D-Branes and Fluxes in Supersymmetric Quantum Mechanics

TL;DR

This paper explores the non-perturbative formulation of Type 0A string theory with D-branes and fluxes using supersymmetric quantum mechanics, linking it to integrable systems like KdV and mKdV hierarchies.

Contribution

It establishes a novel connection between supersymmetric quantum mechanics and non-perturbative string backgrounds involving D-branes and fluxes, utilizing integrable hierarchies.

Findings

Bound state wavefunctions have unusual asymptotics and break supersymmetry.

Closed string physics is described by generalized KdV and non-perturbative equations.

Open string interactions involve generalized mKdV systems and Painleve II hierarchy.

Abstract

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).