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Background-independent operator-algebraic definition of string theory

Develop a background-independent operator-algebraic formulation A of type IIB string theory (and more generally, string/M-theory), together with a characterization of the allowed state space, such that different asymptotic spacetimes arise as distinct GNS representations of A.

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Background

The text advocates an algebraic viewpoint analogous to algebraic QFT: a single abstract algebra with different states yielding different GNS Hilbert spaces and representations corresponding to different backgrounds (e.g., various AdS vacua, flat space, perhaps de Sitter).

At present, such a background-independent algebra A and the specification of its allowed states are not known. Constructing them would unify different holographic dualities and extend beyond contexts with well-understood asymptotics.

References

"At present, we do not have a background-independent definition of $\sA_{\mathrm{IIB}}$, nor a complete characterization of the allowed states."

— Lectures on entanglement, von Neumann algebras, and emergence of spacetime (2510.07017 - Liu, 8 Oct 2025) in Section 8 (Conclusions and discussions)