Black Holes and Quantum Gravity Constraints on Field Theories
It is by now well established that a theory describing physics at energies much below the Planck scale (at which the effects of gravity become important), will effectively take the form of a relativistic Quantum Field Theory (QFT). The question of how such an effective theory embeds in a more fundamental framework of quantum gravity, although of fundamental importance, seems irrelevant for phenomenological studies: the task of a particle physicist trying to describe the nature of Dark Matter, or to guess what the latest collider will discover, is to propose and study the QFT that best resembles the experimental data, without regard to the fundamental UV theory from which it derives.
It has been recently proposed, however, that this approach may sometimes be too naive. There are arguments suggesting that not all consistent-looking quantum field theories are actually consistent with the existence of gravity, i.e. they cannot describe the low energy physics of a full theory of quantum gravity, such as string theory. In these lectures we will study some of the consistency conditions so imposed on effective field theories and the arguments behind them. To do so, we will introduce some notions of QFT in curved spacetimes, and use them to study black holes and their thermodynamic properties.
Some basic knowledge of QFT and General Relativity is strongly recommended.