• Ignacio A. Reyes (Amsterdam U.) - The quantum properties of relativistic stars

Abstract:  These lectures aim to introduce the rich physics of compact relativistic stars. We will review their quantum origin, discuss some existence theorems and study their stability under perturbations. Finally, we will explore the role of QFT in these strongly curved spacetimes. Familiarity with the basics of General Relativity and QFT is assumed. 

Recommended Bibliography: 

• Gravity: An Introduction to Einstein's General Relativity, James Hartle, Chapter 24 “Relativistic Stars”.

• Sections 3.1, 3.2 of https://arxiv.org/abs/1410.4481

• On Massive Neutron Cores, J. R. Oppenheimer and G. M. Volkoff, Phys. Rev. 55, 374 – Published 15, February 1939

• Oscar Fuentealba (Brussels U., PTM) - Lectures on the asymptotic structure of spacetime

Abstract: In these lectures, we will revisit the asymptotic structure of General Relativity and electromagnetism from a Hamiltonian perspective. First, the conformal structure of the Minkowski spacetime and the Bondi-van der Burg-Metzner-Sachs algebra (BMS) group at null infinity are reviewed. We then proceed to show the emergence of the BMS group at spatial infinity, recalling the importance of the so-called parity conditions. The asymptotic conditions of Henneaux and Troessaert are relaxed so as to accommodate logarithmic deformations in the fall-off of the metric. This implies a consistent enlargement of the asymptotic symmetry algebra with a new kind of "logarithmic supertranslations". We will show how the presence of these new symmetries solve the problem of the angular momentum in General Relativity, by constructing supertranslation-invariant Lorentz charges. Similar analysis will be carried out in the context of electromagnetism, where in addition to the tower of infinite u(1) charges, it is possible to find a conjugate infinite-dimensional set of logarithmic u(1) charges. The latter charges will allow us to construct gauge-invariant Poincaré generators, in line with the Coleman-Mandula theorem.

• Lecture 1: Asymptotically flat spacetimes at null infinity.

• Lecture 2: Asymptotic symmetries in electromagnetism.

• Lecture 3: Asymptotically flat spacetimes at spatial infinity.

Recommended Bibliography: 

• R. Sachs, ``Asymptotic symmetries in gravitational theory,'' Phys. Rev. \textbf{128}, 2851-2864 (1962) doi:10.1103/PhysRev.128.2851 

• T. Regge and C. Teitelboim, ``Role of Surface Integrals in the Hamiltonian Formulation of General Relativity,'' Annals Phys. \textbf{88}, 286 (1974) doi:10.1016/0003-4916(74)90404-7 

• A. Strominger, ``Lectures on the Infrared Structure of Gravity and Gauge Theory,'' [arXiv:1703.05448 [hep-th]] 

• M. Henneaux and C. Troessaert, ``The asymptotic structure of gravity at spatial infinity in four spacetime dimensions,'' Proc. Steklov Inst. Math. \textbf{309}, 127 (2020) doi:10.1134/S0081543820030104 [arXiv:1904.04495 [hep-th]] 

• O. Fuentealba, M. Henneaux and C. Troessaert, ``Logarithmic supertranslations and supertranslation-invariant Lorentz charges,'' JHEP \textbf{02}, 248 (2023) doi:10.1007/JHEP02(2023)248 [arXiv:2211.10941 [hep-th]]

• Lucía Córdova (CERN) - Bootstrapping Quantum Field Theories

Abstract: In this talk I will discuss the space of two-dimensional quantum field theories with a global O(N) symmetry. Previous works using S-matrix bootstrap revealed a rich space in which integrable theories appear at special points and an abundance of unknown models hinting at a non conventional UV behaviour. In order to gain more information about the unknown models, we extend the S-matrix set-up by including into the bootstrap form factors and spectral functions for operators like stress tensor and symmetry currents. I will explain how this extended set-up works and show how the associated sum rules allow us to put bounds on quantities like the central charge of the underlying conformal theories in the UV. Based on work with M. Correia, A. Georgoudis and A. Vuignier. 

• Juan Pedraza (Madrid, IFT) - Gravity from optimized computation

Abstract: Inspired by the universality of computation, I advocate for a notion of spacetime complexity, where gravity arises as a consequence of spacetime optimizing the computational cost of its quantum dynamics. This principle is realized in the context of holography, where complexity is understood in terms of state preparation via Euclidean path integrals, and the linearized equations of motion, for any theory of gravity, emerge from the first law of complexity. This suggests gravity has a computational origin. When the leading 1/N bulk quantum corrections are included, the holographic first law is modified by an additional term which could be interpreted as `bulk complexity’, leading to a derivation of semi-classical gravitational equations of motion.