Non-abelian fermionic T-duality in supergravity

Abstract Field transformation rules of the standard fermionic T-duality require fermionic isometries to anticommute, which leads to complexification of the Killing spinors and results in complex valued dual backgrounds. We generalize the field transformations to the setting with non-anticommuting fermionic isometries and show that the resulting backgrounds are solutions of double field theory. Explicit examples of non-abelian fermionic T-dualities that produce real backgrounds are given. Some of our examples can be bosonic T-dualized into usual supergravity solutions, while the others are genuinely non-geometric. Comparison with alternative treatment based on sigma models on supercosets shows consistency.

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Double field theory and membrane sigma-models

Journal of High Energy Physics ◽

10.1007/jhep07(2018)015 ◽

2018 ◽

Vol 2018 (7) ◽

Cited By ~ 13

Author(s):

Athanasios Chatzistavrakidis ◽

Larisa Jonke ◽

Fech Scen Khoo ◽

Richard J. Szabo

Keyword(s):

Field Theory ◽

Sigma Models ◽

Double Field Theory

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Non-Riemannian isometries from double field theory

Journal of High Energy Physics ◽

10.1007/jhep04(2021)072 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Chris D. A. Blair ◽

Gerben Oling ◽

Jeong-Hyuck Park

Keyword(s):

Field Theory ◽

String Theory ◽

Relativistic String ◽

Noether Symmetries ◽

Dimensional Algebra ◽

Infinite Dimensional ◽

Killing Spinors ◽

Double Field Theory ◽

Riemannian Geometries ◽

Killing Equations

Abstract We explore the notion of isometries in non-Riemannian geometries. Such geometries include and generalise the backgrounds of non-relativistic string theory, and they can be naturally described using the formalism of double field theory. Adopting this approach, we first solve the corresponding Killing equations for constant flat non-Riemannian backgrounds and show that they admit an infinite-dimensional algebra of isometries which includes a particular type of supertranslations. These symmetries correspond to known worldsheet Noether symmetries of the Gomis-Ooguri non-relativistic string, which we now interpret as isometries of its non-Riemannian doubled background. We further consider the extension to supersymmetric double field theory and show that the corresponding Killing spinors can depend arbitrarily on the non-Riemannian directions, leading to “supersupersymmetries” that square to supertranslations.

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Algebroids, AKSZ Constructions and Doubled Geometry

Complex Manifolds ◽

10.1515/coma-2020-0125 ◽

2021 ◽

Vol 8 (1) ◽

pp. 354-402

Author(s):

Vincenzo Emilio Marotta ◽

Richard J. Szabo

Keyword(s):

Field Theory ◽

Sigma Models ◽

Global Perspective ◽

Courant Algebroids ◽

Double Field Theory ◽

Natural Notion ◽

Hermitian Geometry ◽

Type Construction

Abstract We give a self-contained survey of some approaches aimed at a global description of the geometry underlying double field theory. After reviewing the geometry of Courant algebroids and their incarnations in the AKSZ construction, we develop the theory of metric algebroids including their graded geometry. We use metric algebroids to give a global description of doubled geometry, incorporating the section constraint, as well as an AKSZ-type construction of topological doubled sigma-models. When these notions are combined with ingredients of para-Hermitian geometry, we demonstrate how they reproduce kinematical features of double field theory from a global perspective, including solutions of the section constraint for Riemannian foliated doubled manifolds, as well as a natural notion of generalized T-duality for polarized doubled manifolds. We describe the L ∞-algebras of symmetries of a doubled geometry, and briefly discuss other proposals for global doubled geometry in the literature.

