Special Issue "Dualities and Geometry"

A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Field Theory".

Deadline for manuscript submissions: closed (15 December 2021).

Special Issue Editors

Dr. Athanasios Chatzistavrakidis
E-Mail Website
Guest Editor
Rudjer Boskovic Institute, 10000 Zagreb, Croatia
Interests: theoretical and mathematical physics; gauge theories; gravity; string theory; generalised geometry
Dr. Dimitrios Giataganas
E-Mail Website
Guest Editor
Department of Nuclear and Particle Physics, University of Athens, 157 72 Athens, Greece
Interests: gauge/gravity duality; quantum field theory; Neural Networks

Special Issue Information

Dear Colleagues,

Duality is a fascinating property of a large variety of physical systems in both high-energy and condensed matter physics. Dualities have played a pivotal role in deepening our understanding of quantum field theory, string theory and quantum gravity. A surge of activity in recent years has also highlighted the interplay between dualities and geometry. New geometric structures have thus emerged in physical settings, such as generalized geometry, graded geometry, Courant algebroids, L-infinity algebras, and non-commutative and non-associative geometry. A fruitful exchange between physics and mathematics at the interface of dualities and geometry is currently underway. The purpose of this Special Issue is to reinforce this dialogue. A non-exhaustive list of topics that we aim to cover includes:

  • String dualities and flux backgrounds.
  • Noncommutative and non-associative physics.
  • L-infinity algebras and their physical applications.
  • Generalised and graded geometry.
  • Higher gauge theories.
  • Double and exceptional field theories.
  • Non-Abelian and Poisson–Lie dualities.
  • Nonrelativistic geometries and strings.
  • Duality in condensed matter physics.
  • AdS/CFT correspondence

Papers on closely related topics, such as the BV/BRST quantization of gauge theories, are also welcome. We invite submissions of both original research and review articles on topics relevant to this Special Issue.

Dr. Athanasios Chatzistavrakidis
Dr. Dimitrios Giataganas
Guest Editors

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 papers will be 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 100 words) can be sent to the Editorial Office for announcement on this website.

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. Universe is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. 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.

Keywords

  • dualities in field and string theories
  • generalized and graded geometry
  • non-commutative and non-associative structures in physics
  • higher gauge theory
  • L-infinity algebras

Published Papers (2 papers)

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Research

Article
Duality, Generalized Global Symmetries and Jet Space Isometries
Universe 2022, 8(1), 10; https://doi.org/10.3390/universe8010010 - 24 Dec 2021
Cited by 1 | Viewed by 324
Abstract
We revisit universal features of duality in linear and nonlinear relativistic scalar and Abelian 1-form theories with single or multiple fields, which exhibit ordinary or generalized global symmetries. We show that such global symmetries can be interpreted as generalized Killing isometries on a [...] Read more.
We revisit universal features of duality in linear and nonlinear relativistic scalar and Abelian 1-form theories with single or multiple fields, which exhibit ordinary or generalized global symmetries. We show that such global symmetries can be interpreted as generalized Killing isometries on a suitable, possibly graded, target space of fields or its jet space when the theory contains higher derivatives. This is realized via a generalized sigma model perspective motivated from the fact that higher spin particles can be Nambu–Goldstone bosons of spontaneously broken generalized global symmetries. We work out in detail the 2D examples of a compact scalar and the massless Heisenberg pion fireball model and the 4D examples of Maxwell, Born–Infeld, and ModMax electrodynamics. In all cases we identify the ’t Hooft anomaly that obstructs the simultaneous gauging of both global symmetries and confirm the anomaly matching under duality. These results readily generalize to higher gauge theories for p-forms. For multifield theories, we discuss the transformation of couplings under duality as two sets of Buscher rules for even or odd differential forms. Full article
(This article belongs to the Special Issue Dualities and Geometry)
Article
Higher Dimensional Lie Algebroid Sigma Model with WZ Term
Universe 2021, 7(10), 391; https://doi.org/10.3390/universe7100391 - 19 Oct 2021
Cited by 1 | Viewed by 244
Abstract
We generalize the (n+1)-dimensional twisted R-Poisson topological sigma model with flux on a target Poisson manifold to a Lie algebroid. Analyzing the consistency of constraints in the Hamiltonian formalism and the gauge symmetry in the Lagrangian formalism, [...] Read more.
We generalize the (n+1)-dimensional twisted R-Poisson topological sigma model with flux on a target Poisson manifold to a Lie algebroid. Analyzing the consistency of constraints in the Hamiltonian formalism and the gauge symmetry in the Lagrangian formalism, geometric conditions of the target space to make the topological sigma model consistent are identified. The geometric condition is an universal compatibility condition of a Lie algebroid with a multisymplectic structure. This condition is a generalization of the momentum map theory of a Lie group and is regarded as a generalization of the momentum section condition of the Lie algebroid. Full article
(This article belongs to the Special Issue Dualities and Geometry)
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