Connection between Fermionic Strings and Quantum Gravity States -- A loop space approach

Abstract

We present physical arguments based on loop space representations for Dirac/Klein gordon determinants that some suitable Fermionic String Ising models at the critical point and defined on the space-time base manifold are formal quantum states of the gravitational field when quantized in the Ashtekar-Sen connection canonical formalism .These results complements our previous Loop Space studies on the subject (Random surface representation for Einstein quantum gravity, Phys.Rev.D52,6941 (1995))