David Roberts scratch 2021

Here are some thoughts by Urs Schreiber


Let me lay out the picture that I have at the moment, also so that you see where you fit in:


Hypothesis H, full quantum version:

For

  • a GG-orbi 10,1|32\mathbb{R}^{10,1\vert \mathbf{32}}-fold 𝒳\mathcal{X} (spacetime)

  • with geometric torsion-free Spin(10,1)\mathrm{Spin}(10,1)-structure (i.e. field of super-gravity)

  • further lifted to tangential Sp(2)\mathrm{Sp}(2)-structure τ\tau (anomaly cancellation),

  • consider the cocycle space π G τ(𝒳)\mathbf{\pi}_G^\tau(\mathcal{X}) of τ\tau-twisted equivariant differential 4-Cohomotopy (i.e. the C-field configuration G-space)

  • and then the GG-equivariant EE-cohomology cocycle space of its loop space E G (Ωπ G τ(𝒳))\mathbf{E}^\bullet_G\big( \Omega \mathbf{\pi}_G^\tau(\mathcal{X}) \big) (quantum states)

  • regarded as a GG-equivariant spectrum (e.g. with E=HE = H\mathbb{C} and 𝒳\mathcal{X} a D6D8D6 \perp D8 spacetime as in SS19 this has homotopy groups the weight systems on horizontal chord diagrams)

Unwinding the definitions, this QFT encodes

  • quantum operations between quantum states of C-field configurations

  • associated with HH-fixed loci of the original spacetime orbifold 𝒳\mathcal{X}.

  • But since these loci are conical black brane loci (as in HSS 18) in the spacetime,

  • we see that we have a “classically controlled quantum system” where the classical control parameter says where in a holographic system we are:

    • in the bulk (11-fixed locus)

    • or on a brane (HH-fixed locus)

      • and if so on which of possibly several intersecting ones (choice of subgroup HGH \subset G).

Now take this mathematical picture and compare to the current folklore in string theory. Within the large hand-waving error bars of the latter, this could match well, I think.

Created on May 14, 2021 at 10:04:37. See the history of this page for a list of all contributions to it.