universe Review Higher Spin Fields in Hyperspace. A Review Dmitri Sorokin 1 and Mirian Tsulaia 2,* 1 Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via F. Marzolo 8, 35131 Padova, Italy;
[email protected] 2 School of Physics M013, The University of Western Australia, 35 Stirling Highway, Crawley, Perth, WA 6009, Australia * Correspondence:
[email protected] Received: 29 October 2017; Accepted: 22 December 2017; Published: 3 January 2018 Abstract: We give an introduction to the so-called tensorial, matrix or hyperspace approach to the description of massless higher-spin fields. Keywords: higher spin theories; supersymmetry; conformal field theory 1. Introduction Every consistent theory of interacting higher spin fields necessarily includes an infinite number of such fields. For this reason, it is extremely important to develop a formalism which effectively includes an infinite number of fields into a simpler field-theoretical object. This formalism should yield correct field equations first of all at the free level and then be promoted to an interacting theory. An elegant geometrical approach to higher spin theories of this kind is known as the method of tensorial spaces. This approach was first suggested by Fronsdal [1]. Its explicit dynamical realization and further extensive developments have been carried out in [2–28]. In a certain sense, the method of tensorial spaces is reminiscent of the Kaluza–Klein theories. In such theories, one usually considers massless field equations in higher dimensions and then, assuming that the extra dimensions are periodic (compact), one obtains a theory in lower dimensions, which contains fields with growing masses.