Week 22.01.2024 – 28.01.2024

In recent years we've greatly expanded our understanding of entanglement in many-body quantum systems; both how it behaves in ground states, and how it grows out-of-equilibrium. While entanglement is very difficult to measure in experiments, it has nevertheless driven progress in 1) the classification of quantum phases of matter and 2) strategies for efficiently simulating many-body systems on classical and quantum computers. I will review some recent progress in these directions. Along the way I will summarise some older results on how entanglement grows in many-body systems, briefly highlight some connections to holography, and present a conjecture about the asymptotic computational difficulty of calculating transport in many-body systems.

As is well known, the string spectrum comprises infinitely many states that can collectively be visualized along Regge trajectories of increasing mass and spin. Its massless and lightest levels, as well as certain higher spins including the leading Regge trajectory, have been the focus of past studies. In principle, access to any state is possible, but the traditional methodology is non-covariant and does not immediately lead to irreducible representations of the Wigner little group. In this talk, we will discuss a new and covariant technology of constructing the string spectrum. It is based on the observation that there is a bigger symmetry behind the Virasoro constraints: the symplectic algebra that commutes with the spacetime Lorenz algebra. This enables excavating string states and their interactions by entire trajectories, rather than individually.

I will describe how various vertices and scattering amplitudes, involving background fields, probe trace anomaly coefficients in a four-dimensional (4D) renormalization group (RG) flow. Specifically, I will explain how to couple dilaton and graviton fields to the degrees of freedom of 4D QFT, ensuring the conservation of the Weyl anomaly along the RG flow for the coupled system. By providing dynamics to the dilaton and graviton fields, I will demonstrate that the graviton-dilaton scattering amplitude receives a universal contribution, exhibiting helicity flipping and being proportional to (Δc−Δa) along any RG flow. Here, Δc and Δa represent the differences in the UV and IR CFT c- and a-trace anomalies, respectively. Using a dispersion relation, (Δc−Δa) can be related to spinning massive states in the spectrum of the QFT. We test our proposal through various perturbative examples. Finally, as an application of the proposal of probing the trace anomalies using scattering amplitude, we have derived a non-perturbative bound on the UV CFT a-anomaly coefficient using numerical S-matrix bootstrap program for massive RG flow.

Recent developments on Feynman integrals and string amplitudes greatly benefitted from multiple polylogarithms and their elliptic analogues — iterated integrals on the sphere and the torus, respectively. In this talk, I will review the Brown-Levin construction of elliptic polylogarithms and propose a generalization to Riemann surfaces of arbitrary genus. In particular, iterated integrals on a higher-genus surface will be derived from a flat connection. The integration kernels of our flat connection consist of modular tensors, built from convolutions of Arakelov Green functions and their derivatives with holomorphic Abelian differentials. At genus one, these convolutions reproduce the Kronecker-Eisenstein kernels of elliptic polylogarithms and modular graph forms. I will conclude with an outlook on open problems and work in progress.