Calibrations and T-duality
type: Item
instance of: scholarly article
title: Calibrations and T-duality
zbMATH Open document ID: 1162.53038
author: Florian Gmeiner
author: Frederik Witt
published in: Communications in Mathematical Physics
publication date: 2009-01-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0605710
review text: The most important result is the following theorem: Any spinor field of the form \(\rho^{ev,od}= e^B\wedge\text{Re}([\psi_L\otimes \psi_R]^{ev,od})\) defines a calibration, where \([\psi_L\otimes \psi_R]\) is the complex form naturally associated with the bi-spinor \(\psi_L\otimes \psi_R\in\Delta\times \Delta\), for \(\Delta\) the spinor bundle associated with TM. For such a \(\rho\), the pair \((L,F)\) is calibrated if and only if \[ A(\psi_L)= c{e^{-B}\wedge \tau_{L,F}\over\| e^{-B}\wedge\tau_{L,F}\| G}\cdot\psi_R, \] where \(A\) denotes the so-called charge conjugation operator and \(c\) is a complex constant, ``\(\cdot\)'' is the usual Clifford action of TM on \(\Delta\).
Mathematics Subject Classification ID: 53C38
Mathematics Subject Classification ID: 81T30
Mathematics Subject Classification ID: 53D99
Mathematics Subject Classification ID: 53C10
Mathematics Subject Classification ID: 53C27
zbMATH DE Number: 5488687
zbMATH Keywords: generalized geometries
zbMATH Keywords: generalized calibrations
zbMATH Keywords: string theory
zbMATH Keywords: spinor
reviewed by: Mihail B. Banaru
MaRDI profile type: Publication
OpenAlex ID: W2036135013
arXiv ID: math/0605710
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DOI: 10.1007/S00220-008-0571-9
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description: scientific article