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 $\textit{single}$ 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?

Motivated by the long-term goal of finding holographic descriptions for $$ \mathcal{N} $$ = 1 and $$ \mathcal{N} $$ = 2 super QCD, we revisit the subject of “noncritical” superstring theory. Focusing on string models with 6d super Poincaré invariance, we provide a careful worldsheet derivation of the leading-order effective theories for the lowest modes. We identify them as -dimensional, gauged supergravities: the SO(4) theory for noncritical IIA and the ISO(4) theory for noncritical IIB. The same theories also arise as consistent truncations on of the 10d IIB and IIA supergravities, respectively, where the chirality flip is as expected from T-duality. These effective supergravities should be interpreted in the following sense. The noncritical string can be viewed as a special case of a discrete series of backgrounds labelled by an integer (which counts the number of NS5 branes in a certain duality frame); the “noncritical” value is = 2, while for → ∞ one recovers a weakly-curved 10d target space. The effective supergravities described here give an accurate description of the interactions among the lowest modes for → ∞, with higher derivative corrections suppressed by powers of 1/ . We discuss BPS solutions of the 7d gauged supergravities and their uplift to 10d solutions. In particular, we find a novel class of solutions with RR flux, parametrized by a function of three variables that solves an elegant PDE. While we cannot solve the PDE in closed form except in trivial cases, we confirm that our solutions correspond to a 10d IIA Hanany-Witten setup with continuous distributions of both “color” D4 branes and “flavor” D6 branes.

Andrea Dei

Pietro Ferrero

On supergravity and noncritical strings

Conformal field theories that exhibit spontaneous breaking of conformal symmetry (a moduli space of vacua) must satisfy a set of bootstrap constraints, involving the usual data (scaling dimensions and OPE coefficients) as well as new data such as the spectrum of asymptotic states in the broken vacuum and form factors. The simplest bootstrap equation arises by expanding a two-point function of local operators in two channels, at short distance using the OPE and at large distance using the EFT in the broken vacuum. We illustrate this equation in what is arguably the simplest perturbative model that exhibits conformal symmetry breaking, namely the real ABC model in d = 4 − ϵ dimensions. We investigate the convergence properties of the bootstrap equation and check explicitly many of the non-trivial relations that it imposes on theory data.

Gabriel Cuomo

Adar Sharon

Moduli spaces in CFT: bootstrap equation in a perturbative example

In this paper, we construct the associated vertex operator algebras for all   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 superconformal field theories of rank one. We give a uniform presentation through free-field realizations, which turns out to be a particularly suitable framework for this task. The elementary building blocks of the construction are dictated by the low energy degrees of freedom on the Higgs branch, which are well understood for rank-one theories. We further analyze the interplay between Higgs and Coulomb data on the moduli space of vacua, which tightly constrain the overall structure of the free field realizations. Our results suggest a plausible bottom-up classification scheme for low-rank SCFTs incorporating vertex algebra techniques.

United Kingdom

Christopher Beem

Anirudh Deb

Mario Martone

Italy

Carlo Meneghelli

Free field realizations for rank-one SCFTs

Using the large-charge expansion, we prove a necessary condition for a CFT to exhibit conformal symmetry breaking, under the assumption that a continuous global symmetry is also broken on the moduli space: there must be a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge. In supersymmetric theories with a continuous R-symmetry and a holomorphic moduli space, the existence of such a tower of operators follows trivially from a BPS condition: their scaling dimensions are then exactly linear in the R-charge. We illustrate the more general statement in several examples of three-dimensional   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 CFTs, where the leading linear behavior receives nontrivial corrections. By considering a suitable scaling limit, we also relate the spectrum of states with large charge on the cylinder (isomorphic to local operators) to the spectrum of massive particles on the moduli space.

Moduli spaces in CFT: large charge operators

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.

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

By leveraging the physics of the Higgs branch, we argue that the conformal central charges <math><mi>a</mi></math> and <math><mi>c</mi></math> of an arbitrary 4D <math><mi>N</mi><mo>=</mo><mn>2</mn></math> superconformal field theory (SCFT) are rational numbers. Our proof of the rationality of <math><mi>c</mi></math> is conditioned on a well-supported conjecture about how the Higgs branch of an SCFT is encoded in its protected chiral algebra. To establish the rationality of <math><mi>a</mi></math>, we further rely on a widely believed technical assumption on the high-temperature limit of the superconformal index.

Brandon C. Rayhaun

Rationality in four dimensions

We propose a holographic description of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super Yang-Mills on the four-dimensional real projective space   <math> <mi>RP</mi> </math>  $$ \mathbbm{RP} $$  4. We first construct the dual background in the framework of five-dimensional   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 8 gauged supergravity, and then uplift it to a new one-half BPS solution of type IIB supergravity. A salient feature of our solution is the presence of a bulk naked singularity whose local behavior resembles that of an O1 −  plane in flat space.

CERN

João Caetano

Holography for   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 on   <math> <mi>RP</mi> </math>  $$ \mathbbm{RP} $$  4

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.