Establish a holographic boundary map for the AdS4 representative

Establish a precise holographic boundary map for the anti-de Sitter representative by specifying admissible boundary conditions, determining the boundary data induced by the quartic biadjoint scalar and SU(2) Yang–Mills representatives, and comparing renormalised observables rather than only bulk profiles.

Background

The solution family contains an AdS4 representative generated by the common scalar seed, but the existence of this bulk geometry does not itself provide an AdS/CFT dictionary.

A holographic interpretation would require a boundary analysis of the scalar and Yang–Mills fields, including their admissible boundary conditions, induced boundary data, and renormalised observables. The paper identifies this as an unresolved direction rather than carrying out the boundary construction.

References

Finally, the $AdS_4$ representative raises a possible holographic question. The existence of an anti-de Sitter member of the solution family does not by itself define an AdS/CFT dictionary . To make such a connection precise, one would need to specify admissible boundary conditions, determine the boundary data induced by the scalar and Yang--Mills representatives, and compare renormalised observables rather than only bulk profiles.

— Towards a Non-Perturbative Classical Double Copy  (2608.14512 - Armstrong-Williams, 14 Aug 2026) in Section Discussion and Further Work