψ α andχβ: ψ α (x 1 )χβ(x 2 )O(x 3 ) . 4 According to eq. (3.34), the only non-vanishing 3-point function occurs when O is in one of the following three Lorentz representations: (l, l), (l + 2, l) and (l, l + 2), with l ≥ 0.…”

Section: (211)mentioning

confidence: 99%

General three-point functions in 4D CFT

Elkhidir

Karateev

Serone

2015

101

We classify and compute, by means of the six-dimensional embedding formalism in twistor space, all possible three-point functions in four dimensional conformal field theories involving bosonic or fermionic operators in irreducible representations of the Lorentz group. We show how to impose in this formalism constraints due to conservation of bosonic or fermionic currents. The number of independent tensor structures appearing in any three-point function is obtained by a simple counting. Using the Operator Product Expansion (OPE), we can then determine the number of structures appearing in 4-point functions with arbitrary operators. This procedure is independent of the way we take the OPE between pairs of operators, namely it is consistent with crossing symmetry, as it should be. An analytic formula for the number of tensor structures for three-point correlators with two symmetric and an arbitrary bosonic (non-conserved) operators is found, which in turn allows to analytically determine the number of structures in 4-point functions of symmetric traceless tensors.

“…As shown in the body of the paper higher spin fields appear naturally in the one-loop effective action of the simplest free theories in any dimension and it is possible to make contact with the literature on classical higher spin theories, [18][19][20][21][22][23][24][25]. Other sources of inspiration have been [26][27][28][29][30][31][32]. The idea of exploring the one-loop effective action is far from new: the list of works which may have some overlap with our paper includes [37][38][39][40][41][42][43][44][45][46], but is likely to be incomplete.…”

Section: Jhep12(2016)084mentioning

confidence: 99%

One-loop effective actions and higher spins

Bonora

Cvitan

Prester

et al. 2016

The idea we advocate in this paper is that the one-loop effective action of a free (massive) field theory coupled to external sources (via conserved currents) contains complete information about the classical dynamics of such sources. We show many explicit examples of this fact for (scalar and fermion) free field theories in various dimensions d = 3, 4, 5, 6 coupled to (bosonic, completely symmetric) sources with a number of spins. In some cases we also provide compact formulas for any dimension. This paper is devoted to two-point correlators, so the one-loop effective action we construct contains only the quadratic terms and the relevant equations of motion for the sources we obtain are the linearized ones.