Topological Quantum Field Theory Seminar   RSS

21/06/2016, 14:30 — 15:30 — Room P3.10, Mathematics Building
Hisham Sati, University of Pittsburgh and New York University

$L_\infty$-algebra of sphere-valued supercocycles in M-theory

In this talk we describe how super $L_\infty$-algebras capture the dynamics of the various fields and branes encoded in supercocycles associated with super Minkowski spacetimes at the rational level. We illustrate how rational 4-sphere-valued supercocycles in M-theory descend to supercocycles in type IIA string theory and capture the dynamics of the Ramond-Ramond fields predicted by the rational image of twisted K-theory, with the twist given by the usual B-field. We explicitly derive the M2/M5 $\leftrightarrow$ F1/Dp/NS5 correspondence via dimensional reduction of sphere valued $L_\infty$ supercocycles in rational homotopy theory. These results highlight, in the context of M-theory, the observations that supercocycles are still rich even in flat superspace and spectra are still rich even rationally. This is joint work with Domenico Fiorenza and Urs Schreiber.

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Current organizers: José MourãoRoger Picken, Marko Stošić


FCT Projects PTDC/MAT-GEO/3319/2014, Quantization and Kähler Geometry, PTDC/MAT-PUR/31089/2017, Higher Structures and Applications.