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 (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.Comment: 27 pages, 4 figure

On the Large RR-charge Expansion in N=2{\mathcal N} = 2 Superconformal Field Theories

In this note we study two point functions of Coulomb branch chiral ring elements with large $R$-charge, in quantum field theories with ${\mathcal N} = 2$ superconformal symmetry in four spacetime dimensions. Focusing on the case of one-dimensional Coulomb branch, we use the effective-field-theoretic methods of arXiv:1706.05743, to estimate the two-point function $${\mathcal Y}_n \equiv |x-y|^{2n\Delta_{\mathcal O}}\left<({\mathcal O}(x))^n(\bar{\mathcal O}(y))^n\right>$$ in the limit where the operator insertion On has large total $R$-charge ${\mathcal J} = n\Delta_{\mathcal O}$. We show that ${\mathcal Y}_n$ has a nontrivial but universal asymptotic expansion at large ${\mathcal J}$, of the form $${\mathcal Y}_n = {\mathcal J}! \left(\frac{\left| {\mathbf N}_{\mathcal O}\right|}{2\pi}\right)^{2{\mathcal J}}{\mathcal J}^\alpha {\tilde{\mathcal Y}}_n$$ where ${\mathcal Y}_n$ approaches a constant as $n\to\infty$, and ${\mathbf N}_{\mathcal O}$ is an $n$-independent constant describing on the normalization of the operator relative to the effective Abelian gauge coupling. The exponent $\alpha$ is a positive number proportional to the difference between the $a$-anomaly coefficient of the underlying CFT and that of the effective theory of the Coulomb branch. For Lagrangian SCFT, we check our predictions against exact results from supersymmetric localization of Baggio et. al. and Gerchkovitz et. al., and find precise agreement for the logarithm ${\mathcal B}_n = \log{\mathcal Y}_n$, up to and including order $\log{\mathcal J}$. We also give predictions for the growth of two-point functions in all rank-one SCFT in the classification of Argyres et. al. In this way, we show the large-$R$-charge expansion serves as a bridge from the world of unbroken superconformal symmetry, OPE data, and bootstraps, to the world of the low-energy dynamics of the moduli space of vacua.Comment: minor change

Boundary Operators in Effective String Theory

Various universal features of relativistic rotating strings depend on the organization of allowed local operators on the worldsheet. In this paper, we study the set of Neumann boundary operators in effective string theory, which are relevant for the controlled study of open relativistic strings with freely moving endpoints. Relativistic open strings are thought to encode the dynamics of confined quark-antiquark pairs in gauge theories in the planar approximation. Neumann boundary operators can be organized by their behavior under scaling of the target space coordinates X, and the set of allowed X-scaling exponents is bounded above by +1/2 and unbounded below. Negative contributions to X-scalings come from powers of a single invariant, or "dressing" operator, which is bilinear in the embedding coordinates. In particular, we show that all Neumann boundary operators are dressed by quarter-integer powers of this invariant, and we demonstrate how this rule arises from various ways of regulating the short-distance singularities of the effective theory.Comment: LaTeX, 37 page