High Energy Physics

Renormalized perturbation theory for QFTs typically produces divergent series, even if the coupling constant is small, because the series coefficients grow factorially at high order. A natural, but historically difficult, challenge has been how to make sense of the asymptotic nature of perturbative series.  In what sense do such series capture the physics of a QFT, even for weak coupling?   I will discuss a recent conjecture that the semiclassical expansion of path integrals for asymptotically free QFTs - that is, perturbation theory - yields well-defined answers once the implications of  resurgence theory are taken into account.   Resurgence theory relates expansions around different saddle points of a path integral to each other, and has the striking practical implication that the high-order divergences of perturbative series encode precise information about the non-perturbative physics of a theory.  These ideas will be discussed in the context of a QCD-like toy model theory, the two-dimensional principal chiral model, where resurgence theory appears to be capable of dealing with the most difficult types of divergences, the renormalons.  Fitting a conjecture by ’t Hooft, understanding the origin of renormalon divergences allows us to see the microscopic origin of the mass gap of the theory in the semiclassical domain.

The cosmological model based on cold dark matter (CDM) and dark energy has been hugely successful in describing the observed evolution and large scale structure of our Universe.  However, at small scales (in the smallest galaxies and at the centers of larger galaxies), a number of observations seem to conflict with the predictions CDM cosmology, leading to recent interest in Warm Dark Matter (WDM) and Self-Interacting Dark Matter (SIDM) models. These small scales, though, are also regions dominated by the influence of baryons. I will present results from high resolution cosmological galaxy simulations that include both baryons and dark matter to show that baryonic physics can significantly alter the dark matter structure and substructure of galaxies, revolutionizing our expectations for galaxy structure and influencing our interpretation of the Dark Matter model.

In the search for dark matter, neutrino experiments can play a key role by doubling as dark matter production and detection experiments. I will describe how the proposed DAEdALUS decay-at-rest neutrino experiment can be used to search for MeV-scale dark matter, with particular emphasis on dark matter produced through a dark photon in rare neutral pion decays. The fact that the dark photon need not be on-shell opens up a wide range of new possibilities for the experimental program of searching for dark matter at neutrino experiments.

I will talk about 4d N=2 gauge theories with a co-dimension-two full surface operator, which exhibit a fascinating interplay of supersymmetric gauge theories, equivariant Gromov-Witten theory and geometric representation theory. For pure Yang-Mills and N=2* theory, a full surface operator can be described as the 4d gauge theory coupled to a 2d N=(2,2) gauge theory. By supersymmetric localizations, we present the exact partition functions of both 4d and 2d theories which satisfy integrable equations. In addition, I will show the validity of the orbifold method in one-loop computations when a full surface operator is inserted, and the form of the structure constants with a semi-degenerate field in SL(N,R) WZNW model is predicted from one-loop determinants.

Recent comparison between observation and expectation could point to problems with the standard cold, non-interacting dark matter picture, one of which being how small the smallest gravitationally bound dark matter halos are. I will review the cold dark matter picture and the experimental tests. One solution to the problems comes from coupling the dark matter to neutrinos. I will describe the model building requirements of such a coupling and determine how to test this scenario.

Moduli fields with Planck suppressed couplings to light species are ubiquitous in string theory and supersymmetry. These scalar fields are expected to dominate the energy budget in the early universe. Their out-of-equilibrium decays can produce dark matter and baryons. Dark matter generated in this non-thermal manner typically has large annihilation rates that are strongly constrained by indirect detection. The resulting bounds on superpartner masses offer dim prospects for collider discovery of supersymmetry. We will discuss extensions of the Minimal Supersymmetric Standard Model (MSSM) that allow low scale supersymmetry accessible by direct searches, while being consistent with astrophysical and cosmological probes. The tension with indirect searches is most easily relieved by allowing the lightest MSSM superpartner to decay into new stable states that play the role of dark matter. We examine the viability of this scenario in models with light Abelian and non-Abelian hidden sectors, and asymmetric dark matter. This latter possibility has a natural connection to theories of baryogenesis.

A new experiment called PTOLEMY (Princeton Tritium Observatory for Light, Early-Universe, Massive-Neutrino Yield) is under development at the Princeton Plasma Physics Laboratory with the goal of challenging one of the most fundamental predictions of the Big Bang – the present-day existence of relic neutrinos produced less than one second after the Big Bang.  Using a gigantic graphene surface to hold 100 grams of a single-atomic layer of tritium, low noise antennas that sense the radio waves of individual electrons undergoing cyclotron motion, and a massive array of cryogenic sensors that sit at the transition between normal and superconducting states, the PTOLEMY project has the potential to challenge one of the most fundamental predictions of the Big Bang, to potentially uncover new interactions and properties of the neutrinos, and to search for the existence of a species of light dark matter known as sterile neutrinos.

We exactly evaluate the partition function (index) of N=4 supersymmetric quiver quantum mechanics in the Higgs phase by using the localization techniques. We show that the path integral is localized at the fixed points, which are obtained by solving the BRST equations, and D-term and F-term conditions. We turn on background gauge fields of R-symmetries for the chiral multiplets corresponding to the arrows between quiver nodes, but the partition function does not depend on these R-charges. We give explicit examples of the quiver theory including a non-coprime dimension vector. The partition functions completely agree with the mathematical formulae of the Poincare polynomials and the wall crossing for the quiver moduli spaces. We also discuss exact computation of the expectation values of supersymmetric (Q-closed) Wilson loops in the quiver theory.

 I will discuss various aspects of non-relativistic field theories on a curved, background spacetime. First things first, we need to know what sort of geometry these theories couple to, as well as the symmetries we ought to impose. I will argue that Galilean-invariant theories should be coupled to a form of Newton-Cartan geometry in which one enforces a one-form shift symmetry, which amounts to a covariant version of invariance under Galilean boosts. I will focus on two main applications of this result, namely consequences of these symmetries at nonzero temperature and the relation to warped CFTs.

We are investigating modifications of general relativity that are operative at the largest observable scales. In this context, we are investigating the model of brane induced gravity in 6D, a higher dimensional generalization of the DGP model. As opposed to different claims in the literature, we have proven the quantum stability of the theory in a weakly coupling regime on a Minkowski background. In particular, we have shown that the Hamiltonian of the linear theory is bounded from below. This result opened a new window of opportunity for consistent modified Friedmann cosmologies. In our recent work it is shown that a brane with FRW symmetries necessarily acts as a source of cylindrically symmetric gravitational waves, so called Einstein-Rosen waves. Their existence essentially distinguishes this model from its codimension-one counterpart and necessitates to solve the non-linear system of bulk and brane-matching equations. A numerical analysis is performed and two qualitatively different and dynamically separated classes of cosmologies are derived: degravitating solutions for which the Hubble parameter settles to zero despite the presence of a non-vanishing energy density on the brane and super-accelerating solutions for which Hubble grows unbounded. The parameter space of both the stable and unstable regime is derived and observational consequences are discussed: It is argued that the degravitating regime does not allow for a phenomenologically viable cosmology. On the other hand, the super-accelerating solutions are potentially viable, however, their unstable behavior questions their physical relevance.