Metric algebroid and Dirac generating operator in Double Field Theory

Abstract We give a formulation of Double Field Theory (DFT) based on a metric algebroid. We derive a covariant completion of the Bianchi identities, i.e. the pre-Bianchi identity in torsion and an improved generalized curvature, and the pre-Bianchi identity including the dilaton contribution. The derived bracket formulation by the Dirac generating operator is applied to the metric algebroid. We propose a generalized Lichnerowicz formula and show that it is equivalent to the pre-Bianchi identities. The dilaton in this setting is included as an ambiguity in the divergence. The projected generalized Lichnerowicz formula gives a new formulation of the DFT action. The closure of the generalized Lie derivative on the spin bundle yields the Bianchi identities as a consistency condition. A relation to the generalized supergravity equations (GSE) is discussed.

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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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Jacobi-Lie T-plurality

SciPost Physics ◽

10.21468/scipostphys.11.2.038 ◽

2021 ◽

Vol 11 (2) ◽

Author(s):

Jose J. Fernandez-Melgarejo ◽

Yuho Sakatani

Keyword(s):

Field Theory ◽

Leibniz Algebra ◽

Lie Derivative ◽

Lie Bialgebra ◽

Drinfel’D Double ◽

Double Field Theory ◽

Generalized Frame ◽

Structure Constants ◽

One To One ◽

The Spectator

We propose a Leibniz algebra, to be called DD^++, which is a generalization of the Drinfel’d double. We find that there is a one-to-one correspondence between a DD^++ and a Jacobi–Lie bialgebra, extending the known correspondence between a Lie bialgebra and a Drinfel’d double. We then construct generalized frame fields E_A{}^M\in\text{O}(D,D)\times\mathbb{R}^+EAM∈O(D,D)×ℝ+ satisfying the algebra \hat{\pounds}_{E_A}E_B = - X_{AB}{}^C\,E_C£̂EAEB=−XABCEC, where X_{AB}{}^CXABC are the structure constants of the DD^++ and \hat{\pounds}£̂ is the generalized Lie derivative in double field theory. Using the generalized frame fields, we propose the Jacobi–Lie TT-plurality and show that it is a symmetry of double field theory. We present several examples of the Jacobi–Lie TT-plurality with or without Ramond–Ramond fields and the spectator fields.

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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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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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Exotic branes in Double Field Theory

EPJ Web of Conferences ◽

10.1051/epjconf/201612505017 ◽

2016 ◽

Vol 125 ◽

pp. 05017 ◽

Cited By ~ 2

Author(s):

Edvard Musaev

Keyword(s):

Field Theory ◽

Double Field Theory

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A NEW FORMULATION OF QUANTUM FIELD THEORY ON S4

International Journal of Modern Physics A ◽

10.1142/s0217751x9400128x ◽

1994 ◽

Vol 09 (18) ◽

pp. 3245-3282 ◽

Cited By ~ 3

Author(s):

B.A. HARRIS ◽

G.C. JOSHI

Keyword(s):

Field Theory ◽

Angular Momentum ◽

Quantum Gravity ◽

Momentum Space ◽

Space Representation ◽

Fundamental Constants ◽

Spherical Space ◽

Recent Developments ◽

New Formulation ◽

Constants Of Nature

Recent developments in quantum gravity suggest that wormholes may influence the observed values of the constants of nature. The Euclidean formulation of quantum gravity predicts that wormholes induce a probability distribution in the space of possible fundamental constants. In particular, the effective action on a large spherical space may lead to the vanishing of the cosmological constant and possibly determine the values of other constants of nature. The ability to perform calculations involving interacting quantum fields, particularly non-Abelian models, on a four-sphere is vital if one is to investigate this possibility. In this paper we present a new formulation of field theory on a four-sphere using the angular momentum space representation of SO(5). We give a review of field theory on a sphere and then show how a matrix element prescription in angular momentum space and a new summation technique based on the complex l plane, overcome previous limitations in calculational techniques. The standard one-loop graphs of QED are given as examples.

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Worldsheet instanton corrections to five-branes and waves in double field theory

Journal of High Energy Physics ◽

10.1007/jhep07(2018)001 ◽

2018 ◽

Vol 2018 (7) ◽

Cited By ~ 8

Author(s):

Tetsuji Kimura ◽

Shin Sasaki ◽

Kenta Shiozawa

Keyword(s):

Field Theory ◽

Double Field Theory

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Higher-derivative heterotic Double Field Theory and classical double copy

Journal of High Energy Physics ◽

10.1007/jhep07(2021)072 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Eric Lescano ◽

Jesús A. Rodríguez

Keyword(s):

Field Theory ◽

Exact Solutions ◽

Maxwell Equations ◽

Action Principle ◽

Low Energy ◽

Gauge Fields ◽

Metric Tensor ◽

Higher Derivative ◽

Double Field Theory ◽

Double Copy

Abstract The generalized Kerr-Schild ansatz (GKSA) is a powerful tool for constructing exact solutions in Double Field Theory (DFT). In this paper we focus in the heterotic formulation of DFT, considering up to four-derivative terms in the action principle, while the field content is perturbed by the GKSA. We study the inclusion of the generalized version of the Green-Schwarz mechanism to this setup, in order to reproduce the low energy effective heterotic supergravity upon parametrization. This formalism reproduces higher-derivative heterotic background solutions where the metric tensor and Kalb-Ramond field are perturbed by a pair of null vectors. Next we study higher-derivative contributions to the classical double copy structure. After a suitable identification of the null vectors with a pair of U(1) gauge fields, the dynamics is given by a pair of Maxwell equations plus higher derivative corrections in agreement with the KLT relation.

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