Partially massless higher-spin theory. (English) Zbl 1377.81062
Summary: We study a generalization of the \(D\)-dimensional Vasiliev theory to include a tower of partially massless fields. This theory is obtained by replacing the usual higher-spin algebra of Killing tensors on (A)dS with a generalization that includes “third-order” Killing tensors. Gauging this algebra with the Vasiliev formalism leads to a fully non-linear theory which is expected to be UV complete, includes gravity, and can live on dS as well as AdS. The linearized spectrum includes three massive particles and an infinite tower of partially massless particles, in addition to the usual spectrum of particles present in the Vasiliev theory [M. A. Vasiliev, in: The many faces of the superworld. Yuri Golfand memorial volume. Singapore: World Scientific. 533–610 (2000; Zbl 0990.81084)], in agreement with predictions from a putative dual CFT with the same symmetry algebra. We compute the masses of the particles which are not fixed by the massless or partially massless gauge symmetry, finding precise agreement with the CFT predictions. This involves computing several dozen of the lowest-lying terms in the expansion of the trilinear form of the enlarged higher-spin algebra. We also discuss nuances in the theory that occur in specific dimensions; in particular, the theory dramatically truncates in bulk dimensions \(D\) = 3\(,\) 5 and has non-diagonalizable mixings which occur in \(D\) = 4\(,\) 7.
MSC:
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
| 83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
Citations:
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