Schreiber cyclic loop spaces 2022

A talk that I have given:

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• Urs Schreiber$\;\;$ (CQTS @ NYU, Abu-Dhabi)

  
  

  Cyclic loop spaces
  via higher topos theory
  in high energy physics

  
  

  at: Loop spaces and Higher category,

  HUST & SCUT (2-3 Dec 2022)

  
  

  notes: pdf

  video: rec

Abstract. One may observe [CMP 371 (2019)] that the construction of cyclified (“twisted”) free loop spaces, when regarded in higher topos theory, turns out to be nothing but the “right base change” to the context of the moduli stack of the circle. This fundamental fact implies at once good formal properties, and lifts the construction to all kinds of higher generalized geometries, such as to orbifolds – where we claim it reproduces Z. Huan's inertia construction –, and to super-rational homotopy types – where we showed that it witnesses the rules of topological T-duality acting on the super D-brane charges. I explain how these cyclified loop stack adjunctions formalize exactly what physicists mean by “double dimensional reduction” in its effect on brane charges/fluxes; and I close with an outlook on using these insights to define T-folds in the generality of twisted equivariant differential (TED) KR-theory.

This is joint work with Hisham Sati.

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Based on:

• Cyclification of Orbifolds

  arXiv:2212.13836

Related talks:

• Super Lie $n$-algebra of Super $p$-branes

  at Fields, Strings, and Geometry Seminar

  Surrey, Dec 2016

• Super topological T-Duality

  at Conf. on Duality in Homotopy theory

  Regensburg, April 2017

• Introduction to Higher Supergeometry

  at Higher Structures in M-Theory 2018

  Durham, Aug 2018