Portal de Periódicos da CAPES

SU(2) flat connection on a Riemann surface and 3D twisted geometry with a cosmological constant

2017; American Physical Society; Volume: 95; Issue: 4 Linguagem: Inglês

10.1103/physrevd.95.044018

2470-0037

Muxin Han, Zichang Huang,

Cosmology and Gravitation Theories

Twisted geometries are understood to be the discrete classical limit of loop quantum gravity. In this paper, SU(2) flat connections on a (decorated) 2D Riemann surface are shown to be equivalent to the generalized twisted geometries in 3D space with cosmological constant. Various flat connection quantities on a Riemann surface are mapped to the geometrical quantities in discrete 3D space. We propose that the moduli space of SU(2) flat connections on a Riemann surface generalizes the phase space of twisted geometry or loop quantum gravity to include a cosmological constant.