The GraviGUT Algebra Is not a Subalgebra of E8E_8, but E8E_8 Does Contain an Extended GraviGUT Algebra

The (real) GraviGUT algebra is an extension of the $\mathfrak{spin}(11,3)$ algebra by a $64$-dimensional Lie algebra, but there is some ambiguity in the literature about its definition. Recently, Lisi constructed an embedding of the GraviGUT algebra into the quaternionic real form of $E_8$. We clarify the definition, showing that there is only one possibility, and then prove that the GraviGUT algebra cannot be embedded into any real form of $E_8$. We then modify Lisi's construction to create true Lie algebra embeddings of the extended GraviGUT algebra into $E_8$. We classify these embeddings up to inner automorphism

Probing Five-Dimensional Black Holes with D-Branes

We consider a one-brane probe in the presence of a five-dimensional black hole in the classical limit. The velocity-dependent force on a slowly-moving probe is characterized by a metric on the probe moduli space. This metric is computed for large black holes using low-energy supergravity, and for small black holes using D-brane gauge theory. The results are compared.Comment: 24 pages, harvma