Backlund Transformations, D-Branes, and Fluxes in Minimal Type 0 Strings

TL;DR

This paper explores non-perturbative solutions in minimal Type 0 string theories, revealing connections between D-branes, fluxes, and integrable systems like the KdV hierarchy, with implications for understanding string backgrounds.

Contribution

It demonstrates that solutions for minimal Type 0 strings are related to KdV solitons and introduces a Backlund transformation linking different background configurations.

Findings

Special properties of solutions at integer Gamma values.

Backlund transformation acts as a solution generator.

D-branes are related to KdV solitons.

Abstract

We study the Type 0A string theory in the (2,4k) superconformal minimal model backgrounds, focusing on the fully non-perturbative string equations which define the partition function of the model. The equations admit a parameter, Gamma, which in the spacetime interpretation controls the number of background D-branes, or R-R flux units, depending upon which weak coupling regime is taken. We study the properties of the string equations (often focusing on the (2,4) model in particular) and their physical solutions. The solutions are the potential for an associated Schrodinger problem whose wavefunction is that of an extended D-brane probe. We perform a numerical study of the spectrum of this system for varying Gamma and establish that when Gamma is a positive integer the equations' solutions have special properties consistent with the spacetime interpretation. We also show that a natural solution-generating transformation (that changes Gamma by an integer) is the Backlund transformation of the KdV hierarchy specialized to (scale invariant) solitons at zero velocity. Our results suggest that the localized D-branes of the minimal string theories are directly related to the solitons of the KdV hierarchy. Further, we observe an interesting transition when Gamma=-1.