TY - JOUR
T1 - T-Dualities and Courant Algebroid Relations
AU - De Fraja, Thomas C.
AU - Marotta, Vincenzo Emilio
AU - Szabo, Richard J.
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
PY - 2025/1
Y1 - 2025/1
N2 - We develop a new approach to T-duality based on Courant algebroid relations which subsumes the usual T-duality as well as its various generalisations. Starting from a relational description for the reduction of exact Courant algebroids over foliated manifolds, we introduce a weakened notion of generalised isometries that captures the generalised geometry counterpart of Riemannian submersions when applied to transverse generalised metrics. This is used to construct T-dual backgrounds as generalised metrics on reduced Courant algebroids which are related by a generalised isometry. We prove an existence and uniqueness result for generalised isometric exact Courant algebroids coming from reductions. We demonstrate that our construction reproduces standard T-duality relations based on correspondence spaces. We also describe how it applies to generalised T-duality transformations of almost para-Hermitian manifolds.
AB - We develop a new approach to T-duality based on Courant algebroid relations which subsumes the usual T-duality as well as its various generalisations. Starting from a relational description for the reduction of exact Courant algebroids over foliated manifolds, we introduce a weakened notion of generalised isometries that captures the generalised geometry counterpart of Riemannian submersions when applied to transverse generalised metrics. This is used to construct T-dual backgrounds as generalised metrics on reduced Courant algebroids which are related by a generalised isometry. We prove an existence and uniqueness result for generalised isometric exact Courant algebroids coming from reductions. We demonstrate that our construction reproduces standard T-duality relations based on correspondence spaces. We also describe how it applies to generalised T-duality transformations of almost para-Hermitian manifolds.
UR - http://www.scopus.com/inward/record.url?scp=85214192533&partnerID=8YFLogxK
U2 - 10.1007/s00220-024-05185-2
DO - 10.1007/s00220-024-05185-2
M3 - Article
AN - SCOPUS:85214192533
SN - 0010-3616
VL - 406
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 1
M1 - 21
ER -