Vectorial AdS_5/CFT_4 duality for spin-one boundary theory

TL;DR

This paper explores a specific vectorial AdS_5/CFT_4 duality involving free Maxwell fields, deriving partition functions and matching Casimir energies to support the duality's validity.

Contribution

It extends previous work by deriving the large N limit of the singlet-sector partition function for a higher spin theory dual to free Maxwell fields and confirms consistency with AdS/CFT expectations.

Findings

Partition functions match AdS/CFT predictions.

Casimir energy on S^3 aligns with duality assumptions.

Supports the validity of the vectorial AdS_5/CFT_4 duality for spin-one theories.

Abstract

We consider an example of vectorial AdS_5/CFT_4 duality when the boundary theory is described by N free complex or real Maxwell fields. It is dual to a particular ("type C") higher spin theory in AdS_5 containing fields in special mixed-symmetry representations. We extend the study of this theory in arXiv:1410.3273 by deriving the expression for the large N limit of the corresponding singlet-sector partition function on S^1 x S^3. We find that in both complex U(N) and real O(N) invariant cases the form of the one-particle partition function is as required by the AdS/CFT duality. We also demonstrate the matching of the Casimir energy on S^3 by assuming an integer shift in the bulk theory coupling.