De-quantizing a black hole

The world’s leading string-theory blogger recently suggested that NP might be in P after all, with a polynomial complexity of n^196883. The specific exponent was a joke, but let’s take it seriously…

The context was a discussion of E. Tang’s recommendation algorithm, which might be regarded as a de-quantized version of a specific algorithm from quantum machine learning. That number 196883 comes from the representation theory of the monster group. Within string theory, it is roughly the number of microstates of the lightest black hole in a special case of AdS3/CFT2.

It is conjectured that quantum black holes are “fast scramblers”, and that black hole evaporation encodes a cryptographic one-way function. So… perhaps the S-matrix of that lightest AdS3 black hole could be shown to be in NP, and then we could “de-quantize the black hole” and get a corresponding O(n^196883) algorithm?

The main problem I have with this scenario – the de-quantized black hole lacks any useful structure, it’s just a point singularity. But here I think of the “field with one element”. It’s not actually a field, but one can define more complex objects on top of it, analogous to constructions that elaborate on genuine fields.

In the same way, there could be an algebraic dressing of the classical black hole, which would provide the Tang-like de-quantization of AdS3 black hole formation and evaporation. Probably modular forms and other Langlands math would be involved.