We study the large-charge bootstrap in three-dimensional CFTs with a global U(1) symmetry using scalar, current, and stress-tensor probes, restricting to parity-even exchanged operators. Under minimal assumptions, the bootstrap requires at least one Regge trajectory with the dispersion relation of the standard Goldstone mode of the conformal superfluid. With additional assumptions, this trajectory is unique, while all non-Goldstone trajectories contribute only to the scalar-scalar channel at this order.

We study the large-charge bootstrap for conformal field theories with a U(1) symmetry extending the analysis of scalar probes to include conserved currents. We formulate the bootstrap equations and analyze their solutions assuming the existence of a non-trivial macroscopic limit and that the spectrum organizes into a finite number of Regge trajectories. We show that current probes lead to additional bootstrap constraints that are absent in the purely scalar case, and we classify the resulting solutions.

The weak gravity conjecture has been invoked to conjecture that the dimensions of charged operators in a CFT should obey a superadditivity relation (sometimes referred to as convexity). In this paper, we study superadditivity of the operator spectrum in theories expanded about the semi-classical saddle point that dominates correlators of large charge operators. We explore this in two contexts. The first is a model with two scalar fields that carry different charges, at a non-trivial Wilson-Fisher fixed point. A careful analysis of the semi-classics for this two field model demonstrates that 'quantum' violations of superadditivity (those not forbidden by the conjecture) persist in the large charge regime. We then turn to study the general properties of CFTs at large charge as bottom-up EFTs. By a trial and error procedure we come up with a seemingly consistent family of examples violating the conjecture. In so doing the presence of a genuine dilaton field appears necessary. On the one hand our result demonstrates that the superadditivity conjecture cannot be proven purely on the basis of a bottom-up analysis. On the other hand, the need for a dilaton, with the corresponding infinite fine tuning, indicates the conjecture-violating EFTs are unlikely to be UV completable.

We use effective string theory to study mesons with large spin J in large N_c QCD 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/J expansion, 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 4d flux tubes. We compare our predictions with 4d QCD spectroscopy data, and suggest potential stringy interpretations 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.

We revisit the computation of the beta function in the two-dimensional ℂℙ(1) sigma model. We show that in different schemes, different diagrams are responsible for the running, such as momentum-independent tadpoles or even UV-finite bubble diagrams. We also comment on the relation between the beta functions and the energy dependence of scattering amplitudes.

We revisit the computation of the beta function in the two-dimensional CP(1) sigma model. We show that in different schemes, different diagrams are responsible for the running, such as momentum- independent tadpoles or even UV-finite bubble diagrams. We also comment on the relation between the beta functions and the energy dependence of scattering amplitudes.

We consider correlators for the flux of energy and charge in the background of operators with large global $U(1)$ charge in conformal field theory (CFT). It has recently been shown that the corresponding Euclidean correlators generically admit a semiclassical description in terms of the effective field theory (EFT) for a conformal superfluid. We adapt the semiclassical description to Lorentzian observables and compute the leading large charge behavior of the flux correlators in general $U(1)$ symmetric CFTs. We discuss the regime of validity of the large charge EFT for these Lorentzian observables and the subtleties in extending the EFT approach to subleading corrections. We also consider the Wilson-Fisher fixed point in $d=4-\epsilon$ dimensions, which offers a specific weakly coupled realization of the general setup, where the subleading corrections can be systematically computed without relying on an EFT.

The Large Charge sector of Conformal Field Theory (CFT) can generically be described through a semiclassical expansion around a superfluid background. In this work, focussing on U(1) invariant Wilson-Fisher fixed points, we study the spectrum of spinning large charge operators. For sufficiently low spin these correspond to the phonon excitations of the superfluid state. We discuss the organization of these states into conformal multiplets and the form of the corresponding composite operators in the free field theory limit. The latter entails a mapping, built order-by-order in the inverse charge n(-1), between the Fock space of vacuum fluctuations and the Fock space of fluctuations around the superfluid state. We discuss the limitations of the semiclassical method, and find that the phonon description breaks down for spins of order n(1/2) while the computation of observables is valid up to spins of order n. Finally, we apply the semiclassical method to compute some conformal 3-point and 4-point functions, and analyze the conformal block decomposition of the latter with our knowledge of the operator spectrum.

We discuss various differences in the instanton-based calculations of the $\beta$ functions in theories such as Yang-Mills and $\mathbb{CP}(N\!-\!1)$ on one hand, and $\lambda\phi^4$ theory with Symanzik's sign-reversed prescription for the coupling constant $\lambda$ on the other hand. Although the aforementioned theories are asymptotically free, in the first two theories, instantons are topological, whereas the Fubini-Lipatov instanton in the third theory is topologically trivial. The spectral structure in the background of the Fubini-Lipatov instanton can be continuously deformed into that in the flat background, establishing a one-to-one correspondence between the two spectra. However, when considering topologically nontrivial backgrounds for Yang-Mills and $\mathbb{CP}(N\!-\!1)$ theories, the spectrum undergoes restructuring. In these cases, a mismatch between the spectra around the instanton and the trivial vacuum occurs.

