Specifically LGC is dual to RS theory with an extra (large) time-like dimension, as reported by Parampreet Singh today in: http://arxiv.org/PS_cache/gr-qc/pdf/0603/0603043.pdf This is the first connection between loop quantum gravity and string theory that I am aware of. The need for an extra time-like dimension is of particular interest as multiple timelike dimensions appear in string theory only under specific instances such as N=2 supersymmetry and 26 dim string theory and both are considered unphysical. Comments on what this means are appropriate. Here is the abstract and a couple quotes from the summary of the paper. Richard Loop cosmological dynamics and dualities with Randall-Sundrum braneworlds Authors: Parampreet Singh The discrete quantum geometric effects play an important role in dynamical evolution in the loop quantum cosmology. These effects which are significant at the high energies lead to the quadratic energy density modifications to the Friedmann equation, as in the Randall-Sundrum braneworld scenarios but with a negative sign. We investigate the scalar field dynamics in this scenario and show the existence of a phase of super-inflation independent of the inverse scale factor modifications as found earlier. In this regime the scalar field mimics the dynamics of a phantom field and vice versa. We also find various symmetries between the expanding phase, the contracting phase and the phantom phase in the loop quantum cosmology. We then construct the scaling solutions in the loop quantum cosmology and show their dual relationship with those of the Randall-Sundrum cosmology. We have shown that in this case the Friedmann equations gets a rho squared modification similar to the Randall-Sundrum scenario but with a negative sign(which also arises in a modified Randall-Sundrum model with a time-like extra dimension). We find that the scaling solutions in the effective theory are dual to those of the Randall-Sundrum scenario if the critical density arising in LGC is identified with the brane tension.