Massive type IIA string theory cannot be strongly coupled

TL;DR

This work argues that massive type IIA string theory lacks a reliable strongly coupled, weakly curved limit with Romans mass $F_0\neq 0$. By deriving a general bound $e^{\phi}\ll 1$ in the weak-curvature regime and analyzing two explicit AdS$_4\times\mathbb{CP}^3$ massive vacua (\mathcal{N}=1 and \mathcal{N}=2) dual to 3d CS-matter theories, the authors show the dilaton initially grows with the gauge rank $N$ but then decreases before entering an M-theory regime. In the \mathcal{N}=2 case, supersymmetric monopole operators with N-independent mass predict light brane states arising from D2-D0 bound states wrapping a vanishing two-cycle at a conifold singularity, a result borne out by a detailed gravity analysis. The paper also develops the flux-quantization inversion for both solutions, establishing phase-transition-like behavior between ABJM-like and nearly Kähler regimes, and provides a field-theoretic interpretation of these gravity results, linking monopole dynamics to wrapped branes and reinforcing the claim that strongly coupled weakly curved massive IIA vacua are generically unavailable.

Abstract

Understanding the strong coupling limit of massive type IIA string theory is a longstanding problem. We argue that perhaps this problem does not exist; namely, there may be no strongly coupled solutions of the massive theory. We show explicitly that massive type IIA string theory can never be strongly coupled in a weakly curved region of space-time. We illustrate our general claim with two classes of massive solutions in AdS4xCP3: one, previously known, with N = 1 supersymmetry, and a new one with N = 2 supersymmetry. Both solutions are dual to d = 3 Chern-Simons-matter theories. In both these massive examples, as the rank N of the gauge group is increased, the dilaton initially increases in the same way as in the corresponding massless case; before it can reach the M-theory regime, however, it enters a second regime, in which the dilaton decreases even as N increases. In the N = 2 case, we find supersymmetry-preserving gauge-invariant monopole operators whose mass is independent of N. This predicts the existence of branes which stay light even when the dilaton decreases. We show that, on the gravity side, these states originate from D2-D0 bound states wrapping the vanishing two-cycle of a conifold singularity that develops at large N.

Figures (5)

• Figure 1: A plot of the function $\rho(\sigma)$ in (\ref{['eq:sigma']}).
• Figure 2: The behavior of $g_s$ as a function of $N=n_6$, for $n_2=k=100$, $n_4=0$ and $n_0=1$. We see both the growth in the first phase (\ref{['eq:as1']}), for $n_6 \ll n_2^3/n_0^2 = 10^6$, and the decay in the second phase (\ref{['eq:as2']}), for $n_6 \gg n_2^3/n_0^2 = 10^6$.
• Figure 3: A plot of $w_0$ as a function of $\psi_1$. It vanishes linearly around the point $\psi_1=\sqrt{3}$.
• Figure 4: Plots of $f_4(\psi_1)$ and $f_6(\psi_1)$. Their asymptotic behavior near $0$ and $\sqrt{3}$ is given in (\ref{['eq:asf0']}), (\ref{['eq:asfs3']}). Notice in particular that $f_6(\sqrt{3})$ is small but non--zero.
• Figure 5: A plot of the function $\rho(\psi_1)$ in (\ref{['eq:rhoN2']}).