High Energy Physics

There appear to be only two essentially distinct ways to understand intersection numbers on moduli spaces of curves --- via Hurwitz numbers or symplectic volumes. In this talk, we will consider polynomials defined by Norbury which bridge the gap between these two pictures. They appear in the enumeration of lattice points in moduli spaces of curves and it appears that their coefficients store interesting information. We will also describe a connection between these polynomials and the topological recursion defined by Eynard and Orantin.

An enormous effort is underway to search for the Higgs boson at the LHC. One new development of the past couple of years is to look into the kinematic region where the Higgs boosted, which has led to the possibility to observe the dominant b-bar decay mode as a single "fat jet" when the Higgs is light. I'll discuss how this technique has great promise not only within the Standard Model, but potentially has even greater promise to find a light Higgs in new physics models such as supersymmetry.

The Petrov classification of the Weyl tensor is an important tool in the study of exact solutions of the Einstein equation in 4d. For example, the Kerr solution was discovered in a study of spacetimes with algebraically special Weyl tensors. Algebraic classification of the Weyl tensor has been extended to higher dimensions. I shall review this classification and describe known families of algebraically special solutions. Recent progress towards obtaining a higher dimensional generalization of the Goldberg-Sachs theorem will be described.

I will discuss recent joint work with A. Ionescu and S. Klainerman on the black hole uniqueness problem. A classical result of Hawking (building on earlier work of Carter and Robinson) asserts that any vacuum, stationary black hole exterior region must be isometric to the Kerr exterior, under the restrictive assumption that the space-time metric shouldbe analytic in the entire exterior region. We prove that Hawking's theorem remains valid without the assumption of analyticity, for black hole exteriors which are apriori assumed to be ''close'' to the Kerr exterior solution in a very precise sense. Our method of proof relies on certain geometric Carleman-type estimates for the wave operator. Time permitting, some more recent developments will also be surveyed.

The seminar is devoted to the solution of the AdS/CFT spectral problem, both for infinite and finite volume cases, using integrability. The basic constructions will be explained using an analogy with the relativistic O(4) sigma model. We devote a special attention to the study of the so called dressing factor. This is a scalar factor of the scattering matrix fixed using discrete crossing symmetry. We will show how to explicitly solve the equations dictated by the crossing symmetry, discuss essential properties of the dressing factor and give a shorthand and suggestive notation for the Bethe Ansatz of AdS/CFT. Then we will sketch a shorthand way to pass from the Bethe Ansatz to the Y-system.

A systematic method to construct 4d N=2 supersymmetric theories by compactifying M5-branes on a Riemann surface was found by Gaiotto last year. This suggests that any physical quantity of the 4d theory should be reflected in another physical quantity of the 2d theory living on the Riemann surface. Indeed, one finds that the instanton partition function of the 4d theories equals the conformal blocks of the 2d theory. I would like to illustrate this construction through explicit examples.

WIMPless dark matter offers an attractive framework in which dark matter can be very light. We investigate the implications of such scenarios on invisible decays of bottomonium states for dark matter with a mass less than around $5 {\rm GeV}$. We relate these decays to measurements of nucleon-dark matter elastic scattering. We also investigate the effect that a coupling to $s$ quarks has on flavor changing $b\to s$ processes involving missing energy.

We apply newly-developed techniques for studying perturbative scattering amplitudes to gauge theories with matter. It is well known that the N=4 SYM theory has a very simple S-matrix; do other gauge theories see similar simplifications in their S-matrices? It turns out the one-loop gluon S-matrix simplifies if the matter representations satisfy some group theoretic constraints. In particular, these constraints can be expressed as linear Diophantine equations involving the higher order Indices (or higher-order Casimirs) of these representations. We solve these constraints to find examples of theories whose gluon scattering amplitudes are as simple as those of the N=4 theory. This class includes the N=2, SU(K) theory with a symmetric and anti-symmetric tensor hypermultiplet. Non-supersymmetric theories with appropriately tuned matter content can also see remarkable simplifications. We find an infinite class of non-supersymmetric amplitudes that are cut-constructible even though naive power counting would suggest the presence of rational remainders.

Gamma rays from WIMP annihilation are an important signal through which we search for non-gravitational interactions of dark matter. In particular, lines in the energy spectrum of gamma rays provide a signal which is difficult for conventional astrophysics to fake, and are thus promising despite the fact that such lines are generically expect to be suppressed, arising from one loop processes. I will discuss two theories which have an interesting family of gamma ray lines and discuss how such lines can reveal information about the WIMPs and the dark sector.

We investigate a simple theory where Baryon number (B) and Lepton number (L) are local gauge symmetries. In this theory B and L are on the same footing and the anomalies are cancelled by adding a single new fermionic generation. There is an interesting realization of the seesaw mechanism for neutrino masses. Furthermore there is a natural suppression of flavour violation in the quark and leptonic sectors since the gauge symmetries and particle content forbid tree level flavor changing neutral currents involving the quarks or charged leptons. Also one finds that the stability of a dark matter candidate is an automatic consequence of the gauge symmetry. Some constraints and signals at the Large Hadron Collider are briefly discussed.