Large charge operators in CFTs invariant under internal symmetry can be generically associated with a superfluid phase of the theory. Therefore their correlation functions can be computed systematically within the effective field theory for the superfluid Goldstone mode. Focusing on the critical O(2) model in three dimensions, I will review this construction and extend it to include also...

I will discuss the large-charge expansion of the conformal dimension Δ_Q of the lowest operator of charge Q in nonrelativistic CFTs using the state-operator correspondence. The latter requires coupling the theory to an external harmonic trap that confines the particles to a spherical cloud, at the edge of which the effective theory breaks down and leads to divergences. Only recently has this...

We compute the spectrum of large charge operators in boundary conformal field theories (BCFTs) using the superfluid effective field theory (EFT). We verify the EFT predictions in weakly coupled examples, where computations can be done in the microscopic description. We end with a discussion of large charge phases of bulk and boundary CFTs beyond the superfluid paradigm. The talk is based on...

We study a 3d N=2 supersymmetric conformal manifold using the large-charge expansion. The exactly marginal operator is shown to continuously interpolate between the "free" phase and the "superfluid" phase in the large-charge limit. We also discuss some novel aspects of the large-charge limit which appear in this model.

In this talk I will introduce a particular formulation of the Weak Gravity Conjecture in AdS space in terms of the self-binding energy of a particle. The holographic CFT dual of this formulation corresponds to a certain convex-like structure for operators charged under continuous global symmetries. Motivated by this, we proposed a conjecture that this convexity is a general property of all...

The large-charge expansion can be employed to find and test dualities in QFT. I illustrate this point by investigating the quartic O(N) model between four and six dimensions, where it develops a metastable UV fixed point that is believed to be equivalent to the IR fixed point of an O(N) model featuring cubic interactions. By focusing on the cubic model just below six dimensions, I show how...

Topological insulators are materials in which the bulk part is insulating but the surface is metallic because of protected gapless states on the surface. The correspondence between the bulk topology and the gapless surface states is called the bulk-boundary correspondence. Recently, higher-order topological insulators with gapless states localizes at hinges and corners of a crystal, rather...

I present an overview on some recent progress in thermal one-point function in CFTs for general odd dimensions. On the one hand, they can be calculated using an extension to finite temperature of analytic bootstrap techniques. On the other hand, they are associated to single-valued polylogarithms which represent multiloop amplitudes in gauge theories. Some possible implications of the latter...

In this talk I will discuss the O(2N) model at criticality in three dimensions in the limit where the charge Q and N are taken to be large. The large-charge expansion turns out to be an asymptotic series and resurgent methods can be applied to obtain an unambiguous semi-classical reconstruction of this expansion. It contains non-perturbative corrections and it allows to extend the validity of...

We discuss the structure of Regge trajectories of 6d N=(2,0) SCFTs combining analyticity in spin with supersymmetry. Focusing on the four-point function of supermultiplet we show how "analyticity in spin" holds for all spins greater than -3. Through the Lorentzian inversion formula we then describe an iterative procedure to "bootstrap" this four-point function starting from protected data, and...

For CFTs that become superfluids at finite density, we show that there exists a single one-derivative term in the Goldstone EFT that has a quantized coefficient. This term requires the ground state on a sphere to have vortices, and results in a spectrum of operators that is remarkably different from CFTs that are parity invariant. We will show how the properties predicted by the Goldstone EFT...