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A<sc>bstract</sc> We use effective string theory to study mesons with large spinJin largeN_cQCD as rotating open strings. In the first part of this work, we formulate a consistent effective field theory (EFT) for open spinning strings with light quarks. Our EFT provides a consistent treatment of the endpoints’ singularities that arise in the massless limit. We obtain results, in a systematic 1/Jexpansion, for the spectrum of the leading and daughter Regge trajectories. Interestingly, we find that the redshift factor associated with the quarks’ acceleration implies that the applicability regime of the EFT is narrower compared to that of static flux tubes. In the second part of this work, we discuss several extensions of phenomenological interests, including mesons with heavy quarks, the quarks’ spin and the daughter Regge trajectories associated with the worldsheet axion, a massive string mode identified in lattice simulations of 4dflux tubes. We compare our predictions with 4dQCD spectroscopy data, and suggest potentialstringyinterpretations of the observed mesons. We finally comment on the relation between the EFT spectrum and the Axionic String Ansatz, a recently proposed characterization of the spectrum of Yang-Mills glueballs. 

A<sc>bstract</sc> 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 ind= 4 −ϵdimensions. We investigate the convergence properties of the bootstrap equation and check explicitly many of the non-trivial relations that it imposes on theory data. 

A<sc>bstract</sc> 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 isalsobroken 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$$ \mathcal{N} $$ $N$= 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.