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Double field theory algebroid and curved L∞-algebras

Journal of Mathematical Physics ◽

10.1063/5.0041479 ◽

2021 ◽

Vol 62 (5) ◽

pp. 052302

Author(s):

Clay James Grewcoe ◽

Larisa Jonke

Keyword(s):

Field Theory ◽

Double Field Theory

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Gauged double field theory as an L∞ algebra

Journal of High Energy Physics ◽

10.1007/jhep06(2021)058 ◽

2021 ◽

Vol 2021 (6) ◽

Author(s):

Eric Lescano ◽

Martín Mayo

Keyword(s):

Field Theory ◽

Algebraic Structure ◽

Classical Field ◽

Field Theories ◽

Lie Derivative ◽

Linear Perturbation ◽

Double Field Theory ◽

Generalized Frame ◽

Symmetry Transformations ◽

Classical Field Theories

Abstract L∞ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze the algebraic structure of Gauged Double Field Theory in the generalized flux formalism. The symmetry transformations consist of a generalized deformed Lie derivative and double Lorentz transformations. We obtain all the non-trivial products in a closed form considering a generalized Kerr-Schild ansatz for the generalized frame and we include a linear perturbation for the generalized dilaton. The off-shell structure can be cast in an L3 algebra and when one considers dynamics the former is exactly promoted to an L4 algebra. The present computations show the fully algebraic structure of the fundamental charged heterotic string and the $$ {L}_3^{\mathrm{gauge}} $$ L 3 gauge structure of (Bosonic) Enhanced Double Field Theory.

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Non-Riemannian gravity actions from double field theory

Journal of High Energy Physics ◽

10.1007/jhep06(2021)173 ◽

2021 ◽

Vol 2021 (6) ◽

Author(s):

A. D. Gallegos ◽

U. Gürsoy ◽

S. Verma ◽

N. Zinnato

Keyword(s):

Field Theory ◽

Quantum Gravity ◽

Condensed Matter ◽

Equations Of Motion ◽

Technical Note ◽

Action Principle ◽

Relativistic Symmetry ◽

Gravitational Theories ◽

Double Field Theory

Abstract Non-Riemannian gravitational theories suggest alternative avenues to understand properties of quantum gravity and provide a concrete setting to study condensed matter systems with non-relativistic symmetry. Derivation of an action principle for these theories generally proved challenging for various reasons. In this technical note, we employ the formulation of double field theory to construct actions for a variety of such theories. This formulation helps removing ambiguities in the corresponding equations of motion. In particular, we embed Torsional Newton-Cartan gravity, Carrollian gravity and String Newton-Cartan gravity in double field theory, derive their actions and compare with the previously obtained results in literature.

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Smooth functorial field theories from B-fields and D-branes

Journal of Homotopy and Related Structures ◽

10.1007/s40062-020-00272-2 ◽

2021 ◽

Vol 16 (1) ◽

pp. 75-153

Author(s):

Severin Bunk ◽

Konrad Waldorf

Keyword(s):

Field Theory ◽

Sigma Models ◽

Lagrangian Approach ◽

Field Theories ◽

Open Strings ◽

Homotopy Invariant ◽

Target Manifold ◽

Definition Of ◽

Smooth Map

AbstractIn the Lagrangian approach to 2-dimensional sigma models, B-fields and D-branes contribute topological terms to the action of worldsheets of both open and closed strings. We show that these terms naturally fit into a 2-dimensional, smooth open-closed functorial field theory (FFT) in the sense of Atiyah, Segal, and Stolz–Teichner. We give a detailed construction of this smooth FFT, based on the definition of a suitable smooth bordism category. In this bordism category, all manifolds are equipped with a smooth map to a spacetime target manifold. Further, the object manifolds are allowed to have boundaries; these are the endpoints of open strings stretched between D-branes. The values of our FFT are obtained from the B-field and its D-branes via transgression. Our construction generalises work of Bunke–Turner–Willerton to include open strings. At the same time, it generalises work of Moore–Segal about open-closed TQFTs to include target spaces. We provide a number of further features of our FFT: we show that it depends functorially on the B-field and the D-branes, we show that it is thin homotopy invariant, and we show that it comes equipped with a positive reflection structure in the sense of Freed–Hopkins. Finally, we describe how our construction is related to the classification of open-closed TQFTs obtained by Lauda–Pfeiffer.

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