The Integrability Of N = 16 Supergravity

Abstract

The maximally extended locally supersymmetric theory in two dimensions is N = 16 supergravity. This theory was recently constructed [1] by dimensional reduction of N = 16 supergravity in three dimensions [2]. On shell, it describes 128 bosonic and 128 fermionic degrees of freedom which are assigned to the two inequivalent spinor representations of SO(16). In three dimensions, their interactions are governed by an E8/SO(16) σ - model. In two dimensions, the nonlinearly realized E8 invariance is enlarged to E9 = E8 (1), the affine (Kac — Moody) extension of E8. The emergence of infinite dimensional symmetries in two dimensions is related to the integrability of the theory: there exists a linear system whose compatibility conditions are equivalent to the equations of motion of the physical degrees of freedom [1]. More recently, an extension of this linear system has been discovered which also yields the equations of motion of some of the off-shell degrees of freedom [3]. This new system possesses a local N = 16 supersymmetry with transformation parameters εI (I = 1,…,16) subject to the condition $$ {\gamma ^\beta }{\text{ }}{\gamma ^\alpha }{D_\beta }{\varepsilon ^j} = \sigma $$