We investigate the space of consistent tree-level extensions of the maximal supergravities in ten dimensions. We parametrize theory space by the first few EFT coefficients and by the on-shell coupling of the lightest massive state, and impose on these data the constraints that follow from 2 → 2 supergraviton scattering. While Type II string theory lives strictly inside the allowed region, we uncover a novel extremal solution of the bootstrap problem, which appears to contain a linear Regge trajectory, with the same slope as string theory. We repeat a similar analysis for supergluon scattering, where we find instead a continuous family of extremal solutions with a single Regge trajectory of varying slope.

United States

Jan Albert

Waltraut Knop

Leonardo Rastelli

Where is tree-level string theory?

We continue the investigation of large N QCD from a modern bootstrap perspective, focusing on the mesons. We make the natural spectral assumption that the 2 → 2 pion amplitude must contain, above the spin-one rho meson, a massive resonance of spin two. By maximizing its coupling we find a very interesting extremal solution of the dual bootstrap problem, which appears to contain at least a full Regge trajectory. Its low-lying states are in uncanny quantitative agreement with the meson masses in the real world.

Italy

France

Johan Henriksson

Alessandro Vichi

Bootstrapping mesons at large N: Regge trajectory from spin-two maximization

We continue the program [1] of carving out the space of large N confining gauge theories by modern S-matrix bootstrap methods, with the ultimate goal of cornering large N QCD. In this paper, we focus on the effective field theory of massless pions coupled to background electromagnetic fields. We derive the full set of positivity constraints encoded in the system of 2 → 2 scattering amplitudes of pions and photons. This system probes a larger set of intermediate meson states, and is thus sensitive to intricate large N selection rules, especially when supplemented with expectations from Regge theory. It also has access to the coefficient of the chiral anomaly. We find novel numerical bounds on several ratios of Wilson coefficients, in units of the rho mass. By matching the chiral anomaly with the microscopic theory, we also derive bounds that contain an explicit N dependence.

Bootstrapping pions at large N. Part II. Background gauge fields and the chiral anomaly

Abstract The theory of topological modular forms (TMF) predicts that elliptic genera of physical theories satisfy a certain divisibility property, determined by the theory’s gravitational anomaly. In this note we verify this prediction in Duncan’s supermoonshine module, as well as in tensor products and orbifolds thereof. Along the way we develop machinery for computing the elliptic genera of general alternating orbifolds and discuss the relation of this construction to the elusive “periodicity class” of TMF.

Japan

Justin Kaidi

Ying-Hsuan Lin

Topological modularity of supermoonshine What is an elliptic object? What is an elliptic object? Elliptic Cohomology Global Anomalies in String Theory

We revisit from a modern bootstrap perspective the longstanding problem of solving QCD in the large N limit. We derive universal bounds on the effective field theory of massless pions by imposing the full set of positivity constraints that follow from 2 → 2 scattering. Some features of our exclusion plots have intriguing connections with hadronic phenomenology. The exclusion boundary exhibits a sharp kink, raising the tantalizing scenario that large N QCD may sit at this kink. We critically examine this possibility, developing in the process a partial analytic understanding of the geometry of the bounds.

Bootstrapping pions at large N

We study the self-gravitating Abrikosov vortex in curved space with and with-out a (negative) cosmological constant, considering both singular and non-singular solutions with an eye to hairy black holes. In the asymptotically flat case, we find that non-singular vortices round off the singularity of the point particle’s metric in 3 dimensions, whereas singular solutions consist of vortices holding a conical singularity at their core. There are no black hole vortex solutions. In the asymptotically AdS case, in addition to these solutions there exist singular solutions containing a BTZ black hole, but they are always hairless. So we find that in contrast with 4-dimensional ’t Hooft-Polyakov monopoles, which can be regarded as their higher-dimensional analogues, Abrikosov vortices cannot hold a black hole at their core. We also describe the implications of these results in the context of AdS/CFT and propose an interpretation for their CFT dual along the lines of the holographic superconductor.