Sommerfeld Theory Colloquium (ASC)

Sommerfeld Theory Colloquium, In February 2016 the LIGO team announced the detection of gravitational

waves (GW) created by the merger of two black holes. In addition

to confirming a major prediction of general relativity, successful

GW detection would provide a powerful new tool for astrophysics.

Given their evident importance, the LIGO results and the methods

which led to them deserve independent critical analysis. This talk

will present the results of one such study in a manner suitable for

non-specialists.

Sommerfeld Theory Colloquium, The conjectured relation between higher spin theories on anti de-Sitter (AdS) spaces and weakly coupled conformal �field theories is reviewed. I shall then outline the evidence in favour of a concrete duality of this kind, relating a speci�c higher spin theory on AdS3

to a family of 2d minimal model CFTs. Finally, I shall explain how

this relation �ts into the framework of the familiar stringy AdS/CFT correspondence.

The study of black holes has revealed a deep connection between

quantum information and spacetime geometry. Its origin must lie

in the quantum theory of gravity, which offers a valuable hint in

our search for a unified theory. Precise formulations of this relation

recently led to new insights in Quantum Field Theory, some of which

have been rigorously proven. An important example is our discovery

of the first universal lower bound on the local energy density. The

energy near a point can be negative but it is bounded below by a

quantity related to the information flowing past the point.

Sommerfeld Theory Colloquium, The knowledge of all correlation functions of a system is equivalent to solving the corresponding quantum many-body

problem. If one can identify the relevant degrees of freedom, the knowledge of a finite set of correlation functions is in

many cases sufficient to determine a sufficiently accurate solution of the corresponding field theory. Complete

factorization is equivalent to identifying the relevant degrees of freedom where the Hamiltonian becomes diagonal. I

will give examples how one can apply this powerful theoretical concept in experiment.

A detailed study of non-translation invariant correlation functions reveals that the pre-thermalized state a system of

two 1-dimensional quantum gas relaxes to after a splitting quench [1], is described by a generalized Gibbs ensemble

[2]. This is verified through phase correlations up to 10th order.

Interference in a pair of tunnel-coupled one-dimensional atomic super-fluids, which realize the quantum Sine-Gordon /

massive Thirring models, allows us to study if, and under which conditions the higher correlation functions factorize

[3]. This allowed us to characterize the essential features of the model solely from our experimental measurements:

detecting the relevant quasi-particles, their interactions and the different topologically distinct vacuum-states the

quasi-particles live in. The experiment thus provides a comprehensive insight into the components needed to solve a

non-trivial quantum field theory.

Our examples establish a general method to analyse quantum systems through experiments. It thus represents a

crucial ingredient towards the implementation and verification of quantum simulators.

Work performed in collaboration with E.Demler (Harvard), Th. Gasenzer und J. Berges (Heidelberg).

Supported by the Wittgenstein Prize, the Austrian Science Foundation (FWF): SFB FoQuS: F40-P10 and

the EU: ERC-AdG QuantumRelax

[1] M. Gring et al., Science, 337, 1318 (2012);

[2] T. Langen et al., Science 348 207-211 (2015).

[3] T. Schweigler et al., Nature 545, 323 (2017), arXiv:1505.03126

Sommerfeld Theory Colloquium, Metagenomics has revealed hundreds to thousands of microbial species

coexisting in almost all microbiota. It is increasingly appreciated

that microbial communities condition their own environments.

To better understand the role of this environmental conditioning in

promoting diversity, we physically model the population dynamics of

microbes that compete for steadily supplied resources. In a model

where cells require multiple nutrients, we find that population dynamics

generally leads to the coexistence of different metabolic types,

which satisfy an extended competitive exclusion principle. Moreover,

we establish that these consortia of metabolic types act as cartels,

whereby population dynamics pins down resource concentrations at

values for which no other strategy can invade. Strikingly, these cartels

also yield maximum biomass, constituting a microbial example

of Adam Smith’s “invisible hand” leading to collective optimal usage

of resources. Curiously, in a model where only total resource acquisition

is considered, diversity can arbitrarily exceed that predicted by

the competitive exclusion principle.

