Superposition Induced Topology Changes in Quantum Gravity
Alexandra Miller (University of California, Santa Barbara)
I will show how one can find classical solutions in quantum gravity with a fixed topology by superposing solutions with a different fixed topology. I work in a particular limit of the LLM geometries, where the dual theory can be described by the free chiral boson in two dimensions. As a consequence of these superposition induced topology changes, one finds that there cannot exist a topology measuring operator in the theory. That is, one cannot determine the topology via a single quantum operator measurement. However, I will also discuss nonlinear methods for extracting the topological information.