High Energy Physics

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is still an open problem. We address this issue by relating the quaternionic-Kähler metric on the hypermultiplet moduli space to the complex contact geometry on its twistor space. In this framework, Euclidean D-brane instantons are captured by contact transformations between different patches. We derive those by recasting the previously known A-type D2-instanton corrections in the language of contact geometry, covariantizing the result under electro-magnetic duality, and using mirror symmetry. As a result, we are able to express the effects of all D-instantons in Type II compactifications concisely as a sum of dilogarithm functions.

In this talk we discuss a proposed dual matrix formulation of N = 4 Super Yang-Mills on R^4 coupled to 4D Einstein supergravity. We review the evidence accumulated so far in favor of this proposal, which includes a successful match of the symmetries of the continuum theory, and the computation of MHV gluon and graviton scattering amplitudes in terms of matrix model correlators. We also discuss some avenues of ongoing investigation.