Notes on Ramond-Ramond spinors and bispinors in double field theory

Abstract

The Ramond-Ramond sector of double field theory (DFT) can be described either as an O(D,D) spinor or an O(D-1,1) x O(1,D-1) bispinor. Both formulations may be related to the standard polyform expansion in terms of even or odd rank field strengths corresponding to IIA or IIB duality frames. The spinor approach is natural in a (bosonic) metric formulation of DFT, while the bispinor is indispensable for supersymmetric DFT. In these notes, we show how these two approaches may be covariantly connected using a spinorial version of the DFT vielbein, which flattens an O(D,D) spinor into a bispinor. We also elaborate on details of the bispinor formulation in both even and odd D and elaborate on the distinction between the IIA/IIB/IIA*/IIB* duality frames.

arXiv comment40 pages; v2: added additional comment in section 4.4 and 7; v3: added new sections 5.3 and 6.3 (published version)

References in corpus (24)

• Double Field Theory
• Generalized metric formulation of double field theory
• Superspace Duality in Low-Energy Superstrings
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• Background independent action for double field theory
• The gauge algebra of double field theory and Courant brackets
• Supergravity as Generalised Geometry I: Type II Theories
• Exploring Double Field Theory
• $E_{11}$, SL(32) and Central Charges
• Double Field Theory of Type II Strings
• Supersymmetric Double Field Theory: Stringy Reformulation of Supergravity
• Stringy Unification of Type IIA and IIB Supergravities under N=2 D=10 Supersymmetric Double Field Theory
• N=1 Supersymmetric Double Field Theory
• Ramond-Ramond Cohomology and O(D,D) T-duality
• Comments on T-dualities of Ramond-Ramond Potentials
• E11, generalised space-time and IIA string theory
• Remarks on the non-Riemannian sector in Double Field Theory
• Superspace with manifest T-duality from type II superstring
• T-Duality and Ramond-Ramond Backgrounds in the Matrix Model
• The Pin Groups in Physics: C, P, and T
• Non-Riemannian geometry of M-theory
• String Theory and non-Riemannian Geometry
• Double supergeometry
• Exploring the geometry of supersymmetric double field theory

Cited by in corpus (2)

• Generalized Dualities and Supergroups
• Gravitational Core of Double Field Theory: Lecture Notes