Where is String Theory? (2102.02847v2)

Abstract: We use the S-matrix bootstrap to carve out the space of unitary, crossing symmetric and supersymmetric graviton scattering amplitudes in ten dimensions. We focus on the leading Wilson coefficient $\alpha$ controlling the leading correction to maximal supergravity. The negative region $\alpha<0$ is excluded by a simple dual argument based on linearized unitarity (the desert). A whole semi-infinite region $\alpha \gtrsim 0.14$ is allowed by the primal bootstrap (the garden). A finite intermediate region is excluded by non-perturbative unitarity (the swamp). Remarkably, string theory seems to cover all (or at least almost all) the garden from very large positive $\alpha$ -- at weak coupling -- to the swamp boundary -- at strong coupling.

Overview of "Where is String Theory?"

The paper "Where is String Theory?" presents a detailed investigation into the parameter space of gravitational theories in ten dimensions with maximal supersymmetry. Utilizing the S-matrix bootstrap methodology, the authors endeavor to delineate the range of permissible values for the leading Wilson coefficient $\alpha$. This coefficient governs the principal correction to maximal supergravity, providing insights into potential ultraviolet (UV) completions of gravity via string theory. The exploration is focused on the scattering amplitudes of gravitons, highlighting the efficacy of the bootstrap in mapping the theoretical landscape.

The research aims to reconcile the theoretical predictions of string theory with the fundamental principles of analyticity, unitarity, and crossing symmetry. The investigation extends to non-perturbative unitarity, prohibiting a finite intermediate region deemed the "swamp." Contrarily, regions where $\alpha \geq 0.14$ are sanctioned by the bootstrap, referred to as the "garden." The paper excludes negative values of $\alpha$ via effective field theory arguments based on linearized unitarity, characterizing these as the "desert." Notably, string theory occupies nearly all the garden, ranging from large positive $\alpha$ at weak coupling to the swamp boundary at strong coupling, which emphasizes its robustness across different coupling regimes.

Numerical Results and Claims

The paper presents the key numerical finding that string theory consistently occupies values in the allowed region for $\alpha$. Specifically, in type IIB superstring theory, the authors cite $$\alpha^\text{IIB} = \frac{1}{2^6} E_{3/2}(\tau,\bar{\tau})$$, where the Eisenstein series contributes across the coupling regime, attesting to its minimum value at strong coupling. A similarly positive range is validated within type IIA superstring theory. The numerical estimations place $\alpha$ within $0.13 \pm 0.02$, affirming string theory as encompassing permissible values under the bootstrap principles.

Theoretical and Practical Implications

This research provides crucial insights into the theoretical landscape of quantum gravity and string theory. By outlining the constraints imposed by the S-matrix bootstrap, the paper strengthens the premise that string theory offers a comprehensive UV completion for gravity across the spectrum of $\alpha$. The implications for future research are vast, suggesting further exploration into the combined space of multiple Wilson coefficients and pursuing analyses in other dimensional frameworks or string theory variants. The potential alignment with the Superconformal Bootstrap indicates overlaps with the AdS/CFT correspondence, warranting in-depth exploration.

Future Developments in AI

Looking ahead, advancements in AI can contribute significantly to solving complex problems highlighted in this paper. AI methodologies can optimize the numerical exploration and extrapolation processes involved, reducing computational error margins and enhancing precision in large data assessments. AI's capability in pattern recognition may facilitate deeper insights into the resonances and behaviors of scattering amplitudes. Developing AI-driven models could further assist in hypothesizing novel theoretical frameworks or identifying overlooked regions, thereby augmenting the quest to unify quantum mechanisms with higher-dimensional supergravity paradigms.

The paper marks a progressive step in the synthesis of string theory with broader theoretical postulations, accentuating refined models that satisfy radial symmetry and analyticity in ten-dimensional quantum gravity. This pursuit continues to be pivotal to understanding the fabric of the universe in higher dimensions, positioning string theory as a formidable candidate in this exploration.