Talks

The analogy between Multi-scale Entanglement Renormalization
Ansatz (MERA) and the spatial slice of three-dimensional anti-de
Sitter space (AdS3) has motivated a great interest in tensor networks
among holographers. I discuss a way to promote this analogy to a
rigorous, quantitative, and constructive relation. A key quantitative
ingredient is the way the strong subadditivity of entanglement entropy
is encoded in MERA and in a holographic spacetime. The upshot is that
the map between MERA and the spatial slice of AdS3 is mediated through
an additional integral transform. Interpreted directly, MERA is a
discretization not of the spatial slice of AdS3, but of the space of
geodesics on the spatial slice of AdS3.

We introduce and systematically study an expansive class of "orbifold Higgs" theories in which the weak scale is protected by accidental symmetries arising from the orbifold reduction of continuous symmetries. The protection mechanism eliminates quadratic sensitivity of the Higgs mass to higher scales at one loop (or more) and does not involve any new states charged under the Standard Model.

An exciting and largely unexplored frontier in observational and theoretical cosmology is to understand the properties of the universe between 400,000 years and one billion years after the big bang. Notably, the first galaxies formed in this time period, perhaps a few hundred million years after the big bang.  These galaxies strongly influenced the gas in their surroundings as well as the formation of subsequent generations of galaxies. The early galaxies emitted ultraviolet light and ionized "bubbles" of hydrogen gas around them.  These ionized bubbles grew, merged, and eventually filled the entire volume of the universe with ionized hydrogen in a process known as reionization. Understanding this process will constrain the properties of the first luminous sources, and fill in a significant gap in our story of structure formation, whereby the universe transitions from simple initial conditions to its present day complexity. I will briefly summarize current observational constraints and describe some new ideas for better determining when the reionization process completed using existing Lyman-alpha forest data.

As an alternative to the Holographic Renormalization procedure, we

introduce a regularization scheme for AdS gravity based on the addition

boundary terms which are a given polynomial of the extrinsic and 

intrinsic curvatures (Kounterterms).

Since these terms are closely related to either topological invariants 

or Chern-Simons densities in the corresponding dimension, they can be 

easily generalized to other gravity theories (Einstein-Gauss-Bonnet, 

Lovelock, etc.).

Finally, a general prescription on how to obtained the standard 

counterterm series in AdS gravity is given.​