Topics in two -dimensional string theory.
Joshua L. Davis · Deep Blue (University of Michigan) · 2006
We explore various topics in two-dimensional string theory. Firstly, we study particle production in time-dependent backgrounds of the c = 1 matrix model, a holographic description of bosonic string theory in 1+1 dimensions. The process is described most efficiently in terms of anomalies, but we also discuss the explicit mode expansions. In matrix cosmology the usual vacuum ambiguity of quantum fields in time-dependent backgrounds is resolved by the underlying matrix model. This leads to a finite energy density for the in state which cancels the effect of anomalous particle production. Secondly, we utilize a novel method to study the thermodynamics of two dimensional type 0A black holes with constant RR flux. Our approach is based on the Hamilton-Jacobi method of deriving boundary counterterms. We demonstrate this approach by recovering the standard results for a well understood example, Witten's black hole. Between this example and the 0A black hole we find universal expressions for the entropy and black hole mass, as well as the infra-red divergence of the partition function. As a non-trivial check of our results we verify the first law of thermodynamics for these systems. Our results disagree with the predictions of a proposed matrix model dual of the 0A black hole. Lastly, we discuss heterotic string theories in two dimensions with gauge groups Spin(24) and Spin(8) x E8. After compactification the theories exhibit a rich spectrum of states with both winding and momentum. At special points some of these stringy states become massless, leading to new peculiar first order phase transitions. The full moduli space of compactified theories is 13 dimensional, when Wilson lines are included. The phase structure is examined by classifying the hypersurfaces in moduli space which support massless quanta or discrete states. Finally, we compute the torus amplitude over much of the moduli space.