This week

In a physical system with conformal symmetry, observables depend on cross-ratios, measures of distance invariant under global conformal transformations (conformal geometry for short). We identify a quantum information-theoretic mechanism by which the conformal geometry emerges at the gapless edge of a 2+1D quantum many-body system with a bulk energy gap. We introduce a novel pair of information-theoretic quantities (c,n) that can be defined locally on the edge from the wavefunction of the many-body system, without prior knowledge of any distance measure. We posit that, for a topological groundstate, the quantity c is stationary under arbitrary variations of the quantum state, and study the logical consequences. We show that stationarity, modulo an entanglement-based assumption about the bulk, implies (i) c is a non-negative constant that can be interpreted as the total central charge of the edge theory. (ii) n is a cross-ratio, obeying the full set of mathematical consistency rules, which further indicates the existence of a distance measure of the edge with global conformal invariance. Thus, the conformal geometry emerges from a simple assumption on groundstate entanglement. The stationarity of c is equivalent to a vector fixed-point equation involving n, making our assumption locally checkable. If time permits, we discuss a class of modular flow on a disk, which creates only edge excitations. We intuitively explain why Virasoro algebra can be revealed from a single wavefunction by analyzing such modular flows.

Diverse observations have established the standard cosmological model, known as $\Lambda CDM$. Within this model, the Universe began in a hot dense state filled with tiny primordial density fluctuations. These fluctuations grew as they collapsed under gravity and eventually became the seeds of the galaxies throughout the Universe. A key question is where did these initial perturbations come from? The leading model for their creation, known as inflation, posits that these arose from quantum vacuum fluctuations that were stretched to cosmic scales by a period of exponential expansion of the Universe. Many models predict that this process will leave distinct statistical signatures on the primordial density perturbations. In this talk I will discuss how we can use the spatial distribution of galaxies to search for these early Universe signatures. In particular, I will show how novel analysis methods will allow us to robustly disentangle the primordial information from late-time physics. These approaches will shed new light on aspects from the number of fields present during inflation to the strength of interactions to symmetries of inflation.

I will be using scattering amplitudes, instead of the Lagrangian of General Relativity (GR), to compute classical observables in GR. In the first part of the seminar I will consider the elastic scattering of two massive particles, describing two black holes, and I will show how to compute the eikonal up to two-loop order, corresponding to third Post-Minkowskian (3PM) order, that contains all the classical information. From it I will compute the first observable that is the classical deflection angle. In the second part of the seminar I will consider inelastic processes with the emission of soft gravitons. In this case the eikonal becomes an operator containing the creation and annihilation operators of the gravitons. The case of soft gravitons can be treated following the Bloch-Nordsieck approach and, in this case, I will be computing two other observables: the zero-frequency limit (ZFL) of the spectrum dE/d\omega of the emitted radiation and the angular momentum loss at 2PM and 3PM. I will consider also the case in which there are static modes localised at $\omega=0$. In the third part of the seminar I will be discussing soft theorems with one graviton emission, first briefly at tree level, and then at loop level following the paper by Weinberg from 1965. Assuming the eikonal resummation and that all infrared divergences in the case of gravity come only from one loop diagrams, I will compute the universal soft terms, corresponding to $\frac{1}{\omega}$, $\log \omega$ and $\omega \log^2 \omega$, first at the tree and one-loop level and then for the last two observables also at two-loop level. I will then use them to compute their contribution to the spectrum of emitted energy. Finally, if I have time left, I I will study the high energy limit. In particular, since the graviton is the massless particle with the highest spin, we expect universality at high energy. I will show that universality at high energy is satisfied both in the elastic and inelastic case, but this happens in the inelastic case in a very non trivial way. I will end with some conclusions and with a list of open problems.