TY  - JOUR
A1  - Bär, Christian
A1  - Mazzeo, Rafe
T1  - Manifolds with many Rarita-Schwinger fields
T2  - Communications in mathematical physics
N2  - The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare; it is even more unexpected for there to be large dimensional spaces of solutions. In this paper we prove the existence of a sequence of compact manifolds in any given dimension greater than or equal to 4 for which the dimension of the space of Rarita-Schwinger fields tends to infinity. These manifolds are either simply connected Kahler-Einstein spin with negative Einstein constant, or products of such spaces with flat tori. Moreover, we construct Calabi-Yau manifolds of even complex dimension with more linearly independent Rarita-Schwinger fields than flat tori of the same dimension.
Y1  - 2021
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/59485
SN  - 0010-3616
SN  - 1432-0916
VL  - 384
IS  - 1
SP  - 533
EP  - 548
PB  - Springer
CY  - Berlin
ER  -