Charting the Landscape of Supercritical String Theory

Special solutions of string theory in supercritical dimensions can interpolate in time between theories with different numbers of spacetime dimensions and different amounts of world sheet supersymmetry. 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.

Figure 1

The dimension-quenching transitions in type 0 string theory define a semi-infinite lattice of connected theories. Diagonal lines are tuned transitions that reduce the spacetime dimensionality by one. Right-pointing downward (dashed) arrows represent transitions with $\mu >0$, and left-pointing downward (dotted) arrows represent transitions with $\mu <0$. Vertical lines are natural transitions reducing the spacetime dimensionality by two. The straight horizontal lines indicate either $T$ duality or orbifolding by a left-moving spacetime fermion number (the 2D version is a thermal $T$ duality). 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 (curved arrows) to the type 0 series by Scherk-Schwarz compactification and $T$ duality ($\mathrm{SS}+\mathrm{T}$) or by a discrete Wilson line (WL) construction [8]. (Orbifolded type 0B transitions to stable type IIA are shown on the right; analogous connections among orbifolded type 0A and critical type IIB theories have been omitted.)

Figure 2

Transitions to bosonic string theory in two dimensions and higher can occur via $c$ duality, starting from points in the type 0 hierarchy. 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 curved solid arrows are the detuned versions of tuned dimension-changing transitions with $\Delta D=1$. The transitions to bosonic string theory in this figure are understood to be superimposed on the corresponding structure in the type 0 series depicted in Fig. 1.