Duality Covariant Solutions in Extended Field Theories

Abstract

Double field theory and exceptional field theory are formulations of supergravity that make certain dualities manifest symmetries of the action. To achieve this, the geometry is extended by including dual coordinates corresponding to winding modes of the fundamental objects. This geometrically unifies the spacetime metric and the gauge fields (and their local symmetries) in a generalized geometry. Solutions to these extended field theories take the simple form of waves and monopoles in the extended space. From a supergravity point of view they appear as 1/2 BPS objects such as the string, the membrane and the fivebrane in ordinary spacetime. In this thesis double field theory and exceptional field theory are introduced, solutions to their equations of motion are constructed and their properties are analyzed. Further it is established how isometries in the extended space give rise to duality relations between the supergravity solutions. Extensions to these core ideas include studying Goldstone modes, probing singularities at the core of solutions and localizing them in winding space. The relation of exceptional field theory to F-theory is also covered providing an action for the latter and incorporating the duality between M-theory and F-theory.

arXiv commentPhD Thesis, 190 p., includes some unpublished material in Section 6.2.3 on localizing solutions in winding space

References in corpus (76)

• Compactifications of F-Theory on Calabi--Yau Threefolds -- II
• Double Field Theory
• String Solitons
• Generalized metric formulation of double field theory
• Superspace Duality in Low-Energy Superstrings
• A Geometry for Non-Geometric String Backgrounds
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• Two-Dimensional Black Hole and Singularities of CY Manifolds
• Generalised Geometry for M-Theory
• Doubled Geometry and T-Folds
• Dualisation of Dualities, I
• Intersecting M-branes
• Exceptional Form of D=11 Supergravity
• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• Double Field Theory and N=4 Gauged Supergravity
• Exploring Double Field Theory
• Differential geometry with a projection: Application to double field theory
• Doubled α'-Geometry
• Duality orbits of non-geometric fluxes
• Duality Invariant M-theory: Gauged supergravities and Scherk-Schwarz reductions
• T-duality for torus bundles via noncommutative topology
• Extended geometry and gauged maximal supergravity
• Dyonic Membranes
• Nonassociative Gravity in String Theory?
• Magnetic Monopoles in String Theory
• Exotic branes and non-geometric backgrounds
• Nonassociative tori and applications to T-duality
• Supersymmetric Double Field Theory: Stringy Reformulation of Supergravity
• T-duality and ${\alpha }^{\prime }$-corrections
• Large Gauge Transformations in Double Field Theory
• Double Field Theory at Order ${\alpha }^{\prime }$
• Covariant action for a string in doubled yet gauged spacetime
• Stringy Unification of Type IIA and IIB Supergravities under N=2 D=10 Supersymmetric Double Field Theory
• Supersymmetric E${}_{7(7)}$ Exceptional Field Theory
• Background Field Equations for the Duality Symmetric String
• The Symmetry of M-Theories
• Generalised geometry for string corrections
• Exceptional field theory: $SL(5)$
• M-theory and Type IIB from a Duality Manifest Action
• Worldsheet Instanton Corrections to the Kaluza-Klein Monopole
• Representations of G+++ and the role of space-time
• Geometry and fluxes of SL(5) exceptional field theory
• U-Manifolds
• E_{11} origin of Brane charges and U-duality multiplets
• Branes are Waves and Monopoles
• Heterotic Effective Action and Duality Symmetries Revisited
• Heterotic $\alpha$'-corrections in Double Field Theory
• Tensor Hierarchy and Generalized Cartan Calculus in SL(3)$\times$SL(2) Exceptional Field Theory
• Supersymmetry for Gauged Double Field Theory and Generalised Scherk-Schwarz Reductions
• Boundary Terms in Generalized Geometry and doubled field theory
• Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT's
• Finite Gauge Transformations and Geometry in Double Field Theory
• Gauged supergravities in 5 and 6 dimensions from generalised Scherk-Schwarz reductions
• U-geometry : SL(5)
• An Action for F-theory: $\mathrm{SL}(2)\times {\mathbb{R}}^{+}$ Exceptional Field Theory
• Fermions and Supersymmetry in ${\mathrm{E}}_{6(6)}$ Exceptional Field Theory
• Worldsheet Instanton Corrections to 522-brane Geometry
• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• Zero Modes for the D=11 Membrane and Five-Brane
• Gauged Linear Sigma Model for Exotic Five-brane
• The KK-Monopole/NS5-Brane in Doubled Geometry
• String and Fivebrane Solitons: Singular or Non-singular?
• World-volume Effective Actions of Exotic Five-branes
• The string partition function in Hull's doubled formalism
• Matrix theory origins of non-geometric fluxes
• Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds
• Dualising consistent IIA / IIB truncations
• Type IIB flux vacua from G-theory II
• On the exceptional generalised Lie derivative for $d\ge 7$
• A Note on the CFT Origin of the Strong Constraint of DFT
• Cosmological Implications from O(D,D)
• Perturbative Double Field Theory on General Backgrounds
• U-gravity : $\mathbf{SL}(N)$
• T-duality Transformation of Gauged Linear Sigma Model with F-term
• U-folds as K3 fibrations
• Gauged Linear Sigma Model with F-term for A-type ALE Space

Cited by in corpus (1)

• Exotic Aspects of Extended Field Theories