On square-zero elements in the IIB supersymmetry algebra

TL;DR

This paper classifies all possible twisting supercharges in type IIB supergravity by analyzing the structure of square-zero elements in the (2,0) super Poincaré algebra, revealing complex orbit stratifications and novel features.

Contribution

It provides a detailed classification of square-zero elements and orbit structures in the (2,0) super Poincaré algebra relevant to type IIB supergravity.

Findings

Identification of two distinct orbits of holomorphic twisting supercharges

Discovery of several mixed topological-holomorphic twists

More involved orbit structure compared to other super Poincaré algebras

Abstract

We describe the variety of square-zero elements in the (2,0) super Poincar\'e algebra in ten dimensions, together with its orbit stratification induced by the action of the spin group and R-symmetry. This provides a classification of all possible twisting supercharges of type IIB supergravity in a flat background. Compared to other varieties of square-zero elements in super Poincar\'e algebras, we find that the orbit structure is more involved and exhibits several novel features. Among other things, we show that there are two distinct orbits of holomorphic twisting supercharges and a number of mixed topological-holomorphic twists.