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Universe
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Dualities and Geometry
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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) | Viewed by 12071

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 Physics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
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 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 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

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Published Papers (6 papers)

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Research

Jump to: Review

11 pages, 292 KiB  
Article
From Hopf Algebra to Braided L∞-Algebra
by Clay James Grewcoe, Larisa Jonke, Toni Kodžoman and George Manolakos
Universe 2022, 8(4), 222; https://doi.org/10.3390/universe8040222 - 1 Apr 2022
Cited by 4 | Viewed by 2004
Abstract
We show that an L∞-algebra can be extended to a graded Hopf algebra with a codifferential. Then, we twist this extended L∞-algebra with a Drinfel’d twist, simultaneously twisting its modules. Taking the L∞-algebra as its own (Hopf) [...] Read more.
We show that an L∞-algebra can be extended to a graded Hopf algebra with a codifferential. Then, we twist this extended L∞-algebra with a Drinfel’d twist, simultaneously twisting its modules. Taking the L∞-algebra as its own (Hopf) module, we obtain the recently proposed braided L∞-algebra. The Hopf algebra morphisms are identified with the strict L∞-morphisms, whereas the braided L∞-morphisms define a more general L∞-action of twisted L∞-algebras. Full article
(This article belongs to the Special Issue Dualities and Geometry)
34 pages, 558 KiB  
Article
D-Branes in Para-Hermitian Geometries
by Vincenzo Emilio Marotta and Richard J. Szabo
Universe 2022, 8(4), 200; https://doi.org/10.3390/universe8040200 - 23 Mar 2022
Cited by 5 | Viewed by 1480
Abstract
We introduce T-duality invariant versions of D-branes in doubled geometry using a global covariant framework based on para-Hermitian geometry and metric algebroids. We define D-branes as conformal boundary conditions for the open string version of the Born sigma-model, where they are given by [...] Read more.
We introduce T-duality invariant versions of D-branes in doubled geometry using a global covariant framework based on para-Hermitian geometry and metric algebroids. We define D-branes as conformal boundary conditions for the open string version of the Born sigma-model, where they are given by maximally isotropic vector bundles which do not generally admit the standard geometric picture in terms of submanifolds. When reduced to the conventional sigma-model description of a physical string background as the leaf space of a foliated para-Hermitian manifold, integrable branes yield D-branes as leaves of foliations which are interpreted as Dirac structures on the physical spacetime. We define a notion of generalised para-complex D-brane, which realises our D-branes as para-complex versions of topological A/B-branes. We illustrate how our formalism recovers standard D-branes in the explicit example of reductions from doubled nilmanifolds. Full article
(This article belongs to the Special Issue Dualities and Geometry)
16 pages, 342 KiB  
Article
Romans Massive QP Manifolds
by Alex S. Arvanitakis, Emanuel Malek and David Tennyson
Universe 2022, 8(3), 147; https://doi.org/10.3390/universe8030147 - 25 Feb 2022
Cited by 4 | Viewed by 1750
Abstract
We introduce QP manifolds that capture the generalised geometry of type IIA string backgrounds with Ramond–Ramond fluxes and Romans mass. Each of these is associated with a BPS brane in type IIA: a D2, D4, or NS5-brane. We explain how these probe branes [...] Read more.
We introduce QP manifolds that capture the generalised geometry of type IIA string backgrounds with Ramond–Ramond fluxes and Romans mass. Each of these is associated with a BPS brane in type IIA: a D2, D4, or NS5-brane. We explain how these probe branes are related to their associated QP-manifolds via the AKSZ topological field theory construction and the recent brane phase space construction. M-theory/type IIA duality is realised on the QP-manifold side as symplectic reduction along the M-theory circle (for branes that do not wrap it); this always produces IIA QP-manifolds with vanishing Romans mass. Full article
(This article belongs to the Special Issue Dualities and Geometry)
26 pages, 395 KiB  
Article
Duality, Generalized Global Symmetries and Jet Space Isometries
by Athanasios Chatzistavrakidis, Georgios Karagiannis and Arash Ranjbar
Universe 2022, 8(1), 10; https://doi.org/10.3390/universe8010010 - 24 Dec 2021
Cited by 4 | Viewed by 2327
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)
18 pages, 346 KiB  
Article
Higher Dimensional Lie Algebroid Sigma Model with WZ Term
by Noriaki Ikeda
Universe 2021, 7(10), 391; https://doi.org/10.3390/universe7100391 - 19 Oct 2021
Cited by 8 | Viewed by 1404
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)

Review

Jump to: Research

17 pages, 356 KiB  
Review
A Matrix Model of Four-Dimensional Noncommutative Gravity
by George Manolakos, Pantelis Manousselis, Danai Roumelioti, Stelios Stefas and George Zoupanos
Universe 2022, 8(4), 215; https://doi.org/10.3390/universe8040215 - 28 Mar 2022
Cited by 7 | Viewed by 2096
Abstract
In this review, we revisit our latest works regarding the description of the gravitational interaction on noncommutative spaces as matrix models. Specifically, inspired by the gauge-theoretic approach of (ordinary) gravity, we make use of the suggested methodology, modified appropriately for the noncommutative framework, [...] Read more.
In this review, we revisit our latest works regarding the description of the gravitational interaction on noncommutative spaces as matrix models. Specifically, inspired by the gauge-theoretic approach of (ordinary) gravity, we make use of the suggested methodology, modified appropriately for the noncommutative framework, of the well-established formulation of gauge theories on them. Making use of a covariant four-dimensional fuzzy space, we formulate the gauge theory with an extended gauge group due to noncommutativity. In turn, in order to decrease the amount of symmetry we employ a symmetry breaking and result with an action which describes a theory that is a minimal noncommutative extension of the original. Full article
(This article belongs to the Special Issue Dualities and Geometry)
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