Courant Sigma Model and ‐algebras

Grewcoe, Clay James; Jonke, Larisa

doi:10.1002/prop.202000021

Cited by 12 publications

(11 citation statements)

References 41 publications

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“…After a short introduction to L ∞ -algebras for classical field theories we shall formulate the model in terms of L ∞ -algebra(s). Construction of an improved DFT membrane sigma model is still work in progress, so we shall close this contribution with some insight obtained so far [19].…”

Section: Pos(corfu2019)156mentioning

confidence: 79%

“…Finally, we need to check homotopy Jacobi identities (3.1) of products (3.8). As explicitly shown in [18], there exist 7 non-trivial identities of which 3 are independent. These three sets of homotopy conditions for the higher products are actually all terms in the Taylor expansions of classical gauge invariance conditions (2.4) and they belong, as expected, to the space L 3 of Noether identities.…”

Section: Pos(corfu2019)156mentioning

confidence: 98%

“…This was done in Ref. [18] and here we shall review parts of this construction. In the next section we shall remind the reader of the rich gauge structure of the Courant sigma model.…”

Section: Pos(corfu2019)156mentioning

confidence: 99%

“…In Ref. [18] we have constructed explicitly the L ∞ -algebra for BV CSM, but in this short note we restrict ourselves to classical theory. We shall start this section with a short overview of L ∞ -algebras following Refs.…”

Section: Courant Sigma Model As L ∞ -Algebramentioning

confidence: 99%

“…We shall start this section with a short overview of L ∞ -algebras following Refs. [31,30] and then exemplify the general construction on the Courant sigma model following [18].…”

Section: Courant Sigma Model As L ∞ -Algebramentioning

confidence: 99%

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$L_\infty$-algebras and membrane sigma models

Grewcoe

Jonke

2020

Proceedings of Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2019)

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Membrane sigma-models have been used for the systematic description of closed strings in nongeometric flux backgrounds. In particular, the conditions for gauge invariance of the corresponding action functionals were related to the Bianchi identities for the fluxes. In this contribution we demonstrate how to express these Bianchi identities in terms of homotopy relations of the underlying L ∞-algebra for the case of the Courant sigma-model. We argue that this result can be utilized in understanding the constraint structure of Double Field Theory and the corresponding membrane sigma-model.

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Section: Pos(corfu2019)156mentioning

confidence: 79%

Section: Pos(corfu2019)156mentioning

confidence: 98%

“…This was done in Ref. [18] and here we shall review parts of this construction. In the next section we shall remind the reader of the rich gauge structure of the Courant sigma model.…”

Section: Pos(corfu2019)156mentioning

confidence: 99%

Section: Courant Sigma Model As L ∞ -Algebramentioning

confidence: 99%

“…We shall start this section with a short overview of L ∞ -algebras following Refs. [31,30] and then exemplify the general construction on the Courant sigma model following [18].…”

Section: Courant Sigma Model As L ∞ -Algebramentioning

confidence: 99%

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$L_\infty$-algebras and membrane sigma models

Grewcoe

Jonke

2020

Proceedings of Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2019)

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Extended doubled structures of algebroids for gauged double field theory

Mori,

Sasaki

2024

J. High Energ. Phys.

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We study an analogue of the Drinfel’d double for algebroids associated with the O(D, D + n) gauged double field theory (DFT). We show that algebroids defined by the twisted C-bracket in the gauged DFT are built out of a direct sum of three (twisted) Lie algebroids. They exhibit a “tripled”, which we call the extended double, rather than the “doubled” structure appearing in (ungauged) DFT. We find that the compatibilities of the extended doubled structure result not only in the strong constraint but also the additional condition in the gauged DFT. We establish a geometrical implementation of these structures in a (2D + n)-dimensional product manifold and examine the relations to the generalized geometry for heterotic string theories and non-Abelian gauge symmetries in DFT.

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Geometric BV for twisted Courant sigma models and the BRST power finesse

Chatzistavrakidis,

Ikeda,

Jonke

2024

J. High Energ. Phys.

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We study twisted Courant sigma models, a class of topological field theories arising from the coupling of 3D 0-/2-form BF theory and Chern-Simons theory and containing a 4-form Wess-Zumino term. They are examples of theories featuring a nonlinearly open gauge algebra, where products of field equations appear in the commutator of gauge transformations, and they are reducible gauge systems. We determine the solution to the master equation using a technique, the BRST power finesse, that combines aspects of the AKSZ construction (which applies to the untwisted model) and the general BV-BRST formalism. This allows for a geometric interpretation of the BV coefficients in the interaction terms of the master action in terms of an induced generalised connection on a 4-form twisted (pre-)Courant algebroid, its Gualtieri torsion and the basic curvature tensor. It also produces a frame independent formulation of the model. We show, moreover, that the gauge fixed action is the sum of the classical one and a BRST commutator, as expected from a Schwarz type topological field theory.

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Courant Sigma Model and ‐algebras

Cited by 12 publications

References 41 publications

$L_\infty$-algebras and membrane sigma models

$L_\infty$-algebras and membrane sigma models

Extended doubled structures of algebroids for gauged double field theory

Geometric BV for twisted Courant sigma models and the BRST power finesse

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