Mixed-symmetry fields in AdS(5), conformal fields, and AdS/CFT

Abstract

Mixed-symmetry arbitrary spin massive, massless, and self-dual massive fields in AdS(5) are studied. Light-cone gauge actions for such fields leading to decoupled equations of motion are constructed. Light-cone gauge formulation of mixed-symmetry anomalous conformal currents and shadows in 4d flat space is also developed. AdS/CFT correspondence for normalizable and non-normalizable modes of mixed-symmetry AdS fields and the respective boundary mixed-symmetry anomalous conformal currents and shadows is studied. We demonstrate that the light-cone gauge action for massive mixed-symmetry AdS field evaluated on solution of the Dirichlet problem amounts to the light-cone gauge 2-point vertex of mixed-symmetry anomalous shadow. Also we show that UV divergence of the action for mixed-symmetry massive AdS field with some particular value of mass parameter evaluated on the Dirichlet problem amounts to the action of long mixed-symmetry conformal field, while UV divergence of the action for mixed-symmetry massless AdS field evaluated on the Dirichlet problem amounts to the action of short mixed-symmetry conformal field. We speculate on string theory interpretation of a model which involves short low-spin conformal fields and long higher-spin conformal fields.

Cubic interaction vertices for continuous-spin fields and arbitrary spin massive fields

“…On the other hands, many interesting formulations for mixed-symmetry massless and massive higher-spin fields were developed (see, e.g., refs. [84][85][86][87][88][89][90][91][92][93][94][95]). Extension of such formulations to continuous-spin fields could be also of some interest.…”

Lagrangian formulation of massive fermionic higher spin fields on a constant electromagnetic background

“…Inclusion of a nontrivial gravitational background is yet another interesting problem to consider (see for example [54][55][56] for recent progress in these directions). It would be interesting also to establish more connection with the recent studies in conformal higher spin fields (see for example [57][58][59][60][61]). We hope to address these questions in future publications.…”

Long, partial-short, and special conformal fields

“…10 This implies that the short, partial-short and long conformal fields in R d−1,1 are dual to the respective massless, partial-massless and massive fields in AdS d+1 . Taking this into account, we speculated [52] on some special regime in AdS superstring theory when parameters κ for all massive higher-spin fields take integer values. One can expect that such conjectured regime in the AdS superstring theory should be related via AdS/CFT correspondence to stringy theory of conformal fields that involves low-spin short conformal fields and higher-spin long conformal fields.…”