Twisted Covariant Form Hierarchies: From Hidden Symmetries in M-theory to Anomalies in Heterotic Backgrounds.

Abstract

In this thesis, we compute the twisted covariant form hierarchies (TCFHs) of minimal supergravity theories in four and five dimensions, as well as, eleven-dimensional super-gravity and the internal space of its warped AdS backgrounds. As a consequence, the form bilinears satisfy a generalised conformal Killing-Yano equation with respect to the TCFH connection. Then, we find the (hidden) symmetries generated by the form bilin-ears in spinning particle actions propagating in certain supersymmetric backgrounds of D = 4, N = 2 and D = 5, N = 1 minimal supergravities, M-brane backgrounds which include the M2-brane, M5-brane, pp-wave and KK-monopole, maximal supersymmetric AdS backgrounds and some AdS backgrounds that arise as near horizon geometries of intersecting M-branes. In addition, we explore whether the form bilinears are sufficient to prove the integrability of particle probe dynamics on M-brane backgrounds. More-over, we show that the covariantly constant forms of heterotic backgrounds with SU(2) and SU(3) holonomy generate a W-symmetry algebra in two-dimensional non-linear su-persymmetric sigma models with the previous backgrounds as target spaces and analyse the consistency conditions of the chiral anomalies arising from all symmetry generators required for the closure of the algebra.

Date of Award	1 Jan 2024
Original language	English
Awarding Institution	King's College London
Supervisor	Georgios Papadopoulos (Supervisor)