Higher-spin current multiplets in operator-product expansions

TL;DR

This paper develops formulas for higher-spin currents in various dimensions, evaluates their two-point functions and central charges, and explores their hierarchies in supersymmetric theories, revealing universal features.

Contribution

It provides a general framework for higher-spin currents, including formulas, two-point functions, and hierarchies, in free and interacting theories across dimensions.

Findings

Higher-spin two-point functions are explicitly calculated.

Higher-spin central charges are evaluated at one loop.

Higher-spin hierarchies in supersymmetric theories show universality.

Abstract

Various formulas for currents with arbitrary spin are worked out in general space-time dimension, in the free field limit and, at the bare level, in presence of interactions. As the n-dimensional generalization of the (conformal) vector field, the (n/2-1)-form is used. The two-point functions and the higher-spin central charges are evaluated at one loop. As an application, the higher-spin hierarchies generated by the stress-tensor operator-product expansion are computed in supersymmetric theories. The results exhibit an interesting universality.