Sommerfeld Theory Colloquium (ASC)

Quantum Gravity in Anti-de Sitter space coupled to a non-gravitating bath has been the setting for novel approaches to the black-hole information paradox. Works from 2 decades ago in the context of Randall-Sundrum braneworlds makes it clear that this system necessarily describes massive gravitons: as soon as one couples AdS gravity to a bath, the graviton gets a mass. These two phenomena are intrinsically linked. We'll review old work that led to this conclusion, and present novel results that elucidate the role of the graviton mass in the determination of the Page curve for evaporating AdS black holes.

A central question in fundamental physics is when an effective field theory can be consistently coupled to gravity at high energies. Over the years, various necessary conditions for this to be possible have been conjectured. String theory is a proposed framework for a quantum gravity theory and hence allows us to quantitatively test and further develop such ideas. In this colloquium I will discuss this with special emphasis on the so-called Weak Gravity Conjecture and the Swampland Distance Conjecture, or its refinement dubbed Emergent String Conjecture. Among other connections to mathematics, we will see how these proposed general principles naturally follow from the geometry of string compactifications near the boundary of moduli space and are deeply routed in string dualities. This includes situations with a minimal amount of supersymmetry in four dimensions.

The conventional models of high energy physics place the elementary particles on a fixed or slowly evolving, nearly flat, spacetime geometry. The space foam predicted for quantum theory of gravity by A.Wheeler and S.Hawking gives a very different picture of the small scale structure of spacetime, with Planck size black holes popping out of vacuum here and there. Recent discoveries in astronomy and astrophysics, the detection of gravitational waves, exploration of Sgt A* , have confirmed the existence of enormous black holes, yet quantum size black holes remain the subject of theoretical amusement. I describe a vast class of statistical mechanical models, which, on the one hand, perform exact calculations in supersymmetric field theories in various dimensions, whose thermodynamic limit, on the other hand, can be interpreted as describing fluctuating geometry, an `emergent gravity'. The configurations of these models are the arrangements of (hyper)cubes, hence the title.

In a recent breakthrough, a complete set of constraints on fermionic occupation numbers, extending Pauli’s original exclusion principle, has been found. We provide an introduction into this new research field. In particular, we show that those generalized Pauli constraints are approximately saturated in various few-fermion systems, i.e. the vector of occupation numbers lies close to the boundary of the allowed region. Striking implications of this quasipinning phenomenon are revealed and discussed: These are the concept of robust quantum information, a hierarchy of natural extensions of the Hartree-Fock ansatz and the existence of an exchange force emerging from the fermionic exchange symmetry. Finally, we explain how these novel research concepts offer a universal perspective on fermionic quantum systems.

With Run II, the LHC experiment already reached an unprecedented

level of precision compared to previous hadron colliders. The amount

of data collected in Run III and the High-Luminosity run will increase

quickly and dramatically. I will discuss specific challenges to theorists

that must be overcome to provide predictions that have the precision

necessary to match the accuracy of data. A few novel ideas to exploit

this precision directly or indirectly will also be discussed.

Condensed matter is found in a variety of phases, the vast majority of which are characterized in terms of symmetry breaking. For example, magnets spontaneously break time-reversal and spin rotation symmetries. A notable exception was provided by the discovery of the quantum Hall effects which exhibit new kinds of topological orders not associated with any symmetry breaking. One of the characterizing features of topological order is the existence of excitations with

exotic properties. These so-called anyonic excitations might make topologically ordered systems ideal building blocks of fault-tolerant quantum computers. In this colloquium, I will start by giving a general introduction to the concept of topological order and then address some of the recent developments. In particular, I will introduce theoretical frameworks that allow us to classify topological phases and discuss dynamical signatures that are useful to experimentally detect them in experiments.

String theory seems to offer an enormous number of possibilities for low energy physics. The huge set of solutions is often known as the String Theory Landscape. In recent years, however, it has become clear that not all quantum field theories can be consistently coupled to gravity. Theories that cannot be ultraviolet completed in quantum gravity are said to be in the Swampland. In this talk, I'll discuss some conjectured properties of quantum gravity, evidences for them, and their applications to cosmology and particle physics.

The functional renormalization group (RG) is an ideal tool for dealing with the diversity of energy scales and competition of instabilities in interacting fermion systems. Starting point is an exact flow equation which yields the gradual evolution from a microscopic model action to the effective low-energy action as a function of a continuously decreasing energy scale. Expanding in powers of the fields yields an exact hierarchy of flow equations for vertex functions. Truncations of this hierarchy have led to powerful new approximation schemes [1].

Applications reviewed in the colloqium include: (i) d-wave superconductivity and other instabilities in the two-dimensional Hubbard model, and (ii) transport through a barrier and resonant tunneling in a one-dimensional Luttinger liquid metal. Recently, the functional RG has been upgraded from a weak-coupling method to a computational tool for strongly interacting fermion systems [2,3].

[1] W. Metzner et al., Rev. Mod. Phys. 84, 299 (2012).

[2] C. Taranto et al., Phys. Rev. Lett. 112, 196402 (2014).

[3] D. Vilardi et al., Phys. Rev. B 99, 104501 (2019).

Although the neutrino oscillations are well established phenomenon, new and unusual oscillation effects in matter are still emerging. I will describe three such effects which have applications to the solar, supernova and low energy atmospheric neutrinos: (i) Parametric resonance for neutrinos propagating in a flux of background neutrinos. (ii) Oscillation waves emitted from borders between layers in a multilayer medium, like in the Earth. (iii) The attenuation effect related to the energy uncertainty in oscillation setup.

From the softest of interactions of a magnetic field with an electron, to the most violent collisions at the Large Hadron Collider, precision quantum field theory produces numbers and functions with interesting number-theoretic properties. In many examples a co-action principle holds, an invariance under a ”cosmic” Galois group. I will provide several arenas in which this principle can be seen at work, including perhaps the richest set of theoretical data, scattering amplitudes in planar N = 4 super-Yang-Mills theory.