Gauge transformations of spectral triples with twisted real structures

We study the coupling of spectral triples with twisted real structures to gauge fields in the framework of noncommutative geometry and, adopting Morita equivalence via modules and bimodules as a guiding principle, give special attention to modifying the inner fluctuations of the Dirac operator. In particular, we analyse the twisted first-order condition as a possible alternative to the approach of arXiv:1304.7583, and elaborate upon the special case of gauge transformations accordingly. Applying the formalism to a toy model, we argue that under certain physically-motivated assumptions the spectral triple based on the left-right symmetric algebra should reduce to that of the Standard Model of fundamental particles and interactions, as in the untwisted case.