Abstract
We review various methods for finding exact solutions of higher spin theory in four dimensions, and survey the known exact solutions of (non)minimal Vasiliev’s equations. These include instanton-like and black hole-like solutions in (A)dS and Kleinian spacetimes. A perturbative construction of solutions with the symmetries of a domain wall is also described. Furthermore, we review two proposed perturbative schemes: one based on perturbative treatment of the twistor space field equations followed by inverting Fronsdal kinetic terms using standard Green’s functions; and an alternative scheme based on solving the twistor space field equations exactly followed by introducing the spacetime dependence using perturbatively defined gauge functions. Motivated by the need to provide a higher spin invariant characterization of the exact solutions, aspects of a proposal for a geometric description of Vasiliev’s equation involving an infinite dimensional generalization of anti de Sitter space are revisited and improved.
Highlights
Higher spin (HS) theory in four dimensions, in its simplest form and when expanded about itsde Sitter vacuum solution, describes a self-interacting infinite tower of massless particles of spin s = 0, 2, 4
Introducing a related class of forms in Z-space, that facilitates a special vacuum two-form in twistor space, the resulting linearized master fields can be brought to a special gauge, referred to as the Vasiliev gauge, in which their symbols defined in a certain normal order are real analytic in twistor space, and the master zero- and one-forms admit Taylor expansions in Y at Z = 0 in terms of Fronsdal fields on the mass shell and subject to physical boundary conditions
Topological HS theory, which has no dynamical degrees of freedom, and which allows a more rigorous definition of black holes, is known to admit many exact solutions whose description goes beyond the scope of this review
Summary
In an alternative approach to the construction of HS equations in spacetime, it has been proposed to view Vasiliev’s equations as describing stationary points of a topological field theory with a path integral measure based on a Frobenius-Chern-Simons bulk action in nine dimensions augmented by topological boundary terms, which are permitted by the Batalin-Vilkovisky formalism, of which only the latter contribute to the on-shell action [16,17] This approach combines the virtues of the on-shell approach to amplitudes for massless particles flat spacetime with those of having a background independent action, in the sense that the on-shell action is fixed essentially by gauge symmetries and given on closed form, which together with the background independence of Vasiliev’s equations provides a machinery for perturbative quantum computations around general backgrounds. Topological HS theory, which has no dynamical degrees of freedom, and which allows a more rigorous definition of black holes, is known to admit many exact solutions whose description goes beyond the scope of this review
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
