Conformal correlators of mixed-symmetry tensors

• Type: Article in International Scientific Journal
• Date: 2015

Authors

Miguel S Costa (Author) FCUP; Tobias Hansen (Author) Other

Journal

Title: JHEP: Journal of High Energy Physics

Vol. 2015

ISSN: 1029-8479

Publisher: Springer

Indexing

ISI Web of Knowledge - 81 Citations

Scopus - 82 Citations

Scientific classification

FOS: Natural sciences > Physical sciences

Other information

Authenticus ID: P-00A-7Z5

DOI: 10.1007/jhep02(2015)151

Abstract (EN): We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to mixed-symmetry tensors by introducing a new commuting or anticommuting polarization vector for each row or column in the Young diagram that describes the index symmetries of the tensor. We determine the tensor structures that are allowed in n - point conformal correlation functions and give an algorithm for counting them in terms of tensor product coefficients. A simple derivation of the unitarity bound for arbitrary mixed-symmetry tensors is obtained by considering the conservation condition in embedding space. We show, with an example, how the new formalism can be used to compute conformal blocks of arbitrary external fields for the exchange of any conformal primary and its descendants. The matching between the number of tensor structures in conformal field theory correlators of operators in d dimensions and massive scattering amplitudes in d + 1 dimensions is also seen to carry over to mixed-symmetry tensors.

Language: English

Type (Professor's evaluation): Scientific