Doctoral Training Activities 2024/2025

This course provides a pedagogical introduction to Effective Field Theory methods (EFTs) for cosmology and gravitational theories, with a particular focus on theories that have been introduced to explain or tackle cosmic acceleration, dark energy, modified gravity, and the cosmological constant problem. Particular emphasis will be given to how low energy global and local symmetries—be they broken or unbroken—determine and organize the EFT expansion of all such theories both at the classical and quantum level. Where possible focus will be given in simple explicit examples.

Lectures 1-2: A brief intro to EFTs and why non-renormalizable theories are renormalizable (at least at low energies). General relativity as the low energy EFT of a massless spin-2 particle, Einstein-Cartan and first-order formulations. Coupling quantized gravity to QFTs, field redefinitions and decoupling limits, 1PI effective actions, loop corrections and the (old) cosmological constant problem.

Lecture 3: EFTs of dark energy, modified gravity I: scalar-tensor theories, large extra dimensions and branes, EFTs of nonlinearly realized global symmetries (axions, DBI, Galileons, conformal Galileons, k-essence, example UV completions).

Lecture 4: EFTs of dark energy, modified gravity II: EFTs of spontaneously broken diffeomorphisms (inflation/quintessence, fluids, solids aka Lorentz-violating massive gravity, Lorentz-invariant massive gravity and its extensions).

Lecture 5: Schwinger-Keldysh formalism, wavefunction of the Universe, cosmological bootstrap and analyticity.

The course only requires basic knowledge of quantum field theory (specifically in the path integral formulation) and general relativity. More details on aspects of the course can be found in the book “The Encyclopaedia of Cosmology”, Set 2: Frontiers in Cosmology: worldscientific.com

The course provides an introduction to string theory, including the bosonic string theory, the 5 supersymmetric string theories in ten spacetime dimensions, toroidal compactification, dualities, M-theory, D-branes and AdS/CFT holography. The course only requires basic knowledge of quantum field theory and general relativity, and in particular does not require previous knowledge about string theory.

In these lectures we cover some of the techniques in data analysis which have been developed in a cosmological context. We start by considering the general problem of estimating parameters from data, focusing on Monte Carlo Markov Chains (MCMC) for small catalogs. Then, we continue with the Fisher matrix formalism to analyse experimental setups before any data are taken. In fact, the Fisher matrix formalism can be of great help to test the requirements of an experiment in order to reach the desired accuracy on the final parameters that need to be tested.

We consider different experimental setups and in each topic will face the built-in of the numerical codes alongside with the theoretical recipes in order to properly construct the observables.

The last lecture will have a hands-on approach: the participants will choose the desired observable and will write their own code in their favored language.

• •07.10.2024: Introduction to statistics. Fisher matrix formalism and MCMC.
• •08.10.2024: Construction of the Fisher matrix and MCMC for various experiments
• •09.10.2024: Hands-on session.

All the codes shown during the lectures are in Python (preferred) and in Mathematica.

1) Flavor physics in the quark sector within the SM

• – Flavor changing charged current (FCCC) processes
• – Flavor changing neutral current (FCNC) processes & DF = 1,2 transitions (one-loop calculation of few relevant DF = 1,2 processes)
• – Low-energy EFT description of flavor physics: running and matching

2) Flavor in the leptonic sector within the SM

• – neutrino oscillation
• – Lepton Flavor Violation
• – anomalous magnetic moments of leptons

3) Flavor physics and new physics in the quark and leptonic sectors

Over three lectures (2h/day), the course will introduce theoretical and phenomenological aspects of hadron-hadron (day 1), lepton-lepton (day 2), and hadron-lepton (day 3) collider experiments at TeV-scale center-of-mass energies. This includes: an introduction to the Drell-Yan and weak boson scattering processes, an introduction to jets in QCD, muon colliders, neutrino-nucleus deep-inelastic scattering, and factorization in gauge theories.

I will give an introduction to the theory of topological matter and anyons, and to the theory of topological quantum information and computation. I will discuss the following subjects: quantum braiding statistics and anyons, topological order, topological quantum codes, fractional quantum Hall systems, topological qubits and topological protection, topological quantum computation. I will introduce these concepts both at a mathematical level and at a physical level, discussing physical systems in which topological order and anyons can arise.

Anomalies in quantum field theory are often thought of as pertaining to the realm of high energy physics. They play however and ever increasing role in condensed matter physics as well. I will give an introduction to the application of anomalies in condensed matter systesm, discuss topological state of matter such as SPT phases and anomaly inflow and anomaly induced transport phenomena sucha Hall and chiral magnetic effects.