Supergravity Fluxes and Generalised Geometry : LMS/EPSRC Durham Symposium on Higher Structures in M theory

Strickland-Constable, Charles (2019) Supergravity Fluxes and Generalised Geometry : LMS/EPSRC Durham Symposium on Higher Structures in M theory. Fortschritte der Physik, 67 (8-9): 1910021. ISSN 0015-8208
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We briefly review the description of the internal sector of supergravity theories in the language of generalised geometry and how this gives rise to a description of supersymmetric backgrounds as integrable geometric structures. We then review recent work, featuring holomorphic Courant algebroids, on the description of $\mathcal N=1$ heterotic flux vacua. This work studied the finite deformation problem of the Hull-Strominger system, guided by consideration of the superpotential functional on the relevant space of geometries. It rewrote the system in terms of the Maurer-Cartan set of a particular $L_\infty$-algebra associated to a holomorphic Courant algebroid, with the superpotential itself becoming an analogue of a holomorphic Chern-Simons functional.

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