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Quantum-Mechanical Systems at Large Quantum Number

Applicant Reffert Susanne
Number 192137
Funding scheme Project funding
Research institution Institut für Theoretische Physik Universität Bern
Institution of higher education University of Berne - BE
Main discipline Theoretical Physics
Start/End 01.09.2020 - 31.08.2024
Approved amount 723'201.00
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Keywords (6)

strongly coupled systems; superconformal field theory; conformal field theory; effective field theory; near-conformal dynamics; semi-classical analysis

Lay Summary (German)

Lead
Das Verständnis von stark wechselwirkende Quantenfeldtheorien ist von grosser Wichtigkeit in der modernen theoretischen Physik, da sie ein wichtiger Aspekt des Standard Modells der Teilchenphysik darstellen. Sie entziehen sich jedoch nach wie vor analytischen Methoden und können oft nur numerisch behandelt werden. In diesem Projekt verfolge ich einen neuen Ansatz, welcher die perturbative Behandlung stark gekoppelter Systeme erlaubt.
Lay summary
Wird eine Quantenfeldtheorie mit einer globalen Symmetriegruppe in einem Sektor mit hoher Ladung betrachtet, so ergeben sich wichtige Vereinfachungen, welche eine perturbative Behandlung und die Berechnung physikalischer Größen erlaubt. Die Expansion in hoher Ladung wird in der Praxis oft in konformen Feldtheorien gemacht, d.h. Theorien welche invariant unter konformen Transformationen sind. Dieses Projekt befasst sich mit dem weiteren Ausbau dieser Methode. Das Projekt verfolgt drei verschiedene Forschungsansaetze: die vertiefte Entwicklung der Methode für konforme Feldtheorien, die Verallgemeinerung zu nicht-konformen Feldtheorien und das Ausnützen von Dualitäten zwischen verschiedenen Systemen mit hoher Ladung. Dies erlaubt die analytische Behandlung von bisher nicht behandelbaren stark gekoppelten Systemen und führt zu neuen Ergebnissen. 
Direct link to Lay Summary Last update: 03.08.2020

Responsible applicant and co-applicants

Employees

Associated projects

Number Title Start Funding scheme
183718 Deformed supersymmetric gauge theories from string and M-theory 01.03.2019 SNSF Professorships

Abstract

Quantum field theory is the basic paradigm for the description of the electroweak and strong interactions, as well as a fundamental tool in condensed matter physics. Despite decades of research, strongly coupled regimes of QFT are largely inaccessible to analytic methods, even though important progress has come from the conformal bootstrap and non-Lagrangian methods.I propose here a novel method of expanding a strongly coupled theory by working in subsectors of large charge under a global symmetry.It allows us to perform a perturbative expansion for strongly coupled theories without any intrinsic small parameters.Together with my collaborators, I first put forward the large-charge approach. It is compelling through its very simplicity and is based on the techniques of effective field theory.We study a model at its infrared fixed point and aim to write down its Wilsonian action, which contains an infinity of terms compatible with the symmetries of the system. While conceptually pleasing, it is often assumed to be of little practical use when a model has no intrinsic scales.But now we make use of the global symmetries of the system by restricting ourselves to a sector of fixed and large global charge. Fixing the charge breaks Lorentz invariance and introduces a scale. We identify the classical ground state at large charge. The low-energy physics is described in terms of the quantum fluctuations around this state, which are typically encoded by Goldstone bosons.All higher contributions to the effective action turn out to be suppressed by inverse powers of the large charge, so it can be truncated after only a few terms. We are able to calculate the CFT data, such as anomalous dimensions and n-point functions which completely characterise the physics in the infrared.In the four years since the first paper, the subject has gained a lot of traction. Both myself and my original collaborators have further developed the field. Comparison with new and existing lattice data shows a very precise agreement with our predictions and provides a strong verification based on an independent methodology.The evident potential of the large-charge approach has in the meantime attracted groups in the US, Switzerland, Spain and Italy with very different backgrounds to the subject. The large-charge method is a subject still in its infancy with a slew of directions and possible applications waiting to be explored. A concerted effort to develop its potential would be extremely timely and would meet with wide interest in communities working, among others, on formal CFTs, supersymmetric gauge theories, particle phenomenology and lattice simulations. Project objectives:The aim of this proposal is advancing our understanding of strongly coupled QFTs in sectors of large charge, using three main avenues of investigation.I. Explore strongly coupled CFTs in sectors of large global charge. I will focus on fermionic CFTs, cross-checks with lattice results and superconformal field theories.II. Beyond CFTs at large charge. As first steps to the extension of the large-charge expansion to general QFTs, I will focus on near-conformal dynamics and complex CFTs.III. Dualities in sectors of large global charge. At large charge, a duality can become a simple equivalence between semi-classical actions. A notable candidate duality is the AdS/CFT correspondence. Novel aspects and impact:Working in a sector of large charge leads to important simplifications, due to the suppression of higher-order terms by inverse powers of the large charge in the effective action. This allows me to calculate the CFT data in theories which have to date eluded analytic treatment. My approach brings for the first time analytical results within reach for theories that are strongly coupled and cannot be otherwise treated perturbatively. It is particularly powerful for theories that lack other controlling parameters.The large-charge method will lead to new results in a variety of normally disjoint fields, due to its applicability to problems in condensed matter physics (critical phenomena), high energy physics, quantum gravity, and superconformal QFTs. It will thus generate a high visibility and wide impact. Today, we stand on the tip of an iceberg of future results and applications. I am very excited to contribute to these developments.
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