Charting the landscape of supercritical string theory

TL;DR

<3-5 sentence high-level summary> The paper develops a global atlas of connections between supercritical and critical string theories through dimension quenching and c-duality, showing that time-evolving tachyon condensates induce domain-wall transitions that repackage worldsheet degrees of freedom and central charge. It introduces a classification framework for which supercritical vacua can flow to ten-dimensional type II backgrounds, identifying precise discrete GSO constraints and geometric actions that preserve a single connected IR vacuum. It further demonstrates how c-duality links type 0 theories to bosonic string theories, including explicit constructions in D=2 via the Berkovits–Vafa embedding, and analyzes the interplay between tachyon profiles, RR/GSO structure, and marginal deformations. Together these results reveal a cosmological, highly interconnected landscape in which supersymmetric and bosonic string theories are facets of a unified network, with implications for the broader string duality web and noncritical string dynamics.

Abstract

Special solutions of string theory in supercritical dimensions can interpolate in time between theories with different numbers of spacetime dimensions (via dimension quenching) and different amounts of worldsheet supersymmetry (via c-duality). These solutions connect supercritical string theories to the more familiar string duality web in ten dimensions, and provide a precise link between supersymmetric and purely bosonic string theories. Dimension quenching and c-duality appear to be natural concepts in string theory, giving rise to large networks of interconnected theories. We describe some of these networks in detail and discuss general consistency constraints on the types of transitions that arise in this framework.

Figures (4)

• Figure 1: Feynman diagrams contributing to the renormalizations of the dilaton and metric. The massive $X^2$ field (solid lines) propagates in the loops, while the massless fields (dashed lines) have oriented propagators. Quantum corrections terminate at one-loop order in perturbation theory.
• Figure 2: The dimension quenching transitions in type 0 string theory define a semi-infinite lattice of connected theories. The diagonal lines are tuned transitions that reduce the spacetime dimensionality by one (right-pointing downward arrows have $\mu > 0$, and left-pointing downward arrows have $\mu < 0$). The vertical lines are natural transitions reducing the spacetime dimensionality by two. The horizontal lines do not represent dynamical transitions; rather, they represent the standard connection between type 0A and 0B string theory by T-duality or orbifolding by left-moving spacetime fermion number $(-1)^{F_{L_S}}$ (the lowest horizontal arrow represents orbifolding, or alternatively a thermal T-duality). The lowest point on the diagram represents two-dimensional string theory of the kind described by the $\hat{c} = 1$ matrix model.
• Figure 3: Natural dimension-quenching transitions of orbifolded type 0 string theories terminate with type II string theory in the critical dimension ($D=10$). These hierarchies are connected laterally to the type 0 series by Scherk-Schwarz compactification and T-duality, or by a discrete Wilson line construction wilsonization. The type 0 hierarchy in the middle is labeled according to the legend in Fig. \ref{['0fig']}.
• Figure 4: Transitions to bosonic string theory in two dimensions and higher can occur via c-duality, starting from points in the type 0 series. The transitions connect type 0 theories in $D$ dimensions to bosonic string theory in $D$ (straight, solid arrows) or $D-1$ (curved, solid arrows) noncompact dimensions, with compact current algebra factors. The straight, solid arrows are c-duality transitions, and the curved solid arrows are the detuned versions of tuned dimension-changing transitions with $\Delta D = 1$. The detuned transitins combine c-duality and dimension quenching. At the bottom of the type 0 series, c-duality connects type 0B in $2D$ to two copies of bosonic string theory in $2D$, while the analogous flow connects type 0A to a single copy of bosonic string theory in $2D$. Both of these endpoints are also connected by tuned transitions to type 0 string theory in $3D$. The transitions to bosonic string theory in this figure are understood to be superimposed on the corresponding structure in the type 0 hierarchy depicted in Fig. \ref{['0fig']} (which is displayed in light blue; color is available in the electronic version).