String Theory and Water Waves

We uncover a remarkable role that an infinite hierarchy of non-linear differential equations plays in organizing and connecting certain {hat c}<1 string theories non-perturbatively. We are able to embed the type 0A and 0B (A,A) minimal string theories into this single framework. The string theories arise as special limits of a rich system of equations underpinned by an integrable system known as the dispersive water wave hierarchy. We observe that there are several other string-like limits of the system, and conjecture that some of them are type IIA and IIB (A,D) minimal string backgrounds. We explain how these and several string-like special points arise and are connected. In some cases, the framework endows the theories with a non-perturbative definition for the first time. Notably, we discover that the Painleve IV equation plays a key role in organizing the string theory physics, joining its siblings, Painleve I and II, whose roles have previously been identified in this minimal string context.Comment: 49 pages, 4 figure

D-Branes and Fluxes in Supersymmetric Quantum Mechanics

Type 0A string theory in the (2,4k) superconformal minimal model backgrounds, with background ZZ D-branes or R-R fluxes can be formulated non-perturbatively. The branes and fluxes have a description as threshold bound states in an associated one-dimensional quantum mechanics which has a supersymmetric structure, familiar from studies of the generalized KdV system. The relevant bound state wavefunctions in this problem have unusual asymptotics (they are not normalizable in general, and break supersymmetry) which are consistent with the underlying description in terms of open and closed string sectors. The overall organization of the physics is very pleasing: The physics of the closed strings in the background of branes or fluxes is captured by the generalized KdV system and non-perturbative string equations obtained by reduction of that system (the hierarchy of equations found by Dalley, Johnson, Morris and Watterstam). Meanwhile, the bound states wavefunctions, which describe the physics of the ZZ D-brane (or flux) background in interaction with probe FZZT D-branes, are captured by the generalized mKdV system, and non-perturbative string equations obtained by reduction of that system (the Painleve II hierachy found by Periwal and Shevitz in this context).Comment: 41 pages, LaTe