Aspects of symmetry in type IIB and heterotic backgrounds

Abstract

In this thesis, we study various aspects of symmetries of particle and string systems in supersymmetric type IIB and heterotic backgrounds. We present the twisted covariant form hierarchies (TCFHs) of type IIB supergravity and explore the conditions under which the form bilinears generate symmetries for spinning particle and string probes in IIB brane solutions. We also calculate the TCFHs of type IIB AdSn ×w N10−n backgrounds, and we show that the form bilinears for the AdS5 solution and some near-horizon geometries of intersecting branes are Killing-Yano or closed conformal Killing-Yano forms, and thus generate symmetries for some spinning particle actions. Furthermore, we provide the conserved charges associated with Killing-Stäckel tensors responsible for the integrability of the geodesic flow in spherically symmetric IIB brane solutions. Regarding the 2-dimensional heterotic sigma models with holonomy included in SU(2) and SU(3), we show that they are invariant under a W-symmetry algebra generated by the covariantly constant forms of these backgrounds. The closure of the algebra requires additional generators, which we identify. We find and investigate the anomalies due to chiral fermions in the sigma model action using the Wess-Zumino consistency conditions. Finally, we demonstrate that they cancel
at one-loop order by adding appropriate finite local counterterms in the effective action or assuming the transformations are appropriately quantum mechanically corrected.

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