2024/03/04 by Diaz, Felipe, Iazeolla, Carlo, Sundell, Per · 2 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2403.02283
In this work and in the companion paper arXiv:2403.02301, we initiate an approach to holography based on the AKSZ formalism. As the first step, we refine Vasiliev's holography proposal in arXiv:1203.5554 by obtaining 4D higher-spin gravity (HSG) and 3D coloured conformal higher-spin gravity (CCHSG) -- i.e., coloured conformal matter fields coupled to conformal higher-spin gauge fields and colour gauge fields -- as two distinct and classically consistent reductions of a single parent theory. The latter consists, on-shell, of a flat superconnection valued in a fractional-spin extension of Vasiliev's higher-spin algebra. The HSG and CCHSG reductions are characterized by dual structure groups and two-form cohomology elements, and their embedding in a common parent model provides a rationale for deriving holographic relations from multi-dimensional AKSZ partition functions on cylinders with dual boundary conditions, to appear separately. In this work we i) construct the underlying non-commutative geometry as a metaplectic operator algebra represented in a Hermitian module of a pair of conformal particles; ii) identify a discrete modular group, arising from twisted boundary conditions of the first-quantized system, and connecting different boundary conditions of the second-quantized system; and iii) identify the holonomies, structure groups and two-form cohomology elements that characterize the HSG and CCHSG reductions, and equate the dual second Chern classes.