Opening Room: Aula 1, Piano -1

Branes and supersymmetry breaking (Branes and Supersymmetry breaking - Stefano Massai (LMU, Munich) and Daniele Musso (ICTP, Trieste))

• Stefano Massai (LMU, Munich)
• Daniele Musso (ICTP, Trieste)

Room: Aula 1, Piano -1 The lectures will give a pedagogical introduction to various aspects of anti-brane supersymmetry breaking in string theory. The first part is based on the holographic standpoint meant both as an application to study QFT at strong coupling and as a mean of investigation of bulk physics from a dual perspective. Symmetry and supersymmetry breaking patterns are encoded in the Ward identity structure of a QFT. Holographic models realize such a structure at strong coupling through a precise holographic renormalization program. This setting is suitable to describe neatly supersymmetry breaking at strong coupling and the appearance of the goldstino in a wide and general context. The application of these techniques to cascading gauge theories offers a powerful way to study anti-branes placed in conifold bulk geometries and characterize their supersymmetry breaking. In the second part we will discuss the dynamics of anti-branes in flux compactifications, their decay channels and the quest for long-lived metastable vacua in string theory. We will cover the following topics: • The backreaction of anti-branes in warped throats • Infrared dynamics and vacuum stability • Applications: de Sitter uplift and black hole microphysics.

Branes and supersymmetry breaking - Discussion session (Branes and Supersymmetry breaking - Stefano Massai (LMU, Munich) and Daniele Musso (ICTP, Trieste))

• Stefano Massai (LMU, Munich)
• Daniele Musso (ICTP, Trieste)

Room: Aula 1, Piano -1

Axions in cosmology (Axions in Cosmology - Francisco Pedro (IFT, Madrid) and Lorenzo Ubaldi (Tel Aviv University))

• Francisco Pedro (IFT, Madrid)
• Lorenzo Ubaldi (Tel Aviv University)

Room: Aula 1, Piano -1 • Lorenzo Ubaldi I first introduce the axion as a solution to the strong CP problem, and then explain how such a light boson would be produced via the misalignment mechanism in the early universe and contribute to the energy density of cold dark matter. String theoretic or supersymmetric frameworks further predict the existence of moduli, that can decay into relativistic axions. The latter would contribute to the cosmological relativistic degrees of freedom, the so-called dark radiation. I discuss briefly the bounds on this scenario from cosmic microwave background measurements. • Francisco Pedro In this talk I will discuss some aspects of axions in the early universe, with particular emphasis on the various models of inflationary cosmology based on axionic fields. I will discuss natural inflation, aligned inflation in its various guises, N-flation and monodromy models. Throughout the talk I will make the connection between the field theoretic mechanisms for axion inflation and their embedding into string compactifications. I will review the Weak Gravity Conjecture and its potential impact on axion inflation in string theory.

Axions in Cosmology - Discussion session (Axions in Cosmology - Francisco Pedro (IFT, Madrid) and Lorenzo Ubaldi (Tel Aviv University))

• Francisco Pedro (IFT, Madrid)
• Lorenzo Ubaldi (Tel Aviv University)

Room: Aula 1, Piano -1

Scattering amplitudes and soft theorems (Scattering amplitudes and soft theorems - Paolo Benincasa (IFT, Madrid) and Matteo Rosso (Humboldt Universitaet, Berlin))

• Paolo Benincasa (IFT, Madrid)
• Matteo Rosso (Humboldt Universitaet, Berlin)

Room: Aula 1, Piano -1 This lecture is thought to provide a pedagogical introduction to the subject of scattering amplitudes, with focus on the recent developments about soft theorems. The lecture will be structured in two parts, the first of which will concern fundamental concepts such as unitarity and analyticity, as well as the singularity structure of the amplitudes and their physical importance. As far as the second part is concerned, we will review the so-called "soft theorems", their origin and the renewed interest in their structure. The relation with asymptotic symmetries will be highlighted, the attempt being to emphasize what is known and what is new. More in detail, in the first part we will touch the following topics: • Generalities: Definition and the Lorentz little group; • Analyticity, unitarity and locality; • BCFW method and the singularity structure of perturbative field theories; • Soft limits. As far as the second part is concerned: • Statement and history of soft theorems; historical importance: QCD, double scalars as probes of N = 8 moduli space. Sketch of a derivation. • Relation of soft theorems to asymptotic symmetries of the theory; definition of BMS symmetry for gravitational scattering and its relevance. • Soft theorems as Ward identities, soft bosons as Goldstone bosons.

Scattering amplitudes and soft theorems - Discussion session (Scattering amplitudes and soft theorems - Paolo Benincasa (IFT, Madrid) and Matteo Rosso (Humboldt Universitaet, Berlin))

• Paolo Benincasa (IFT, Madrid)
• Matteo Rosso (Humboldt Universitaet, Berlin)

Room: Aula 1, Piano -1

Gauged Supergravity: formalism & applications (Gauged supergravity: formalism and applications - Giuseppe Dibitetto (Uppsala University) and Alessandra Gnecchi (Leuven University))

• Giuseppe Dibitetto (Uppsala University)
• Alessandra Gnecchi (KU Leuven)

Room: Aula 1, Piano -1 The embedding tensor formulation of (half-)maximal gauged supergravities in various dimensions plays a crucial role in understanding string dualities within the context of string compactifications. We will start by first giving an overview of the aforementioned formalism in 4D. Later, we will continue by discussing the embedding tensor/fluxes and Domain Wall/brane dictionaries for compactifications of type II string and M-theory. Among its many applications, gauged Supergravity provides a framework for the construction of black holes in Anti de Sitter (AdS) spacetime. These will be the focus of the second part of the seminar. We will review Supersymmetric solutions in 4 and 5 dimensions, with particular emphasis on the 1/4 BPS black holes in 4D that have triggered new investigations in recent years. We will illustrate the relations between the ungauged and gauged Supergravity solutions that emerged from the latest studies. Finally, the M-theory origin of AdS black holes and their role for holography will be discussed.

Gauged Supergravity: formalism & applications - Discussion session (Gauged supergravity: formalism and applications - Giuseppe Dibitetto (Uppsala University) and Alessandra Gnecchi (Leuven University))

• Giuseppe Dibitetto (Uppsala University)
• Alessandra Gnecchi (KU Leuven)

Room: Aula 1, Piano -1

Aspects of 6D theories: geometric engineering and holography (Aspects of 6D theories: geometric engineering and holography - Fabio Apruzzi (UNC, Chapel Hill) and Michele Del Zotto (Harvard University))

• Fabio Apruzzi (UNC, Chapel Hill)
• Michele Del Zotto (Harvard University)

Room: Aula 1, Piano -1 6D theories are in between the most elusive and interesting supersymmetric systems whose existence is predicted by string theory. The main aim of the first part of these lectures is to convince the audience that this is the case, and to review their geometric engineering in M-theory and F-theory, with emphasis on the recent results obtained by means of the latter. In the second part of the lectures, we will focus on the brane constructions in type IIA, involving NS5, D6, and D8 branes. We will then link holographically these brane configurations to the AdS_7 gravity dual solutions of massive IIA supergravity.

Aspects of 6D theories: geometric engineering and holography - Discussion session (Aspects of 6D theories: geometric engineering and holography - Fabio Apruzzi (UNC, Chapel Hill) and Michele Del Zotto (Harvard University))

• Fabio Apruzzi (UNC, Chapel Hill)
• Michele Del Zotto (Harvard University)

Room: Aula 1, Piano -1

Closure and Christmas greetings Room: Aula 1, Piano -1