Physics

Light bosons, including light axions, dark photons, and dilaton/moduli, are well motivated extensions to the Standard Model of particle physics and intriguing dark matter candidates. Much progress has been made in recent years in both astrophysical and lab searches for these light bosons with the understanding that these light bosons act like weak classical waves which permeate the space we occupy. 

In this talk, I will discuss some novel phenomenon of light bosons in the dark sector, based on important in medium effects of these particles. I will show how to take advantage of medium effects of the photon to optimize searches for these light bosons with data coming from cosmic microwave background (CMB) experiments, and improve sensitivity to light dark photons and axions by orders of magnitude. I will also show how thinking of dark photon as weak classical waves breaks down during production of light bosons in both early and late universe, when gauged strings are produced in an event we call the string Bosenova, as well as the resulting observable consequences.

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Quantum entanglement measures of many-body states have been increasingly useful to characterize phases of matter. Here we explore the surprising connection between symmetry-protected topology (SPT) and separability of their boundary mixed states. More specifically, we consider lattice systems in d space dimensions with anomalous symmetry G, where the anomaly is characterized by a bulk SPT invariant in the group cohomology Hd+2(G,U(1)). We show that any mixed state ρ that is strongly symmetric under G, in the sense that G ρ ∝ ρ, is necessarily (d+2)-nonseparable, i.e. is not the mixture of tensor products of d+2 states in the Hilbert space. Furthermore, such states cannot be prepared from any (d+2)-separable states using finite-depth local quantum channels, so the non-separability is long-ranged in nature. The anomaly-nonseparability connection also allows us to generate simple examples of mixed states with nontrivial multi-partite entanglement.

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Feynman diagrams and the associated integrals are crucial in perturbative quantum field theory for translating theory input into concrete, observable quantities. I will talk about the fascinating interplay of physics and mathematics that emerges from the ensemble of these diagrams. From linear algebra to quantum mechanics or wave phenomena to Fourier analysis - physics and mathematics tend to regularly exchange ideas that often lead to breakthroughs on the other side. I will illustrate two new examples of such exchanges I contributed to. One exchange is from the mathematical theory of tropical geometry to evaluating intricate, physically relevant Feynman integrals that have been inaccessible before. In the second exchange, we used ensembles of Feynman diagrams and their renormalization to prove a long-standing conjecture in geometric group theory. The results give new insights into the 'dark matter'-problem in the moduli spaces of graphs and curves' cohomology.  Both these moduli spaces' cohomologies are of fundamental interest in algebraic geometry, topology and geometric group theory.

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