T‐duality and non‐geometric solutions from double geometry

Cederwall, Martin

doi:10.1002/prop.201400069

Cited by 36 publications

(21 citation statements)

References 63 publications

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“…which preserves both the undoubled diffeomorphisms (2.23) and the GL(n)×GL(n) local symmetries (2.15) as is equipped with proper connections: for undoubled ordinary diffeomorphisms, 23) and for GL(n) × GL(n) rotations,…”

Section: Non-riemannian Differential Geometry As Bookkeeping Devicementioning

confidence: 99%

Remarks on the non-Riemannian sector in Double Field Theory

Cho

Park

2020

Eur. Phys. J. C

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Taking O(D, D) covariant field variables as its truly fundamental constituents, Double Field Theory can accommodate not only conventional supergravity but also non-Riemannian gravities that may be classified by two non-negative integers, (n,n). Such non-Riemannian backgrounds render a propagating string chiral and anti-chiral over n andn dimensions respectively. Examples include, but are not limited to, Newton-Cartan, Carroll, or Gomis-Ooguri. Here we analyze the variational principle with care for a generic (n,n) non-Riemannian sector. We recognize a nontrivial subtlety for nn = 0, which seems to suggest that the various non-Riemannian gravities should better be identified as different solution sectors of Double Field Theory rather than viewed as independent theories. Separate verification of our results as string worldsheet beta-functions may enlarge the scope of the string landscape far beyond Riemann. arXiv:1909.10711v1 [hep-th] 24 Sep 2019 1.1 Double Field Theory as the O(D, D) completion of General Relativity While the initial motivation of Double Field Theory was to reformulate supergravity in an O(D, D) manifest manner [2-7] ([58-60] for reviews), through subsequent further developments [61-64], DFT has evolved and can be now identified as Stringy Gravity, i.e. pure gravitational theory that string theory seems to predict foremost. 1 More specifically, DFT is the string theory based, O(D, D) completion of General Relativity: taking the O(D, D) symmetry of string theory as the first principle, this Stringy Gravity assumes the whole massless NS-NS sector of closed string as the fundamental gravitational multiplet and interacts with other superstring sectors (R-R [67-69], R-NS [70], and heterotic Yang-Mills [71-73]). Having said that, regardless of supersymmetry, it can also couple to various matter fields which may appear in lower dimensional effective field theories [70, 74, 75], just as General Relativity (GR) does so. In particular, supersymmetric extensions have been completed to the full (i.e. quartic) order in fermions for D = 10 case 1 At least formally let alone its phenomenological validity, c.f. [65, 66].

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Section: Non-riemannian Differential Geometry As Bookkeeping Devicementioning

confidence: 99%

Remarks on the non-Riemannian sector in Double Field Theory

Cho

Park

2020

Eur. Phys. J. C

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“…Among the most pressing ones is to determine the dynamics, if not in all cases, at least in some important ones, such as affine and hyperbolic cases. It is also desirable to obtain a better understanding of finite transformations, which in double field theory are reasonably well understood [22,[24][25][26], but which have been elusive in the exceptional cases, for fundamental or technical reasons. A generic treatment is desirable.…”

Section: Jhep02(2018)071 7 Conclusionmentioning

confidence: 99%

Extended geometries

Cederwall

Palmkvist

2018

J. High Energ. Phys.

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We present a unified and completely general formulation of extended geometry, characterised by a Kac-Moody algebra and a highest weight coordinate module. Generalised diffeomorphisms are constructed, as well as solutions to the section constraint. Generically, additional ("ancillary") gauge transformations are present, and we give a concrete criterion determining when they appear. A universal form of the (pseudo-)action determines the dynamics in all cases without ancillary transformations, and also for a restricted set of cases based on the adjoint representation of a finite-dimensional simple Lie group. Our construction reproduces (the internal sector of) all previously considered cases of double and exceptional field theories.

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“…The gerbes G j,k and G k,j come with associated Courant algebroids C j,k and C k,j (by which we always mean the corresponding Q-manifolds as given in [13]), which encode the relevant Lie 2-algebra of symmetries. 5 Both gerbes and both associated Courant algebroids can be pulled back to the correspondence space K. Tensoring the gerbes, we obtain the gerbe G K with associated Courant algebroid C K . The space relevant for Double Field Theory is now a graded submanifold E K of C K .…”

Section: Introduction and Resultsmentioning

confidence: 99%

Extended Riemannian geometry III: global Double Field Theory with nilmanifolds

Deser

Sämann

2019

J. High Energ. Phys.

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We describe the global geometry, symmetries and tensors for Double Field Theory over pairs of nilmanifolds with fluxes or gerbes. This is achieved by a rather straightforward application of a formalism we developed previously. This formalism constructs the analogue of a Courant algebroid over the correspondence space of a T-duality, using the language of graded manifolds, derived brackets and we use the description of nilmanifolds in terms of periodicity conditions rather than local patches. The strong section condition arises purely algebraically, and we show that for a particularly symmetric solution of this condition, we recover the Courant algebroids of both nilmanifolds with fluxes. We also discuss the finite, global symmetries of general local Double Field Theory and explain how this specializes to the case of T-duality between nilmanifolds.

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T‐duality and non‐geometric solutions from double geometry

Cited by 36 publications

References 63 publications

Remarks on the non-Riemannian sector in Double Field Theory

Remarks on the non-Riemannian sector in Double Field Theory

Extended geometries

Extended Riemannian geometry III: global Double Field Theory with nilmanifolds

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