Talks

In this talk I will discuss a new use for conformal field theory crossing equation in the context of AdS/CFT:  the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. I will revisit this problem and the dual 1/N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1/N^2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. The second approach involves Mellin space. As an example, I’ll show how the polar part of the four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order data. The anomalous dimensions computed with both methods agree. In the case of \phi^4 theory in AdS, the crossing solution reproduces a previous computation of the one-loop bubble diagram. I will end with a discussion on open problems and new developments.

We are currently entering the era of precision CMB polarization observations. The most exciting scientific targets are a possible detection of primordial gravitational waves and a measurement of the sum of the neutrino masses. The former depends on the extensive landscape of early Universe models, while the latter has been forecasted to present a clear, and reachable, scientific target. First, if large angular B modes are detected, we should firmly establish that these are sourced by primordial gravitational waves. I will discuss that cross correlating the B-mode signal with the curl-lensing field could help establish the nature of the detected B-modes. Second, I will propose to look beyond Gaussianity in the tensor sector. Scalar non-Gaussianities are tightly constrained by Planck, but couplings between tensors and scalars are currently not constrained and future CMB polarization surveys could open a new window into the early Universe, by searching for tensor non-Gaussianites. Finally, a detection of the normal hierarchy of the neutrino mass requires an excellent measurement of the amplitude of primordial fluctuations. The required measurement can only be achieved if we are able to measure the large angle E-mode polarization spectrum, which currently lies beyond reach, at least within the foreseeable future. I will present a possible solution and show how this simple methodology can be used to constrain exotic primordial physics at the same time.