On Supergravity and Noncritical Strings

TL;DR

This paper explores noncritical superstring theories with 6d super Poincaré invariance, deriving effective supergravities, analyzing solutions, and connecting them to known string backgrounds and dualities, with implications for holography of super QCD.

Contribution

It provides a worldsheet derivation of 7d maximally supersymmetric gauged supergravities from noncritical strings and relates them to 10d supergravities via consistent truncations and dualities.

Findings

Identification of 7d supergravities as effective theories for noncritical strings

Derivation of BPS solutions and their 10d uplift

Connection to Hanany-Witten brane setups and dualities

Abstract

Motivated by the long-term goal of finding holographic descriptions for ${\mathcal N}=1$ and ${\mathcal N}=2$ super QCD, we revisit the subject of ''noncritical'' superstring theory. Focusing on string models with 6d super Poincar\'e invariance, we provide a careful worldsheet derivation of the leading-order effective theories for the lowest modes. We identify them as $\textit{seven}$-dimensional, $\textit{maximally supersymmetric}$ gauged supergravities: the $SO(4)$ theory for noncritical IIA and the $ISO(4)$ theory for noncritical IIB. The same theories also arise as consistent truncations on $S^3$ of the 10d IIB and IIA supergravities, respectively, where the chirality flip is as expected from T-duality. These effective supergravities should be interpreted in the following sense. The noncritical string can be viewed as a special case of a discrete series of backgrounds labelled by an integer $k$ (which counts the number of NS5 branes in a certain duality frame); the ''noncritical'' value is $k=2$, while for $k \to \infty$ one recovers a weakly-curved 10d target space. The effective supergravities described here give an accurate description of the interactions among the lowest modes for $k \to \infty$, with higher derivative corrections suppressed by powers of $1/k$. We discuss BPS solutions of the 7d gauged supergravities and their uplift to 10d solutions. In particular, we find a novel class of solutions with RR flux, parametrized by a function of three variables that solves an elegant PDE. While we cannot solve the PDE in closed form except in trivial cases, we confirm that our solutions correspond to a 10d IIA Hanany-Witten setup with continuous distributions of both ''color'' D4 branes and ''flavor'' D6 branes.