Transitive Courant Algebroids, String Structures and T-duality

Baraglia, David; Hekmati, Pedram

doi:10.48550/arxiv.1308.5159

Cited by 23 publications

(69 citation statements)

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“…To prove (54), one first shows that the map R (0) in fact satisfies (55). This is follows by repeated use of (33) together with (3). With the help of this observation, one has…”

Section: Courant Algebroid Connectionsmentioning

confidence: 88%

“…2 Sorry, Bernhard. 3 But not the same! Note that ρ(ψ λ ).f = ψ λ , Df E and ψ λ , Df E • ψ λ E = Df .…”

Section: Courant Algebroid Connectionsmentioning

confidence: 99%

“…is the induced local frame defined uniquely by relations ψ λ , ψ µ E E = δ µ λ . Apart from the C ∞ (M )linearity in all inputs, this definition gives a tensor R with interesting symmetries, similar 3 to those of ordinary Riemann curvature tensor. We summarize these observations in the form of a proposition.…”

Section: Courant Algebroid Connectionsmentioning

confidence: 99%

“…Proof. From (1,3,15) and (32) it follows that R (0) is C ∞ (M )-linear in all inputs except for the third one, where (51) applies:…”

Section: Courant Algebroid Connectionsmentioning

confidence: 99%

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Courant Algebroid Connections and String Effective Actions

Jurčo

Vysoký

2017

Noncommutative Geometry and Physics 4

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Courant algebroids are a natural generalization of quadratic Lie algebras, appearing in various contexts in mathematical physics. A connection on a Courant algebroid gives an analogue of a covariant derivative compatible with a given fiber-wise metric. Imposing further conditions resembling standard Levi-Civita connections, one obtains a class of connections whose curvature tensor in certain cases gives a new geometrical description of equations of motion of low energy effective action of string theory. Two examples are given. One is the so called symplectic gravity, the second one is an application to the the so called heterotic reduction. All necessary definitions, propositions and theorems are given in a detailed and self-contained way.

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“…To prove (54), one first shows that the map R (0) in fact satisfies (55). This is follows by repeated use of (33) together with (3). With the help of this observation, one has…”

Section: Courant Algebroid Connectionsmentioning

confidence: 88%

“…2 Sorry, Bernhard. 3 But not the same! Note that ρ(ψ λ ).f = ψ λ , Df E and ψ λ , Df E • ψ λ E = Df .…”

Section: Courant Algebroid Connectionsmentioning

confidence: 99%

Section: Courant Algebroid Connectionsmentioning

confidence: 99%

“…Proof. From (1,3,15) and (32) it follows that R (0) is C ∞ (M )-linear in all inputs except for the third one, where (51) applies:…”

Section: Courant Algebroid Connectionsmentioning

confidence: 99%

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Courant Algebroid Connections and String Effective Actions

Jurčo

Vysoký

2017

Noncommutative Geometry and Physics 4

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“…A natural generalization of bosonic DFT is heterotic DFT [11,12,27,28], where the latter also includes the gauge fields present in the heterotic string. In generalized geometry the heterotic string was also discussed in [29,30,31](see also [32,33]). For abelian gauge fields this generalization is formally straightforward extending the global symmetry group from O(D, D) to O(D, D + n).…”

Section: Introductionmentioning

confidence: 99%

T-duality, non-geometry and Lie algebroids in heterotic double field theory

Blumenhagen

Sun

2015

J. High Energ. Phys.

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A number of issues in heterotic double field theory are studied. This includes the analysis of the T-dual configurations of a flat constant gauge flux background, which turn out to be non-geometric. Performing a field redefinition to a non-geometric frame, these T-duals take a very simple form reminiscent of the constant Q-and R-flux backgrounds. In addition, it is shown how the analysis of arXiv:1304.2784 generalizes to heterotic generalized geometry. For every field redefinition specified by an O(D, D + n) transformation, the structure of the resulting supergravity action is governed by the differential geometry of a corresponding Lie algebroid.

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Notes on generalized global symmetries in QFT

Sharpe

2015

Fortschritte der Physik

140

141

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It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as special cases of more general 2-groups and higher groups, and discuss examples of quantum field theories admitting actions of more general higher groups than merely one-form and higher-form symmetries. We discuss analogues of topological defects for some of these higher symmetry groups, relating some of them to ordinary topological defects. We also discuss topological defects in cases in which the moduli `space' (technically, a stack) admits an action of a higher symmetry group. Finally, we outline a proposal for how certain anomalies might potentially be understood as describing a transmutation of an ordinary group symmetry of the classical theory into a 2-group or higher group symmetry of the quantum theory, which we link to WZW models and bosonization.Comment: 47 pages, LaTeX; v2: references added; v3: more references added; v4: added pub info; v5: added referenc

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Transitive Courant Algebroids, String Structures and T-duality

Cited by 23 publications

References 0 publications

Courant Algebroid Connections and String Effective Actions

Courant Algebroid Connections and String Effective Actions

T-duality, non-geometry and Lie algebroids in heterotic double field theory

Notes on generalized global symmetries in QFT

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