High Energy Physics

We describe how to recover the quantum numbers of extremal black holes from their near horizon geometries. This is achieved by constructing the gravitational Noether-Wald charges which can be used for non-extremal black holes as well. These charges are shown to be equivalent to the U(1) charges of appropriately dimensionally reduced solutions. Explicit derivations are provided for 10 dimensional type IIB supergravity and 5 dimensional minimal gauged supergravity, with illustrative examples for various black hole solutions. We further discuss how to derive the thermodynamic quantities and their relations explicitly in the extremal limit, from the point of view of the near-horizon geometry. We relate our results to the entropy function formalism.

In this talk, I will describe recent work in string phenomenology from the perspective of computational algebraic geometry. I will begin by reviewing some of the long-standing issues in heterotic model building and the goal of producing realistic particle physics from string theory. This goal can be approached by creating a large class of heterotic models which can be algorithmically scanned for physical suitability. I will outline a well-defined set of heterotic compactifications over complete intersection Calabi-Yau manifolds using the monad construction of vector bundles. Further, I will describe how a combination of analytic methods and computer algebra can provide efficient techniques for proving stability and calculating particle spectra.

It is an open question why gravity is so much weaker than the other three interactions we know. One possible answer which has been suggested is that this mismatch is only apparently so, and a feature we observe on large distances. The strength of gravity on small distances could grow faster than an extrapolation of Newton\'s law would imply, such that it becomes comparable to the other interactions at distances that will be testable in the soon future. The concrete scenario for this is that our world could have additional compactified extra dimensions. If that was the case, quantum gravitational effects could become observable at the Large Hadron Collider. The most prominent features in these models are the production of mini black holes, and graviton emission.