EMPG Special Seminar Day 2013

I provide an overview of the symmetry which encompasses diverse subjects like non-relativistic CFTs, duals to flat holography and tensionless string theory. The focus of the latter part of the talk would be on tensionless strings following arXiv:1303.0291.

I will discuss a geometrical construction of Lie superalgebras for curved backgrounds which support rigid conformal supersymmetry.

The homogeneity theorem for supergravity backgrounds tells us that any backgrounds of 11-dimensional, type I/heterotic or type II supergravity theories preserving a fraction greater than one half of the supersymmetry of the underlying theory are necessarily locally homogeneous. Moreover, this homogeneity is due precisely to the supersymmetry, so that at every point of the spacetime one can find a frame for the tangent space made out of Killing vectors constructed out of the Killing spinors. I will talk about the theorem's context, proof, and further work upon the theme.

Lie 2-algebras are obtained by categorifying Lie algebras and thus present us with fertile ground for the generalisation of known physical models. We will discuss in particular semi-strict Lie 2-algebras, some of their salient properties, and examples generalizing the notion of a Poisson structure for 2-plectic manifolds. We then construct the natural generalisation of known 0-dimensional matrix models (such as the IKKT model and the 0-dimensional BLG model), based on these higher order structures, and show that some of their solutions describe quantisations of specific 2-plectic manifolds.

We consider stationary extreme black hole solutions to the Einstein-Yang-Mills equations in four dimensions, allowing for a negative cosmological constant. We prove that any axisymmetric black hole of this kind possesses a near-horizon AdS₂ symmetry and deduce its near-horizon geometry must be that of the abelian embedded extreme Kerr-Newman (AdS) black hole. We also show that the near-horizon geometry of any static black hole is a direct product of AdS₂ and a constant curvature space.