High Energy Physics

I will introduce the spectral function method in the context of conformal bootstrap. I will discuss some applications of this method in two dimensions: (1) substantial evidence for the conjecture that the only unitary c>1 CFT with Virasoro primaries of bounded spin is Liouville theory, (2) detailed modular constraints on the spectrum of small c CFTs, (3) spectral density of large c CFTs with large gap, in connection to the (non-)universality of BTZ black hole entropy.

Sub-GeV dark matter is a theoretically motivated but largely unexplored paradigm of dark matter. In this talk, I will discuss recent work on the direct detection of sub-GeV dark matter through dark matter-electron scattering. I will present some motivated models that can be probed with these techniques as well as projections for current and near-term noble liquid, semiconductor, and scintillator experiments. Finally, I will discuss some new techniques that may allow us to more robustly discriminate between dark matter signatures and background.

I will discuss the chiral algebra W_infty which is obtained from the Virasoro algebra by adding fields of spin 3, 4, .... Via a non-local non-linear map one can show that it is equivalent to Tsymbaliuk's Yangian of affine u(1). In this way we find an infinite number of commuting conserved charges. Diagonalizing these, the representation theory reduces to combinatorial study of plane partitions, 3-dimensional generalization of the Young diagrams. Tsymbaliuk's presentation can be derived from RTT relations using Maulik-Okounkov's free boson R-matrix.

Recently a boundary energy-momentum tensor Tzz has been constructed from the soft graviton operator for any 4D quantum theory of gravity in asymptotically flat space. Up to an "anomaly" which is one-loop exact, Tzz generates a Virasoro action on the 2D celestial sphere at null infinity. Here we show by explicit construction that the effects of the IR divergent part of the anomaly can be eliminated by a one-loop renormalization that shifts Tzz.

Utilizing the Fermi measurement of the gamma-ray spectrum toward the Galactic Center, we derive some of the strongest constraints to date on the dark matter (DM) lifetime in the mass range from hundreds of MeV to above an EeV. Our profile-likelihood based analysis relies on 413 weeks of Fermi Pass 8 data from 200 MeV to 2 TeV, along with up-to-date models for diffuse gamma-ray emission within the Milky Way. We model Galactic and extragalactic DM decay and include contributions to the DM-induced gamma-ray flux resulting from both primary emission and inverse-Compton scattering of primary electrons and positrons. For the extragalactic flux, we also calculate the spectrum associated with cascades of high-energy gamma-rays scattering off of the cosmic background radiation. We argue that a decaying DM interpretation for the 10 TeV-1 PeV neutrino flux observed by IceCube is disfavored by our constraints. We interpret the results in terms of individual final states and in the context of simplified scenarios such as a hidden-sector glueball model.

The subject of quantum field theory in mixed states of quantum matter is an old and rich one. The natural setting to discuss field theory in a mixed state is the Schwinger-Keldysh formalism. The subject of this talk is the set of peculiar symmetries that arise in Schwinger-Keldysh theories, and how they may be accounted for in effective field theory. In particular, when the mixed state is thermal, the effective description is constrained by two BRST-like supercharges which, at low energies, generate an algebra akin to minimal supersymmetric quantum mechanics. If time allows, I will also discuss a sort of Schwinger-Keldysh bootstrap for effective actions on more complicated closed-time-contours, which describe the out-of-time-ordered correlation functions that diagnose early-time chaotic growth in quantum systems.

The conformal bootstrap aims to calculate scaling dimensions and correlation functions in various theories, starting from general principles such as unitarity and crossing symmetry.  I will explain that local operators are not independent of each other but organize into analytic functions of spin, and I will present a formula which quantifies the consequences of this fact.  This will include a controlled approximation to the operator spectrum at large spin, as well as new bounds over the strength of bulk higher-derivative interactions in large-N theories with a sparse spectrum. These bounds, previously conjectured to exist using gauge-gravity duality, encode causality of the bulk theory.  Based on 1703.00278.

Just like how milli-electric charged particles can exist, so can milli-magnetic charged particles.  We review simple ways of evading the standard quantization arguments and why there are no model independent constraints on magnetically charged particles, milli-charged or not.  We then provide the first ever model independent bounds coming from magnetar cooling arguments.

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.