Gauge Symmetry, Topology, and (Emergent) Quantum Fields

Dear Colleagues,

Quantum field theories defined by a (non-abelian) gauge principle on 4D spacetime play a central role in our quantitative understanding of nature at its most fundamental level. The Standard Model of particle physics (SM), built upon this principle and largely developed within a perturbative framework, has been highly successful. For over 55 years, it has consistently matched data from collider experiments at the energy frontier.

Nevertheless, the SM leaves several important experimental and observational questions unanswered. (i) Do gauge theories intrinsically explain the constants of nature ћ and c? Is quantisation a consequence of topology? (ii) Do we have means, based on the gauge principle, of exploiting the full nonperturbative wealth and beauty of gauge-field phenomena to understand dimensionless SM parameters such as charges, mixing angles, and CP violating phases beyond their mere introduction and experimental determination? (iii) Does the gauge principle in nonperturbative approaches, according to the Yang–Mills theories, allow us to address the Dark Sector in cosmology and astrophysics? That is, is there a theoretically sound and experimentally supported way of addressing the Universe’s ground-state structure? And can dark matter and dark energy be subjected to a unified description in terms of the gauge principle? (iv) How would a nonperturbative understanding of Yang–Mills theories influence our theoretical notion of masses, spins, magnetic moments, and internal quantum numbers assigned to elementary matter particles of the SM beyond the idea of point particles? (v) What are the implications of gauge theory-based models of stable elementary particles for our understanding of the physics of ultrahot/ultradense plasmas and certain condensed-matter systems (strongly correlated electrons in the plane)? (vi) What concepts are common to addressing gravity and gauge theories nonperturbatively?

Progress on these questions requires a thorough understanding of isolated and collective nonperturbative phenomena. Such studies necessarily involve one or more of the following concepts and results: self-duality and Bogomolny–Prasad–Sommerfield saturation; topological charge and charge density; holonomy; the Atiyah–Singer index theorem; the Atiyah–Drinfeld–Hitchin–Manin–Nahm construction; correlations of topological charge density; gauge changes and gauge fixing; semiclassical approximations; criticality; the renormalisation group; universality classes;  analytic structures of physical quantities; loop expansions; matching conditions; and related topics.

This Special Issue invites original research articles to address problems associated with questions questions (i) through (vi). Given the extensive literature on nonperturbative aspects of gauge theories and gravity, we also welcome comprehensive review articles that summarize developments within a specific research field.

We look forward to receiving your contributions.

Dr. Ralf Hofmann
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.