TY - JOUR

T1 - Energy of sections of the Deligne-Hitchin twistor space

AU - Beck, Florian

AU - Heller, Sebastian

AU - Roeser, Markus

N1 - Funding Information: The first author is supported by the DFG Emmy-Noether grant on “Building blocks of physical theories from the geometry of quantization and BPS states”, number AL 1407/2-1. The second author was supported by RTG 1670 “Mathematics inspired by string theory and quantum field theory” funded by the Deutsche Forschungsgemeinschaft (DFG) while much of this work was carried out. The second author would also like to thank Lynn Heller and Franz Pedit for discussions about the Willmore functional, and Jun-ichi Inoguchi for discussions about dual surfaces.

PY - 2021/8

Y1 - 2021/8

N2 - We study a natural functional on the space of holomorphic sections of the Deligne-Hitchin moduli space of a compact Riemann surface, generalizing the energy of equivariant harmonic maps corresponding to twistor lines. We give a link to a natural meromorphic connection on the hyperholomorphic line bundle recently constructed by Hitchin. Moreover, we prove that for a certain class of real holomorphic sections of the Deligne-Hitchin moduli space, the functional is basically given by the Willmore energy of corresponding (equivariant) conformal map to the 3-sphere. As an application we use the functional to distinguish new components of real holomorphic sections of the Deligne-Hitchin moduli space from the space of twistor lines.

AB - We study a natural functional on the space of holomorphic sections of the Deligne-Hitchin moduli space of a compact Riemann surface, generalizing the energy of equivariant harmonic maps corresponding to twistor lines. We give a link to a natural meromorphic connection on the hyperholomorphic line bundle recently constructed by Hitchin. Moreover, we prove that for a certain class of real holomorphic sections of the Deligne-Hitchin moduli space, the functional is basically given by the Willmore energy of corresponding (equivariant) conformal map to the 3-sphere. As an application we use the functional to distinguish new components of real holomorphic sections of the Deligne-Hitchin moduli space from the space of twistor lines.

KW - math.DG

UR - http://www.scopus.com/inward/record.url?scp=85090438685&partnerID=8YFLogxK

U2 - 10.1007/s00208-020-02042-0

DO - 10.1007/s00208-020-02042-0

M3 - Article

VL - 380

SP - 1169

EP - 1214

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 3-4

ER -