Killing-Yano equations with torsion, worldline actions and G-structures

TY - JOUR

T1 - Killing-Yano equations with torsion, worldline actions and G-structures

AU - Papadopoulos, G.

PY - 2012/6/7

Y1 - 2012/6/7

N2 - We determine the geometry of the target spaces of supersymmetric non-relativistic particles with torsion and magnetic couplings, and with symmetries generated by the fundamental forms of G-structures for G = U(n), SU(n), Sp(n), Sp(n) center dot Sp(1), G(2) and Spin(7). We find that the Killing-Yano equation, which arises as a condition for the invariance of the worldline action, does not always determine the torsion coupling uniquely in terms of the metric and fundamental forms. We show that there are several connections with skew-symmetric torsion for G = U(n), SU(n) and G(2) that solve the invariance conditions. We describe all these compatible connections for each of the G-structures and explain the geometric nature of the couplings.

AB - We determine the geometry of the target spaces of supersymmetric non-relativistic particles with torsion and magnetic couplings, and with symmetries generated by the fundamental forms of G-structures for G = U(n), SU(n), Sp(n), Sp(n) center dot Sp(1), G(2) and Spin(7). We find that the Killing-Yano equation, which arises as a condition for the invariance of the worldline action, does not always determine the torsion coupling uniquely in terms of the metric and fundamental forms. We show that there are several connections with skew-symmetric torsion for G = U(n), SU(n) and G(2) that solve the invariance conditions. We describe all these compatible connections for each of the G-structures and explain the geometric nature of the couplings.

U2 - 10.1088/0264-9381/29/11/115008

DO - 10.1088/0264-9381/29/11/115008

M3 - Article

SN - 0264-9381

VL - 29

SP - -

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 11

M1 - 115008

ER -