Canonical approach to Courant brackets for D-branes

Abstract

We present an extension of the Courant bracket to the ones for Dp-branes by analyzing Hamiltonians and local superalgebras. Contrast to the basis of the bracket for a fundamental string which consists of the momentum and the winding modes, the ones for Dp-branes contain higher rank R-R coupling tensors. We show that the R-R gauge transformation rules are obtained by these Courant brackets for Dp-branes where the Dirac-Born-Infeld gauge field and the "two-vierbein field" play an essential role. Canonical analysis of the worldvolume theories naturally gives the basis of the brackets and the target space backgrounds keeping T-duality manifest at least for NS-NS sector. In a D3-brane analysis S-duality is manifest as a symmetry of interchanging the NS-NS coupling and the R-R coupling.

27 pages, ver2: typos corrected, references added, ver3: R-R gauge vectors are corrected, ver4: Contribution of the canonical bracket for DBI fields is added

References in corpus (12)

• Double Field Theory
• Generalised Geometry for M-Theory
• The gauge algebra of double field theory and Courant brackets
• Generalized Geometry and M theory
• Supergravity as Generalised Geometry I: Type II Theories
• Gauged Double Field Theory
• SO(5,5) duality in M-theory and generalized geometry
• The local symmetries of M-theory and their formulation in generalised geometry
• Double Field Theory, T-Duality, and Courant Brackets
• Double Field Theory for Double D-branes
• D-branes and doubled geometry
• Fermionic T-duality and U-duality in type II supergravity

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• Semi-doubled Sigma Models for Five-branes
• Currents, charges and algebras in exceptional generalised geometry
• One-Loop $\beta$ Function of the Double Sigma Model with Constant Background
• Gauging Unbroken Symmetries in F-theory
• Gauge Transformation of Double Field Theory for Open String
• Boundary Conditions and the Generalized Metric Formulation of the Double Sigma Model
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• Perturbative F-theory 10-brane and M-theory 5-brane
• Brane current algebras and generalised geometry from QP manifolds
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• Higher Courant-Dorfman algebras and associated higher Poisson vertex algebras