Sommerfeld Theory Colloquium, Quantum mechanics is important for determining the geometry of

spacetime. We will review the role of quantum fluctuations that determine

the large scale structure of the universe. In some model universes

we can give an alternative description of the physics in terms

of a theory of particles that lives on its boundary. This implies that

the geometry is an emergent property. Furthermore, entanglement

plays a crucial role in the emergence of geometry. Large amounts of

entanglement are conjectured to give rise to geometric connections,

or wormholes, between distant and non-interacting systems.

Sommerfeld Theory Colloquium, The observed deviations from the laws of gravity of Newton and Einstein

in galaxies and clusters can logically speaking be either due to

the presence of unseen dark matter particles or due to a change in

the way gravity works in these situations. Until recently there was

little reason to doubt that general relativity correctly describes gravity

in all circumstances. In the past few year insights from black hole

physics and string theory have lead to a new theoretical framework in

which the gravitational laws are derived from the quantum entanglement

of the microscopic information that is underlying space-time.

An essential ingredient in the derivation is of the Einstein equations

is that the vacuum entanglement obeys an area law, a condition that

is known to hold in Anti-de Sitter space due to the work of Ryu

and Takayanagi. We will argue that in de Sitter space due to the

positive dark energy, that the microscopic entanglement entropy also

contains also a volume law contribution in addition to the area law.

This volume law contribution is related to the thermal properties of

de Sitter space and leads to a total entropy that precisely matches the

Bekenstein-Hawking formula for the cosmological horizon. We study

the effect of this extra contribution on the emergent laws of gravity,

and argue that it leads to a modification compared to Einstein gravity.

We provide evidence for the fact this modification explains the

observed phenomena in galaxies and clusters currently attributed to

dark matter.

Sommerfeld Theory Colloquium, The upshot of extensive studies of �uctuations in condensed matter systems is that

their qualitative importance is typically con#ned to isolated critical points of

continuous transitions between phases of matter. This conventional wisdom also

predicts the number of low energy Goldstone modes based on the so-called “G/H”

pattern of symmetry breaking. I will discuss a class of systems, some quite wellknown,

that violate this standard paradigm. Namely, they exhibit a fewer than “G/H”

number of low-energy modes due to an emergent Higgs mechanism. Even more

spectacularly, such systems exhibit “critical” ordered phases, with universal power-law

properties reminiscent of a critical point, but requiring no #ne-tuning and extending

throughout the ordered phase. One exciting recently discovered state is the heliconical

nematic that in addition to above phenomena also exhibits spontaneous chiral

symmetry breaking.

Sommerfeld Theory Colloquium, Over the past ten years, there has been a growing interest among physicists

for ‘active matter’, a codename that encompasses systems in which energy is

taken from the environment to generate self-propulsion at the single particle

level. Active particles, such as run-and-tumble bacteria, self-diffusiophoretic

colloids or actin filaments in motility assays, are strongly out-of-equilibrium

and exhibit much richer behaviours than their passive counterpart.

In this talk I will review recent progresses regarding the physics of active

particles. I will show how simple concepts like pressure, the force density

exerted by assemblies of particles on their container, play a new role for

active systems because of the lack of equation of state. I will also show how

new collective phenomena emerge, from the transition to collective motion

to the existence of cohesive matter without cohesive forces, that have no

counterpart in thermal equilibrium.

Sommerfeld Theory Colloquium, I will review for a general audience some recent developments in our

understanding of the mathematical structure of scattering amplitudes

in quantum field theory. Many of these developments involve properties

that have been discovered ”experimentally”: not in actual experiments,

but by carrying out a tedious calculation and then observing

that the result has some remarkable hidden simplicity. I will give

examples of this phenomenon, and in particular I will discuss some

aspects of the geometry of the ”amplituhedron”, a geometric object

that is believed to completely encode certain scattering amplitudes.