On integrable models from pp-wave string backgrounds

TL;DR

This paper constructs new integrable string backgrounds in type IIB supergravity by replacing flat transverse space with superconformal blocks, leading to models like complex sine-Gordon and supersymmetric Liouville theories.

Contribution

It introduces a method to generate integrable string models from superconformal field theory blocks within supergravity backgrounds, expanding the landscape of solvable string theories.

Findings

Explicit construction of solutions with RR 5-form and superconformal blocks.

Emergence of integrable models such as complex sine-Gordon and Liouville theories.

Generalization of pp-wave backgrounds including axionic instantons and wormhole geometries.

Abstract

We construct solutions of type IIB supergravity with non-trivial Ramond-Ramond 5-form in ten dimensions by replacing the transverse flat space of pp-wave backgrounds with exact $N=(4,4)$ $c=4$ superconformal field theory blocks. These solutions, which also include a dilaton and (in some cases) an anti-symmetric tensor field, lead to integrable models on the world-sheet in the light-cone gauge of string theory. In one instance we demonstrate explicitly the emergence of the complex sine-Gordon model, which coincides with integrable perturbations of the corresponding superconformal building blocks in the transverse space. In other cases we arrive at the supersymmetric Liouville theory or at the complex sine-Liouville model. For axionic instantons in the transverse space, as for the (semi)-wormhole geometry, we obtain an entire class of supersymmetric pp-wave backgrounds by solving the Killing spinor equations as in flat space, supplemented by the appropriate chiral projections; as such, they generalize the usual Neveu-Schwarz five-brane solution of type IIB supergravity in the presence of a Ramond-Ramond 5-form. We also present some further examples of interacting light-cone models and we briefly discuss the role of dualities in the resulting string theory backgrounds.