Schreiber
The (co-)reflective categories of supergravity

A talk that I gave:

Abstract. In string theory, the global formulation of the dynamics of super p-branes requires target super spacetimes to be refined to super-stacks (FSS 13). This raises the mathematical problem of classifying the admissible (“anomaly free”) Cartan geometries for such higher supergeometry. In this talk I present a category theoretic analysis which greatly facilitates solving this problem. I discuss how the (higher) topos of super-stacks is stratified by a system of opposing (co-)reflective subcategories that serve to characterize its geometric content. In closing I will give a very brief outlook on how this serves to solve the classification problem.

id id fermionic e bosonic bosonic R rheonomic reduced infinitesimal infinitesimal & étale contractible ʃ discrete discrete differential * \array{ && id &\dashv& id \\ && \vee && \vee \\ &\stackrel{fermionic}{}& \e &\dashv& \rightsquigarrow & \stackrel{bosonic}{} \\ && \bot && \bot \\ &\stackrel{bosonic}{} & \rightsquigarrow &\dashv& \R & \stackrel{rheonomic}{} \\ && \vee && \vee \\ &\stackrel{reduced}{} & \Re &\dashv& \Im & \stackrel{infinitesimal}{} \\ && \bot && \bot \\ &\stackrel{infinitesimal}{}& \Im &\dashv& \& & \stackrel{\text{étale}}{} \\ && \vee && \vee \\ &\stackrel{contractible}{}& ʃ &\dashv& \flat & \stackrel{discrete}{} \\ && \bot && \bot \\ &\stackrel{discrete}{}& \flat &\dashv& \sharp & \stackrel{differential}{} \\ && \vee && \vee \\ && \emptyset &\dashv& \ast }

This diagram shows the system of reflectors and coreflectors on the supergeometric topos. The symbol “\dashv\,\,” denotes adjunctions of (co-)reflectors and the symbol “\vee\,\,” denotes inclusion of (co-)reflective subcategories. More details are at differential cohomology in a cohesive topos.

The discussion that applies this system of operations to the above problem is at Obstruction theory for parameterized higher WZW terms.

Related talks include

Related lecture notes include


Revised on November 26, 2015 09:13:08 by Urs Schreiber (193.51.104.24)