On twisted reality conditions
Tomasz Brzezinski, Ludwik Dabrowski, Andrzej Sitarz
TL;DR
This paper investigates the twisted reality condition in spectral triples, proposes an 'untwisting' procedure, and explores its relation to conformal rescaling and minimal twist methods in noncommutative geometry.
Contribution
It introduces a systematic method to 'untwist' twisted spectral triples and connects this to conformal rescaling and minimal twist techniques.
Findings
Developed an explicit untwisting procedure for twisted spectral triples.
Established links between untwisting and conformal rescaling.
Analyzed the untwisting of the minimal twist in even spectral triples.
Abstract
We study the twisted reality condition of Math. Phys. Anal. Geom. 19 (2016),no. 3, Art. 16, for spectral triples, in particular with respect to the product and the commutant. Motivated by this we present the procedure, which allows one to "untwist" the twisted spectral triples studied in Lett. Math. Phys. 106 (2016), 1499-1530. We also relate this construction to conformally rescaled real twisted spectral triples, and discuss the untwisting of the `minimal twist' procedure of an even spectral triple.
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