2018
DOI: 10.1007/s00023-018-0694-2
|View full text |Cite
|
Sign up to set email alerts
|

Extended Riemannian Geometry I: Local Double Field Theory

Abstract: We present an extended version of Riemannian geometry suitable for the description of current formulations of double field theory (DFT). This framework is based on graded manifolds and it yields extended notions of symmetries, dynamical data and constraints. In special cases, we recover general relativity with and without 1-, 2-and 3-form gauge potentials as well as DFT. We believe that our extended Riemannian geometry helps to clarify the role of various constructions in DFT. For example, it leads to a covari… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

6
149
1

Year Published

2018
2018
2019
2019

Publication Types

Select...
7

Relationship

2
5

Authors

Journals

citations
Cited by 65 publications
(158 citation statements)
references
References 72 publications
6
149
1
Order By: Relevance
“…In the first subsection, following the notation and setup of Roytenberg and Weinstein, we discuss the subalgebra corresponding to the pure gauge structure, given by the C-bracket algebra, which in turn is the O(D, D) covariantization of the Courant algebroid. The results in this subsection were obtained by Deser and Saemann [20] in a geometrical setup that involves symplectic NQmanifolds and a derived bracket construction [21]. In the second subsection we extend this to the L ∞ algebra that also encodes fields and their off-shell gauge transformations.…”
Section: Double Field Theory and L ∞ Algebrasmentioning
confidence: 75%
See 1 more Smart Citation
“…In the first subsection, following the notation and setup of Roytenberg and Weinstein, we discuss the subalgebra corresponding to the pure gauge structure, given by the C-bracket algebra, which in turn is the O(D, D) covariantization of the Courant algebroid. The results in this subsection were obtained by Deser and Saemann [20] in a geometrical setup that involves symplectic NQmanifolds and a derived bracket construction [21]. In the second subsection we extend this to the L ∞ algebra that also encodes fields and their off-shell gauge transformations.…”
Section: Double Field Theory and L ∞ Algebrasmentioning
confidence: 75%
“…The general variation of the action is given by 20) where the star denotes the position of the free index on the epsilon symbol and we used the definition of the inner product. Comparing with the expected form of the field equation,…”
Section: Chern-simons Theorymentioning
confidence: 99%
“…(See also [33][34][35][36] for further investigations of the geometry of DFT.) The basic fields are the dilaton density and the frame field E A M , which is a vector under generalized diffeomorphisms, as in (2.1), and transforms under local frame transformations,…”
Section: α 1 -Deformed Glpdqˆglpdq Frame Formulationmentioning
confidence: 99%
“…The final two lines are also rewritable as total δ r0s variations: 36) as one may verify by a direct computation. Thus, we have succeeded in rewriting E MN as a total δ r0s variation and a modification of the gauge algebra, where we recall again the the p1 Ø 2q antisymmetrization is left implicit.…”
mentioning
confidence: 99%
“…For the first time, they actually appeared in the context of higher spin gauge theories [2] and were also discussed in the mathematics literature (see e.g. [3][4][5][6]). Motivated by the study of field theory truncations of string field theory [7], the authors of [8] argued that the symmetry and the action of any consistent perturbative gauge symmetry is controlled by an L ∞ algebra.…”
Section: Introductionmentioning
confidence: 99%