We propose an algebraic construction of the operator-state correspondence in nonrelativistic conformal field theories by explicitly constructing an automorphism of the Schrödinger algebra relating generators in different frames. It is shown that the construction follows closely that of relativistic conformal field theories.

Abstract At finite density, the spontaneous breakdown of an internal non-Abelian symmetry dictates, along with gapless modes, modes whose gap is fixed by the algebra and proportional to the chemical potential: the gapped Goldstones. Generically the gap of these states is comparable to that of other non-universal excitations or to the energy scale where the dynamics is strongly coupled. This makes it non-straightforward to derive a universal effective field theory (EFT) description realizing all the symmetries. Focusing on the illustrative example of a fully broken SU(2) group, we demonstrate that such an EFT can be constructed by carving out around the Goldstones, gapless and gapped, at small 3-momentum. The rules governing the EFT, where the gapless Goldstones are soft while the gapped ones are slow, are those of standard nonrelativistic EFTs, like for instance nonrelativistic QED. In particular, the EFT Lagrangian formally preserves gapped Goldstone number, and processes where such number is not conserved are described inclusively by allowing for imaginary parts in the Wilson coefficients. Thus, while the symmetry is manifestly realized in the EFT, unitarity is not. We comment on the application of our construction to the study of the large charge sector of conformal field theories with non-Abelian symmetries.

In arXiv:1909.01269 it was shown that the scaling dimension of the lightest charge n operator in the U(1) model at the Wilson-Fisher fixed point in D=4−ε can be computed semiclassically for arbitrary values of λn, where λ is the perturbatively small fixed point coupling. Here we generalize this result to the fixed point of the U(1) model in 3−ε dimensions. The result interpolates continuously between diagrammatic calculations and the universal conformal superfluid regime for CFTs at large charge. In particular it reproduces the expectedly universal O(n0) contribution to the scaling dimension of large charge operators in 3D CFTs.

We revisit the question of hadronic decays of a giga-electron-volt-mass Higgs-like scalar. A number of extensions of the Standard Model predict the Higgs sector with additional light scalars. Currently operating and planned Intensity Frontier experiments will probe for the existence of such particles, while theoretical computations are plagued by uncertainties. The goal of this paper is to bring the results in a consolidated form that can be readily used by experimental groups. To this end, we provide a physically motivated fitting ansatz for the decay width that reproduces the previous nonperturbative numerical analysis. We describe systematic uncertainties of the nonperturbative method and provide explicit examples of the influence of extra resonances above 1.4 GeV onto the total decay width.

It is shown that higgsplosion scenario is impossible within local QFT framework.

We calculate the scaling dimensions of operators with large global charge and spin in 2+1 dimensional conformal field theories. By the state-operator correspondence, these operators correspond to superfluids with vortices and can be systematically studied using effective field theory. As the spin increases from zero to the unitarity bound, the superfluid state corresponding to the lowest dimension operator passes through three distinct regimes: (1) a single phonon, (2) two vortices, and (3) multiple vortices. We also calculate correlation functions with two such operators and the Noether current.

In this note we show that given a conformally invariant theory in flat space-time, it is not always possible to couple it to gravity in a Weyl invariant way.

Hellerman et al. (arXiv:1505.01537) have shown that in a generic CFT the spectrum of operators carrying a large U(1) charge can be analyzed semiclassically in an expansion in inverse powers of the charge. The key is the operator state correspondence by which such operators are associated with a finite density superfluid phase for the theory quantized on the cylinder. The dynamics is dominated by the corresponding Goldstone hydrodynamic mode and the derivative expansion coincides with the inverse charge expansion. We illustrate and further clarify this situation by first considering simple quantum mechanical analogues. We then systematize the approach by employing the coset construction for non-linearly realized space-time symmetries. Focussing on CFT3 we illustrate the case of higher rank and non-abelian groups and the computation of higher point functions. Three point function coefficients turn out to satisfy universal scaling laws and correlations as the charge and spin are varied.

In this note we show that given a conformally invariant theory in flat space-time, it is not always possible to couple it to gravity in a Weyl invariant way.

It is known that not all summation methods are linear and stable. Zeta function regularization is in general nonlinear. However, in some cases formal manipulations with zeta function regularization (assuming linearity of sums) lead to correct results. We consider several examples and show why this happens.

In this paper we demonstrate how, using the coset construction, a theory can be systematically made Weyl invariant by gauging the scale symmetry. We show that an analog of the inverse Higgs constraint allows the elimination of the Weyl vector (gauge) field in favor of curvatures. We extend the procedure -- previously coined Ricci gauging -- and discuss its subtlety for the case of theories with higher derivatives of conformally variant fields.