What are the options for adding anti-de Sitter space compatibility to the table?

The question of incorporating anti-de Sitter (AdS) space compatibility into our theoretical "table" – a metaphor for our current framework of physics – is a profound challenge at the frontier of theoretical physics. AdS space, a universe with constant negative curvature, is not just a mathematical curiosity; it is a cornerstone of modern theories like string theory and the holographic principle. To add this compatibility, several strategic avenues are open.

First, one must deepen the engagement with string theory and M-theory, where AdS geometries naturally emerge as stable ground-state solutions. This involves not just acknowledging these solutions but rigorously exploring the landscape of AdS vacua and their potential connections to our observed universe through compactification mechanisms.

Second, the powerful tool of the AdS/CFT correspondence (holographic duality) offers a revolutionary path. Instead of directly modifying the "table" for AdS gravity, one can work with a conformal field theory (CFT) defined on its boundary. Achieving compatibility then translates to understanding how our known physics might be encoded as a holographic projection from such a boundary theory, potentially linking quantum gravity to well-defined quantum systems.

Third, for cosmological model-building, one can investigate theories of modified gravity or specific matter couplings that admit AdS solutions as physically relevant sectors. This requires examining stability, perturbation spectra, and possible phase transitions from AdS to other cosmological backgrounds.

Finally, a pragmatic approach is to treat AdS as a critical theoretical laboratory. Even if our universe is not globally AdS, the profound insights gained from studying physics in this space – from black hole thermodynamics to quantum information – provide indispensable tools and concepts. Thus, adding AdS compatibility means enriching the foundational toolkit of theoretical physics, allowing for sharper formulations of problems in quantum gravity and strongly coupled systems, whose lessons can be translated into more realistic settings. The integration is less about forcing our universe into an AdS box and more about leveraging its unique mathematical structure to expand and stress-test the very foundations of our physical understanding.