Exploring the geometry of supersymmetric double field theory

Butter, Daniel

doi:10.1007/jhep01(2022)152

Cited by 7 publications

(26 citation statements)

References 43 publications

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“…Another approach to supersymmetrisation of the E 11 exceptional field theory may be a suitable extended superspace approach. This has been studied for the E 7 exceptional field theory in [117] where only the four-dimensional (external) geometry was elevated to (4|32)-dimensional superspace, see also [118][119][120]. Should a suitable generalisation of this construction be found for the E 11 exceptional field theory, it could provide a framework for the construction of an action for M-branes propagating in the resulting generalised target superspace.…”

Section: Discussionmentioning

confidence: 99%

A master exceptional field theory

Bossard,

Kleinschmidt,

Sezgin

2021

Preprint

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We construct a pseudo-Lagrangian that is invariant under rigid E 11 and transforms as a density under E 11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E 11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E 11representation together with the E 11 coset fields. We show that, in combination with gauge-invariant and E 11 -invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condition. For another choice, we reobtain the E 8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E 10 sigma model.

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Section: Discussionmentioning

confidence: 99%

A master exceptional field theory

Bossard,

Kleinschmidt,

Sezgin

2021

Preprint

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“…on what we now call type I double field theory couched it in a superspace setting [2]. We revisited Siegel's work recently [20]. Let us briefly highlight some of the crucial features of this superspace approach:…”

Section: Jhep02(2023)187mentioning

confidence: 99%

“…The extended group H L is dual to the super-Maxwell ∞ algebra recently explored in [21,22]. Using the Poláček-Siegel framework for gauge symmetries in double field theory [23] (see also appendix B of [20] for a detailed discussion), this lets one naturally define the torsion and curvature tensors that either vanish or involve only physical components (i.e. the generalized Ricci tensor and scalar in the Riemann tensor).…”

Section: Jhep02(2023)187mentioning

confidence: 99%

“…This approach was essentially pioneered by Siegel [2], who addressed what we now call type I and heterotic double field theory, and reintroduced by Hatsuda, Kamimura, and Siegel [26,27] and Cederwall [28]. Our previous work [20] addressed type I DFT (D = 10, s = 16) and here we will be concerned with type II (D = 10, s = 32). The details are essentially the same so we will be brief.…”

Section: Elements Of Osp(d D|2s) and The Supervielbeinmentioning

confidence: 99%

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Type II double field theory in superspace

Butter

2023

J. High Energ. Phys.

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We explore type II supersymmetric double field theory in superspace. The double supervielbein is an element of the orthosymplectic group OSp(10, 10|64), which also governs the structure of generalized superdiffeomorphisms. Unlike bosonic double field theory, the local tangent space must be enhanced from the double Lorentz group in order to eliminate unphysical components of the supervielbein and to define covariant torsion and curvature tensors. This leads to an infinite hierarchy of local tangent space symmetries, which are connected to the super-Maxwell∞ algebra. A novel feature of type II is the Ramond-Ramond sector, which can be encoded as an orthosymplectic spinor (encoding the complex of super p-forms in conventional superspace). Its covariant field strength bispinor itself appears as a piece of the supervielbein. We provide a concise discussion of the superspace Bianchi identities through dimension two and show how to recover the component supersymmetry transformations of type II DFT. In addition, we show how the democratic formulation of type II superspace may be recovered by gauge-fixing.

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“…These structures simplify the calculations in DFT compare to GR. For instance, the supersymmetric DFT has a more straightforward SUSY structure than the conventional supergravities [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

The Off-Shell Recursion for Gravity and the Classical Double Copy for currents

Cho,

Kim,

Lee

2021

Preprint

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We construct the off-shell recursion for gravity and the graviton current for the perturbative double field theory (DFT). We first formulate the perturbative DFT, which is equivalent but simpler to perturbative general relativity, to all-orders in fluctuations of generalised metric. The perturbative action and equations of motion (EoM) are derived to arbitrary order for pure gravity case. We then derive the graviton off-shell recursion, the gravity counterpart of the Berends-Giele recursion in Yang-Mills theory, through the so-called perturbiner method using the EoM of the perturbative DFT. We solve the recursion iteratively and obtain the graviton off-shell currents explicitly. We then discuss the classical double copy for the off-shell currents. We present the current KLT relation for gravity by extending the result proposed by Mizera and Skrzypek for the nongravitational effective field theories. The relation represents graviton currents by squaring gluon currents with the KLT kernel up to gauge transformation and regular terms that do not have any pole. Finally we discuss the off-shell conservation of currents for nonlinear gauge choices. Contents 1 Introduction 1 2 Perturbation of Double Field Theory 3 2.1 Perturbation of the generalised metric 3 2.2 Perturbation of DFT equations of motion for pure gravity 6 3 Off-Shell Recursion for Gravity 8 3.1 Perturbiner method for Yang-Mills theory 9 3.2 Perturbiner expansion for DFT 10 4 Solving the Recursions and the Classical Double Copy for Currents 11 4.1 Current KLT relation 12 4.2 Currents in the spinor-helicity basis 14 4.3 Class 1: MHV currents 15 4.4 Class 2: Two opposite helicities 18 5 Conservation of the off-shell currents 19 5.1 Conservation of gluon currents in Gervais-Neveu gauge condition 19 5.2 Conservation of the graviton currents 21 6 Conclusion 22 A Explicit form of the Graviton Recursions 24 B Gluon off-shell currents in the Lorentz gauge 25 C Gauge transformation terms in the rank-4 current KLT relation 31

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Exploring the geometry of supersymmetric double field theory

Cited by 7 publications

References 43 publications

A master exceptional field theory

A master exceptional field theory

Type II double field theory in superspace

The Off-Shell Recursion for Gravity and the Classical Double Copy for currents

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