TY - JOUR

T1 - Courant Algebroids, Poisson–Lie T-Duality, and Type II Supergravities

AU - Ševera, Pavol

AU - Valach, Fridrich

N1 - Funding Information:
Supported by the NCCR SwissMAP of the Swiss National Science Foundation. F.V. was supported also by the GAČR Grant EXPRO 19-28628X.
Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2020/4/1

Y1 - 2020/4/1

N2 - We reexamine the notions of generalized Ricci tensor and scalar curvature on a general Courant algebroid, reformulate them using objects natural w.r.t. pull-backs and reductions, and obtain them from the variation of a natural action functional. This allows us to prove, in a very general setup, the compatibility of the Poisson–Lie T-duality with the renormalization group flow and with string background equations. We thus extend the known results to a much wider class of dualities, including the cases with gauging (so called dressing cosets, or equivariant Poisson–Lie T-duality). As an illustration, we use the formalism to provide new classes of solutions of modified supergravity equations on symmetric spaces.

AB - We reexamine the notions of generalized Ricci tensor and scalar curvature on a general Courant algebroid, reformulate them using objects natural w.r.t. pull-backs and reductions, and obtain them from the variation of a natural action functional. This allows us to prove, in a very general setup, the compatibility of the Poisson–Lie T-duality with the renormalization group flow and with string background equations. We thus extend the known results to a much wider class of dualities, including the cases with gauging (so called dressing cosets, or equivariant Poisson–Lie T-duality). As an illustration, we use the formalism to provide new classes of solutions of modified supergravity equations on symmetric spaces.

UR - http://www.scopus.com/inward/record.url?scp=85083194667&partnerID=8YFLogxK

U2 - 10.1007/s00220-020-03736-x

DO - 10.1007/s00220-020-03736-x

M3 - Article

AN - SCOPUS:85083194667

SN - 0010-3616

VL - 375

SP - 307

EP - 344

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -