Duality Symmetric String and M-Theory

Abstract

We review recent developments in duality symmetric string theory. We begin with the world sheet doubled formalism which describes strings in an extended space time with extra coordinates conjugate to winding modes. This formalism is T-duality symmetric and can accommodate non-geometric T-fold backgrounds which are beyond the scope of Riemannian geometry. Vanishing of the conformal anomaly of this theory can be interpreted as a set of spacetime equations for the background fields. These equations follow from an action principle that has been dubbed Double Field Theory (DFT). We review the aspects of generalised geometry relevant for DFT. We outline recent extensions of DFT and explain how, by relaxing the so-called strong constraint with a Scherk Schwarz ansatz, one can obtain backgrounds that simultaneously depend on both the regular and T-dual coordinates. This provides a purely geometric higher dimensional origin to gauged supergravities that arise from non-geometric compactification. We then turn to M-theory and describe recent progress in formulating an E_{n(n)} U-duality covariant description of the dynamics. We describe how spacetime may be extended to accommodate coordinates conjugate to brane wrapping modes and the construction of generalised metrics in this extend space that unite the bosonic fields of supergravity into a single object. We review the action principles for these theories and their novel gauge symmetries. We also describe how a Scherk Schwarz reduction can be applied in the M-theory context and the resulting relationship to the embedding tensor formulation of maximal gauged supergravities.

Review article. 122 pages. V2 Published Version in Physics Reports

References in corpus (41)

• Gluon scattering amplitudes at strong coupling
• Double Field Theory
• Modeling Multiple M2's
• Generalised Geometry for M-Theory
• Doubled Geometry and T-Folds
• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• Exceptional Field Theory III: E${}_{8(8)}$
• Differential geometry with a projection: Application to double field theory
• On non-abelian T-dual geometries with Ramond fluxes
• Doubled α'-Geometry
• Duality orbits of non-geometric fluxes
• The E_{11} origin of all maximal supergravities
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• Lectures on Generalized Complex Geometry for Physicists
• Non-abelian T-duality, Ramond Fields and Coset Geometries
• Generalized E(7(7)) coset dynamics and D=11 supergravity
• Background Field Equations for the Duality Symmetric String
• Worldsheet Instanton Corrections to the Kaluza-Klein Monopole
• Moduli Stabilization in Non-Geometric Backgrounds
• Gauged Supergravities from Twisted Doubled Tori and Non-Geometric String Backgrounds
• Branes are Waves and Monopoles
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• Supersymmetry for Gauged Double Field Theory and Generalised Scherk-Schwarz Reductions
• Double field formulation of Yang-Mills theory
• Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT's
• Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions
• D-branes in Nongeometric Backgrounds
• E11, generalised space-time and IIA string theory
• Worldsheet Instanton Corrections to 522-brane Geometry
• The KK-Monopole/NS5-Brane in Doubled Geometry
• Worldsheet CFTs for Flat Monodrofolds
• D-branes and doubled geometry
• T-duality in Ramond-Ramond backgrounds
• E11, generalised space-time and IIA string theory; the R-R sector
• Geometries, Non-Geometries, and Fluxes
• Exceptional geometry and tensor fields
• Mirrorfolds with K3 Fibrations
• T-duality Invariant Approaches to String Theory
• Backreacted T-folds and non-geometric regions in configuration space
• Non-gravitational exceptional supermultiplets
• A Note on Supersymmetric Chiral Bosons

Cited by in corpus (49)

• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• T-duality and ${\alpha }^{\prime }$-corrections
• Type IIB Supergravity Solutions with AdS${}_5$ From Abelian and Non-Abelian T Dualities
• Covariant action for a string in doubled yet gauged spacetime
• M-theory and Type IIB from a Duality Manifest Action
• Exceptional field theory: $SO(5,5)$
• Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
• Heterotic $\alpha$'-corrections in Double Field Theory
• The Odd story of ${\alpha }^{\prime }$-corrections
• Quantum Gravity, Dynamical Phase Space and String Theory
• NS-branes, source corrected Bianchi identities, and more on backgrounds with non-geometric fluxes
• Gauge theory of Kaluza-Klein and winding modes
• Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT's
• Finite Gauge Transformations and Geometry in Double Field Theory
• Generalized Metric Formulation of Double Field Theory on Group Manifolds
• An Action for F-theory: $\mathrm{SL}(2)\times {\mathbb{R}}^{+}$ Exceptional Field Theory
• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• Effective actions of non-geometric fivebranes
• Non-geometric branes are DFT monopoles
• Non-linear Kaluza-Klein theory for dual fields
• An O(D,D) Invariant Hamiltonian Action for the Superstring
• Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds
• Type IIB supergravity solution for the T-dual of the eta-deformed AdS_5 x S^5 superstring
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• Non-abelian tri-vector deformations in d=11 supergravity
• Conserved Currents of Double Field Theory
• The embedding tensor of Scherk-Schwarz flux compactifications from eleven dimensions
• World-volume Effective Action of Exotic Five-brane in M-theory
• A Note on the CFT Origin of the Strong Constraint of DFT
• Cosmological Implications from O(D,D)
• Dirac structures on nilmanifolds and coexistence of fluxes
• Nonassociative geometry and twist deformations in non-geometric string theory
• U-gravity : $\mathbf{SL}(N)$
• Probing the String Winding Sector
• T-duality Transformation of Gauged Linear Sigma Model with F-term
• T-duality, Non-geometry and Lie Algebroids in Heterotic Double Field Theory
• The Asymmetric CFT Landscape in D=4,6,8 with Extended Supersymmetry
• One-Loop $\beta$ Function of the Double Sigma Model with Constant Background
• Gauge Transformation of Double Field Theory for Open String
• New Cosmological Signatures from Double Field Theory
• Metastring Theory and Modular Space-time
• Non-commutativity from the double sigma model
• U-dualities in Type II string theories and M-theory
• Loop Corrections in Double Field Theory: Non-trivial Dilaton Potentials
• Equivalence of open/closed strings
• Exceptional Field Theory for $E_{6(6)}$ supergravity
• Renormalization of a Lorentz invariant doubled worldsheet theory
• C-spaces, generalized geometry and double field theory
• Gaugings and other aspects in supergravity