Higher-spin theory and holography

Abstract

This special issue of Journal of Physics A: Mathematical and Theoretical reviews recent developments in higher-spin gauge theories and their applications to holographic dualities.The analysis of higher-spin theories has a very long history, but it took until the mid 1980s for the first consistent higher-spin interactions to be constructed by Bengtsson, Bengtsson and Brink [1] and Berends, Burgers and van Dam [2]. Somewhat later it was shown by Fradkin and Vasiliev [3] that consistent higher-spin gauge theories that involve gravity should necessarily be defined on a curved background. The first consistent interacting higher-spin theories were then formulated at the classical level by Vasiliev in the early 1990s [4]. These higher-spin theories involve an infinite number of massless higher-spin fields that support higher-spin gauge symmetries, and indeed, are largely characterized by this underlying gauge symmetry. The simplest examples are provided by higher-spin theories on (anti)-de Sitter spaces, and in a sense, this anticipated the AdS/CFT correspondence. Indeed, in the tensionless limit of string theory, the massive excitations of string theory become massless, and hence define higher-spin gauge fields. On the other hand, from the dual gauge theory perspective, this is the limit in which the field theory becomes free, and therefore has many conserved higher-spin currents. By the usual AdS/CFT dictionary, these are dual to the higher-spin gauge symmetries of the bulk description.Following this line of argument, Sundborg [5] and Witten [6] suggested in 2001 that a duality relating a higher-spin theory on AdSd to a weakly coupled (d − 1)-dimensional conformal field theory should exist. A concrete proposal was then made by Klebanov and Polyakov [7] who conjectured that the simplest version of a higher-spin gauge theory on AdS4 should be dual to the 3d O(N ) vector model. Recently, much support for this conjecture was obtained by Giombi and Yin [8], and in turn, this has triggered a significant amount of activity in this general area. Among other things, the constraints that are implied by the higher-spin symmetries were analysed (see the paper by Maldacena and Zhiboedov in this issue [9]), and a fairly concrete proposal for how higher-spin theories are related to string theory was made (see the paper by Chang, Minwalla, Sharma and Yin in this issue [10]). Furthermore, a lower dimensional version of the conjecture was put forward by Gaberdiel and Gopakumar [11] that was subsequently also checked in some detail. These dualities hold the promise of offering insights into the inner workings of the AdS/CFT correspondence since they are complex enough to capture the essence of the duality, while at the same time being sufficiently simple in order to allow for a detailed analysis. Moreover, the methods specifically developed in higher-spin theory may be useful for understanding a general mechanism underlying holography, both in higher-spin models and beyond (see the paper by Vasiliev in this issue [12]).Another fascinating aspect of these higher-spin theories lies in the fact that the higher-spin symmetries mix generically fields of different spin, and in particular, the spin-2 metric and higher-spin excitations are related to one another by gauge transformations. As a result, higher-spin theories require a modification of the standard framework of Riemannian geometry since the usual diffeomorphism-invariant tensors are not gauge invariant any longer. In particular, higher-spin theories may therefore open the way towards understanding fundamental concepts of space-time geometry; for example, they may well have key lessons in store for how string theory resolves space-time singularities.In this issue we have collected together a number of review papers, summarizing the aforementioned recent developments, as well as research papers indicating current directions of interest in the study of higher-spin gauge theories. We hope that it will be useful, both for beginners interested in an introduction to the subject, and for experts already working in the field. Three of the reviews deal with the holographic dualities mentioned above: the paper by Giombi and Yin [13] reviews the situation for AdS4/CFT3, while the review by Gaberdiel and Gopakumar [14] deals with the lower-dimensional AdS3/CFT2 version. In addition, the review by Jevicki, Jin and Ye [15] explains a possible way of proving the duality using collective fields. There are two reviews on the construction of black holes in higher-spin gauge theories: the review by Iazeolla and Sundell [16] reviews the situation for 4d higher-spin theories, while the review by Ammon, Gutperle, Kraus and Perlmutter [17] deals with the three-dimensional case for which much progress has been made recently. Finally, the review of Sagnotti [18] explains various general aspects of higher-spin gauge theories. The research papers deal with different aspects of current developments; some are concerned with the holographic duality, while others develop the general theory of higher-spin fields.