Opening

• Valentina Giangreco Puletti
• Gianluca Grignani (PG)

Room: Aula C, second floor

Defects in conformal and supersymmetric field theories

• Simone Giacomelli ((ICTP Trieste))
• Marco Meineri (EPFL Lausanne)

Room: Aula C, second floor In a quantum or statistical field theory, the action of operators on the vacuum describes how a physical system is affected by a probe. Often, the probes are extended objects: the word-line of a heavy particle, a boundary or an interface, etc. We describe some general features of extended probes, in highly symmetric QFTs. We first focus on conformal field theories. We discuss properties of the Operator Product Expansion in the presence of defects and give examples of topological and non topological conformal defects. We then move to the case of supersymmetric theories, in which we can construct defects with two-dimensional (or higher) support. We explain how certain kinds of extended probes are able to detect the phases of the theory. Finally, we describe the relevance of defects in constructing a large class of superconformal N=2 theories in four dimensions, and how one can use properties of topological defects in two dimensions to compute the expectation value of line operators in these theories.

Defects in conformal and supersymmetric field theories - Discussion session

• Simone Giacomelli (ICTP Trieste)
• Marco Meineri (EPFL Lausanne)
• Stefano Cremonesi (Durham)

Room: Aula C, second floor

Soft terms in string compactifications

• Francesco Muia (Oxford)
• Susha Parameswaran (Liverpool)

Room: Aula C, second floor Supersymmetry is a generic prediction of string theory. Given that it is not an exact symmetry of nature, in order to connect string compactifications to particle physics, we must understand how supersymmetry is broken. This issue is intimately related to the moduli stabilisation problem in string theory, as the latter determines the vacuum structure of the theory. Interestingly, SUSY-breaking in string theory is typically soft, which means that the supersymmetric cancellation of quadratic divergences in the Higgs mass endures. Such breaking is then parameterised by soft terms, which roughly determine the masses of superpartners. If SUSY-breaking generates soft-terms at energy scales accessible to particle accelerators (as expected if low-energy SUSY is the correct way of addressing the hierarchy problem) then, remarkably, they would directly relate properties of the string compactification to experiments. We will begin by reviewing the motivation and description of soft SUSY-breaking in the MSSM and supergravity, commenting on current constraints from the LHC. We will then describe the main mechanisms for moduli stabilisation, SUSY-breaking and mediation in string theory. Putting these tools together we will illustrate, within the Heterotic and Type IIB theories, interesting possibilities for the soft-terms in string compactifications. A particular focus will be on the interplay with cosmology, which has been best studied in Type IIB models. The presence of moduli in these compactifications leads to a modification of the standard Big Bang Theory, in which the reheating of the universe is driven by the decay of the lightest modulus. In particular, we will show that such non-standard cosmological history of the universe plays a crucial role in constraining SUSY-breaking in string models. Interestingly, it turns out that, once all the cosmological constraints are taken into account, it is actually rather difficult to get low-energy SUSY from string theory. Finally, we will briefly review the cosmological scenarios which could arise from such string compactifications.

Soft terms in string compactifications - Discussion session

• Francesco Muia (Oxford)
• Susha Parameswaran (Liverpool)
• Michele Cicoli (BO)

Room: Aula C, second floor

Black hole mergers and gravitational waves

• Sebastiano Bernuzzi (P)
• Paolo Pani (Rome Sapienza)

Room: Aula C, second floor The broad scope of these lectures is to introduce the basic elements which are necessary to understand the GW signals from a BH binary merger recently-observed by LIGO, and to provide the basis of some state-of-the-art applications in this rapidly-growing field. Content i) A GW physics primer. ii) Introduction to the post-Newtonian formalism. The case of circular inspiral. iii) Black-hole perturbations and quasinormal modes (QNMs) iv) GWs from a radial plunge of a test particle into a black hole: QNM ringing v) Black-hole spectroscopy: tests of gravity and of near-horizon physics vi) Numerical Relativity and Effective-One-Body (EOB) approach

Black hole mergers and gravitational waves - Discussion session

• Sebastiano Bernuzzi (P)
• Paolo Pani (Rome Sapienza)
• Daniele Dorigoni (Durham)

Room: Aula C, second floor

Topological states of matter and non-supersymmetric dualities

• Andrea Amoretti (Wuerzburg)
• Giandomenico Palumbo (Utrecht)

Room: Aula C, second floor In the first part of the lecture, we will briefly introduce topological phases of matter and their main properties by employing effective quantum field theories, such as Chern-Simons and relativistic fermion theories. In particular, we will review the role of the Dirac theory in these quantum phases by focusing on the fractional quantum Hall effect with filling factor 1/2 (FQHE-1/2), where an emergent particle-hole symmetry plays a prominent role. The second part of the lecture deals with dualities and their possible application to topological states of matter. Specifically, we will review recent papers where, starting from a relativistic form of flux attachment designed to transmute the statistics of particles, a web of new dualities can be derived. This includes the usual particle-vortex duality for bosons as well as the recently discovered counterpart for fermions in the FQHE-1/2 and on the surface states of three-dimensional topological insulators.

Topological states of matter and non-supersymmetric dualities - Discussion session

• Andrea Amoretti (Wuerzburg)
• Giandomenico Palumbo (Utrecht)
• Andrea Campoleoni (Université Libre de Bruxelles)

Room: Aula C, second floor

Exact results for superconformal field theories

• Marco Baggio (KUL Leuven)
• Antonio Sciarappa (KIAS Seoul)

Room: Aula C, second floor One of the most widely used approaches to study interacting quantum field theories is perturbation theory, where physical quantities are expressed as a series expansion in some small parameter. Despite its many successes, the perturbative approach cannot be used to study important physical phenomena like confinement and chiral symmetry breaking in QCD for which non-perturbative and strong-coupling effects play a key role. While these are still largely open problems, in the last few years the field has witnessed tremendous progress in understanding the non-perturbative and strongly coupled behaviors of many interesting quantum field theories, especially in the supersymmetric context where we can now compute several observables of interest, such as partition functions and correlation functions, exactly in the coupling constant. In these lectures we will present some of these recent developments, focusing in particular on four dimensional N=2 supersymmetric field theories. After introducing the theories of interest, we will discuss how these are related to integrable systems and how this correspondence can be used to compute their partition function around a generic strong-coupling point. In the case where these theories also enjoy conformal symmetry, the partition function encodes detailed information about correlation functions of chiral operators. We will describe how the 3-point functions of chiral primaries can be computed exactly using techniques from localization and the tt* equations.

Exact results for superconformal field theories - Discussion session

• Marco Baggio (KUL Leuven)
• Antonio Sciarappa (KIAS Seoul)
• Davide Cassani (LPTHE Jussieu)

Room: Aula C, second floor