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Calin Iuliu Lazaroiu
기하학 수리물리 연구단
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N = 1 Geometric Supergravity and Chiral Triples on Riemann Surfaces

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Title
N = 1 Geometric Supergravity and Chiral Triples on Riemann Surfaces
Author(s)
Vicente Cortés; C. I. Lazaroiu; C. S. Shahbazi
Publication Date
2019-04
Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS, v.2019, no.4, pp.148 -
Publisher
SPRINGER
Abstract
We construct a global geometric model for the bosonic sector and Killing spinor equations of four-dimensional N = 1 supergravity coupled to a chiral non-linear sigma model and a Spinc 0 structure. The model involves a Lorentzian metric g on a four-manifold M, a complex chiral spinor and a map ϕ : M →Mfrom M to a complex manifold M endowed with a novel geometric structure which we call a chiral triple. Using this geometric model, we show that if M is spin then the Kähler-Hodge condition on M suffices to guarantee the existence of an associated N = 1 chiral geometric supergravity. This positively answers a conjecture proposed by D. Z. Freedman and A. V. Proeyen. We dimensionally reduce the Killing spinor equations to a Riemann surface X, obtaining a novel system of partial differential equations for a harmonic map with potential ϕ : X → M. We characterize all Riemann surfaces X admitting supersymmetric solutions with vanishing superpotential, showing that such solutions ϕ are holomorphicmaps satisfying a certain condition involving the canonical bundle of X and the chiral triple of the theory. Furthermore, we determine the biholomorphism type of all Riemann surfaces carrying supersymmetric solutions with complete Riemannian metric and finite-energy scalar map ϕ. © Springer-Verlag GmbH Germany, part of Springer Nature 2019
URI
https://pr.ibs.re.kr/handle/8788114/6929
ISSN
0010-3616
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
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