Torsional instantons in quantum gravity

We show that, in the first order gravity theory coupled to axions, the Giddings-Strominger wormhole can be interpreted as an instanton corresponding to nonvanishing torsion. The topological charge characterising these pseudoparticles is the Nieh-Yan topological index. As a result, the axion charge of the baby universes created by these instantons is found to be quantized in terms of the Nieh-Yan integers. Tunneling between universes of different Nieh-Yan charges implies a nonperturbative vacuum state in quantum gravity. This new ground state introduces an additional `quantum' coupling constant (vacuum angle) in quantum gravity, which is identified as the Barbero-Immirzi topological parameter. Phenomenological implications of such a rich vacuum structure in gravity theory are also discussed.