Reductions of Exceptional Field Theories

Abstract

Double Field Theory (DFT) and Exceptional Field Theory (EFT), collectively called ExFTs, have proven to be a remarkably powerful new framework for string and M-theory. Exceptional field theories were constructed on a case by case basis as often each EFT has its own idiosyncrasies. Intuitively though, an $E_{n-1(n-1)}$ EFT must be contained in an $E_{n(n)}$ ExFT. In this paper we propose a generalised Kaluza-Klein ansatz to relate different ExFTs. We then discuss in more detail the different aspects of the relationship between various ExFTs including the coordinates, section condition and (pseudo)-Lagrangian densities. For the $E_{8(8)}$ EFT we describe a generalisation of the Mukhi-Papageorgakis mechanism to relate the d = 3 topological term in the $E_{8(8)}$ EFT to a Yang-Mills action in the $E_{7(7)}$ EFT.

arXiv commentplain latex, 32 pages, v2 typos fixed, v3 some additional discussion, published version

References in corpus (64)

• Double Field Theory: A Pedagogical Review
• On Lagrangians and Gaugings of Maximal Supergravities
• Generalized Geometry and M theory
• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• The gauge structure of generalised diffeomorphisms
• Exceptional Field Theory III: E${}_{8(8)}$
• Exploring Double Field Theory
• Double Field Theory of Type II Strings
• M2 to D2
• Exceptional Field Theory II: E${}_{7(7)}$
• Generalised T-Duality and Non-Geometric Backgrounds
• Gauged Double Field Theory
• Duality orbits of non-geometric fluxes
• The E_{11} origin of all maximal supergravities
• Duality Invariant Actions and Generalised Geometry
• Duality Invariant M-theory: Gauged supergravities and Scherk-Schwarz reductions
• Extended geometry and gauged maximal supergravity
• Exotic Branes in String Theory
• Exotic branes and non-geometric backgrounds
• The effective action of Double Field Theory
• Exceptional field theory: $SL(5)$
• On Brillouin Zones
• Eisenstein Series and String Thresholds
• Exceptional field theory: $SO(5,5)$
• Non-geometric backgrounds in string theory
• Ramond-Ramond Cohomology and O(D,D) T-duality
• Branes are Waves and Monopoles
• Duality Invariance: From M-theory to Double Field Theory
• Tensor Hierarchy and Generalized Cartan Calculus in SL(3)$\times$SL(2) Exceptional Field Theory
• The group theory of oxidation
• Gauge theory of Kaluza-Klein and winding modes
• Boundary Terms in Generalized Geometry and doubled field theory
• Self-dual forms: Action, Hamiltonian and Compactification
• 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
• Gauged Linear Sigma Model for Exotic Five-brane
• Counting supersymmetric branes
• Loops in exceptional field theory
• Generalised geometry, eleven dimensions and E11
• World-volume Effective Actions of Exotic Five-branes
• U-duality covariant gravity
• The E(11) origin of all maximal supergravities - the hierarchy of field-strengths
• Exotic branes and non-geometric fluxes
• Remarks on the non-Riemannian sector in Double Field Theory
• E${}_9$ exceptional field theory I. The potential
• $P$ fluxes and exotic branes
• Minimal unitary representations from supersymmetry
• Non-Riemannian geometry of M-theory
• Covariant actions for models with non-linear twisted self-duality
• E11, generalised space-time and equations of motion in four dimensions
• Weaving the Exotic Web
• Worldsheet Description of Exotic Five-brane with Two Gauged Isometries
• O(d+1,d+1) enhanced double field theory
• Kaluza-Klein reduction on a maximally non-Riemannian space is moduli-free
• Exotic E11 branes as composite gravitational solutions
• Effective Action for Non-Geometric Fluxes from Duality Covariant Actions
• On the exceptional generalised Lie derivative for $d\ge 7$
• Exotic branes in Exceptional Field Theory: the SL(5) duality group
• World-volume Effective Action of Exotic Five-brane in M-theory
• Exotic Branes in Exceptional Field Theory: $E_{7(7)}$ and Beyond
• From Exceptional Field Theory to Heterotic Double Field Theory via K3
• Exact ${\nabla }^4{R}^4$ couplings and helicity supertraces
• Connecting M-theory and type IIB parameterizations in Exceptional Field Theory
• O-folds: Orientifolds and Orbifolds in Exceptional Field Theory

Cited by in corpus (1)

• The Geometry, Branes and Applications of Exceptional Field Theory