Operator algebra of free conformal currents via twistors. (English) Zbl 1284.81169
Summary: Operator algebra of (not necessarily free) higher-spin conformal conserved currents in generalized matrix spaces, that include 3d Minkowski space-time as a particular case, is shown to be determined by an associative algebra \(M\) of functions on the twistor space. For free conserved currents, \(M\) is the universal enveloping algebra of the higher-spin algebra. Proposed construction greatly simplifies computation and analysis of correlators of conserved currents. Generating function for \(n\)-point functions of 3d (super)currents of all spins, built from \(N\) free constituent massless scalars and spinors, is obtained in a concise form of certain determinant. Our results agree with and extend earlier bulk computations in the HS \(AdS_4/CFT_3\) framework. Generating function for \(n\)-point functions of 4d conformal currents is also presented.
MSC:
| 81R40 | Symmetry breaking in quantum theory |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
| 15A66 | Clifford algebras, spinors |
Keywords:
generalized matrix spacesReferences:
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