Quantum Fields and Strings

It has been known for a long time that instanton effects control the large order behavior of the perturbation series in quantum mechanics and gauge theories. I present a study of this connection in the context of matrix models in 1/N-expansion and topological strings. I will show how to compute the one-instanton corrections for a generic matrix model. Due to a recent matrix model inspired formalism for the topological string amplitudes on local Calabi-Yau manifolds, this can be used to compute nonperturbative effects in topological string theory and make predictions about the asymptotics of the string perturbation series. I discuss various cases where our predictions can be tested, yielding spectacular agreement with the asymptotics extracted by standard numerical methods.

Some recent investigations into the structure of the AdS/CFT correspondence rely on input from increasingly complicated technical calculations. Two related examples in planar N=4 super Yang-Mills theory include testing consequences of integrability and exploring iteration relations amongst multiloop gluon scattering amplitudes. I will review the latest developments in these areas and the methods used to carry out relevant calculations through four loops.

I'll discuss a reformulation of twistor-string theory as a heterotic string. This clarifies why conformal supergravity arises and provides a link between the Berkovits and Witten pictures. The talk is based on arXiv:0708:2276 with Lionel Mason.

I will discuss a solution generating technique that allows to generate stationary axisymmetric solutions of five-dimensional gravity, starting from static ones. This technique can be used to add angular momentum to static configurations. It can also be used to add KK-monopole charge to asymptotically flat five-dimensional solutions, thus generating geometries that interpolate between five-dimensional and four-dimensional solutions.

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.