High Energy Physics

We study the eigenstate thermalization hypothesis in chaotic conformal field theories (CFTs) of arbitrary dimensions by computing the reduced density matrices of small size in energy eigenstates. We show that in the infinite volume limit this operator is well-approximated by a “universal” density matrix which is its projection to the primary operators that have nonzero thermal one-point functions. These operators in all two-dimensional CFTs and holographic higher-dimensional CFTs are the polynomials of stress tensor. We compute the time-dependent two-point correlators and Renyi entropies of the universal density martix, and compare the results to the thermal Gibbs state and black holes in various dimensions. We demonstrate that the two-dimensional universal density matrix is close in trace distance to the reduced Gibbs state. We put forward the truncation of density matrix to the stress tensor sector as a “hydrodynamic” method to study the out-of-equilibrium dynamics of strong-coupled field theories

Recently a new solution to the hierarchy problem was proposed which makes use of the cosmological evolution of a light scalar field, a scanner, instead of symmetry or anthropic arguments to select a small Higgs mass. In the original proposal this scanner field could be the QCD axion and thus such class of solution became known as ``relaxion’’. Two central features required of the relaxion are a reason for why a small Higgs mass is special from the scanner’s viewpoint and a mechanism fo the scanner to dissipate its energy in order to stop in a value associated with small Higgs mass. In this talk we propose a novel mechanism that achieves both goals and opens new possibilities for the relaxion. We show that particle production can create an effective friction force for the relaxion and show how it can be used to ``select’’ the TeV scale as a special energy scale from reasonable initial conditions. This allows for the scanning to happen much faster than in previous relaxion models, which usually require very large amounts of inflation, and also allows for the scanning to take place after inflation has ended.

I will discuss a new class of supersymmetric Wilson loop operators in pure N=2 Yang-Mills-Chern-Simons theory. These Wilson loops preserve one supercharge on-shell and wrap arbitrary Legendrian knots in the standard contact R^3.  I will also explain a relation, motivated by a global picture of contact three-manifolds, between these loop operators and chiral current algebra in two dimensions.  This talk is directly related to, but independent of, my preceding Friday talk in the Mathematical Physics seminar.

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.

In the first part of the talk, I will explain how the lengths of non-minimal geodesics in AdS3 conical defect backgrounds can be interpreted as the entanglement entropy of certain subalgebras in the dual CFT. This part will be based on 1608.02040. In the second part of the talk, I will discuss how the Ryu-Takayanagi area term seems to be the analog of a certain edge term for EE in a gauge theory, and how one might try to test this. This part is more speculative.

A very close supernova explosion could have caused a mass extinction

of life in Earth. In 1996, Brian Fields, the late Dave Schramm and the
speaker proposed looking for unstable isotopes such as Iron 60 that could
have been deposited by a recent nearby supernova explosion. A group from
the Technical University of Munich has discovered Iron 60 in deep-ocean
sediments and ferromanganese crusts due to one or more supernovae that
exploded O(100) parsecs away about 2.5 million years ago. These results
have recently been confirmed by a group from the Australian National
University, and the Munich group has also discovered supernova Iron 60 in
lunar rock samples and in microfossils of magnetotactic bacteria. 
This colloquium will discuss the data and their interpretation
in terms of supernova models, and the possible implications for
life on Earth.

Cold dark matter provides a remarkably good description of cosmology and astrophysics. However, observations connected with small scales might be in tension with this framework. In particular, structure formation simulations suggest that the density profiles of dwarf spheroidal galaxies should exhibit cusps, in contrast to observations. I will show that Fermi repulsion can explain the observed cored density profiles in dwarf galaxies for sub-keV fermionic dark matter.  While in conventional dark matter scenarios, such sub-keV thermal dark matter would be excluded by free streaming bounds, I will argue that these constraints are ameliorated in models with dark matter at lower temperature than conventional thermal scenarios. Finally, I will outline a class in which the dark matter typically has a lower temperature than the thermal expectation, dubbed Flooded Dark Matter, and discuss aspects of model building.

The moduli space of vacua of 3d N=4 gauge theories splits essentially into two ``branches”: the Higgs branch parametrised by the vevs of hypermultiplet scalars and the Coulomb branch parametrised by the vevs of dressed monopole operators. They can be described as complex algebraic varieties. I will present a new approach to the analysis of the Higgs and Coulomb branches based on the type IIB brane realisation of the gauge theory. Focusing on abelian theories, I will show how the addition of new ingredients in the brane setup can be linked to the path integral insertions of Higgs or Coulomb operators. I will explain how this construction can be used to derive the ring relations and study mirror symmetry.

This talk applies effective field theory to the back-reaction of sources with finite size but infinite mass. The main tool for calculating back-reaction is a general relation between a source's effective action and the boundary conditions of `bulk’ fields in the near-source limit. As applied to the Maxwell (or Einstein) fields for point sources this boundary condition reproduces standard Gauss’ Law expressions, but the same arguments imply source-dependent boundary conditions for the Schrodinger (or Dirac) field of an orbiting particle. As applied to the quantum mechanics of a particle interacting with a source through an inverse-square potential EFTs remove the guess-work from the (well-known) ambiguities in the determination of boundary conditions at the origin, and provides a simple interpretation of the classical renormalization effects that are known to arise in this case. EFT arguments show why the RG evolution associated with this classical renormalization is likely universal for a great many types of point sources. The EFT boundary conditions also modify how finite-size effects alter bound-state orbits in the Coulomb problem, and in particular give them a non-standard dependence on the mass of the orbiting particle. It is argued that this might provide a solution to the `proton-radius puzzle’, in which experiments seem to indicate a different proton radius depending on whether or not it is measured using electrons or muons.

1. The notion of wall-crossing structure (as defined by Maxim Kontsevich and myself in arXiv: 1303.3253)
provides the  universal framework for description of different types of wall-crossing formulas (e.g. Cecotti-Vafa in 2d or KSWCF in 4d). It also gives
a language and tools for proving algebraicity and analyticity of arising generating series (e.g. for BPS invariants).

2. Holomorphic Floer theory is the Floer theory of a pair of complex Lagrangian subvarieties  of a complex symplectic manifold (maybe infinite-dimensional).
This geometry underlies several important topics, both in mathematics and physics. Those  include  questions about analytic continuation of exponential integrals
(e.g. Feynman integrals),
deformation quantization of holomorphic symplectic manifolds (and related Riemann-Hilbert correspondences), Geometric Langlands correspondence, etc.

3. It was known for a long time that many a priori divergent series (like e.g. formal WKB series for solutions of equations with a small parameter) become analytic or meromorphic functions after taking their Laplace transform
(Borel resummation). This property was called  the resurgence property of the divergent series. The relation of the resurgence phenomenon to simplest wall-crossing formulas was realized in the early 90's in the work of French mathematicians (Ecale, Voros, Pham , Malgrange and  others).

I plan to discuss how the combination of 1 and 2 can be applied to 3 in a very general situation.
Main idea goes back to our theory of Donaldson-Thomas invariants (arXiv: 0811.2435).
Namely, analyticity of the formal series  follows from existence of a global analytic object which is glued from the local ones by means of the formal series.
This analytification of  an a priori formal variety is a by-product of the growth estimates on the data of the underlying wall-crossing structure.

In case of the Holomorphic Floer theory (which underlies e.g. the Stokes phenomenon for the WKB solutions of PDE or difference equations) one needs an estimate on the number of pseudo-holomorphic discs
with the boundary on the union of our Lagrangian subvarieties. In practice it often appears as an estimate on the number of gradient lines between two critical points
of the action or potential.