Exploding attractors, winding dimensions, and increasing entropy

First we present a mechanism for catalyzed vacuum bubble production obtained by combining moduli stabilization with a generalized attractor phenomenon in which moduli are sourced by compact objects. Next we show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks. Finally, we demonstrate that the boundary entropy of a critical one-dimensional quantum system can increase under renormalization group flow as the bulk theory flows between two nearby critical points.