Selected Publications

We systematically study correlators of a generic conformal field theory with a global O(2) symmetry in a sector of large global charge. We focus in particular on three- and four-point correlators with conserved current insertions sandwiched between spinful excited states corresponding to phonons over the large-charge vacuum. We also discuss loop corrections to the scaling dimensions and observe multiple logarithms in even dimensions.

We show that the standard notion of entanglement is not defined for gravitationally anomalous two-dimensional theories because they do not admit a local tensor factorization of the Hilbert space into local Hilbert spaces. Qualitatively, the modular flow cannot act consistently and unitarily in a finite region, if there are different numbers of states with a given energy traveling in the two opposite directions. We make this precise by decomposing it into two observations: First, a two-dimensional CFT admits a consistent quantization on a space with boundary only if it is not anomalous. Second, a local tensor factorization always leads to a definition of consistent, unitary, energy-preserving boundary condition. As a corollary we establish a generalization of the Nielsen-Ninomiya theorem to all two-dimensional unitary local QFTs: No continuum quantum field theory in two dimensions can admit a lattice regulator unless its gravitational anomaly vanishes. We also show that the conclusion can be generalized to six dimensions by dimensional reduction on a four-manifold of nonvanishing signature. We advocate that these points be used to reinterpret the gravitational anomaly quantum-information-theoretically, as a fundamental obstruction to the localization of quantum information.

In this review we study quantum field theories and conformal field theories with global symmetries in the limit of large charge for some of the generators of the symmetry group. At low energy the sectors of the theory with large charge are described by a hybrid form of Goldstone’s theorem, involving its relativistic and non-relativistic forms. The associated effective field theory in the infrared allows the computation of anomalous dimensions, and operator product expansion coefficients in a well defined expansion in inverse powers of the global charge. This applies even when the initial theory does not have a reliable semiclassical approximation. The large quantum number expansion complements, and may provide an alternative approach to the bootstrap and numerical treatments. We will present some general features of the symmetry breaking patterns and the low-energy effective actions, and a fairly large number of examples exhibiting the salient features of this method.
Phys.Rept. 933 (2021) 1-66, 2020

We study the $O(4)$ Wilson–Fisher fixed point in $2+1$ dimensions in fixed large-charge sectors identified by products of two spin-$j$ representations $(j_L,j_R)$. Using effective field theory we derive a formula for the conformal dimensions $D(j_L, j_R)$ of the leading operator in terms of two constants, $c_{ 3 / 2}$ and $c_{ 1 / 2}$, when the sum $j_L + j_R$ is much larger than the difference $|j_L-j_R|$. We compute $D(j_L,j_R)$ when $j_L= j_R$ with Monte Carlo calculations in a discrete formulation of the $O(4)$ lattice field theory, and show excellent agreement with the predicted formula and estimate $c_{ 3 / 2}=1.068(4)$ and $c_{ 1 / 2}=0.083(3)$.
in PRL, 2019

Recent Publications

More Publications

. Spinning correlators in large-charge CFTs. 2022.


. 2D CFTs - Large Charge is not enough. Phys.Rev.D 105 (2022) 8, 086029, 2021.


. Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements. 2021.


. Convexity, large charge and the large-N phase diagram of the φ⁴ theory. JHEP, 2021.


. Following the flow for large N and large charge. Phys.Lett.B, 2021.


. Large R-charge EFT correlators in N=2 SQCD. 2021.


Selected Talks

I will discuss the IR fixed point of the O(N) vector model in 3 dimensions (Wilson-Fisher point) in the framework of the large charge expansion. First I will construct an EFT valid for any N, then verify the prediction of the model in the double scaling limit of large N, large charge and finally discuss the use of resurgence to extend the validity of the EFT to sectors of small charge.

Working in sectors of large global charge leads to important simplifications when studying strongly coupled CFTs. In this talk I will introduce the large-charge expansion via the simple example of the O(2) model and apply it in a number of other situations displaying a richer structure, such as non-Abelian vector models, supersymmetric, asymptotically safe theories and walking dynamics.

We apply the large-charge expansion to O(N) vector models starting from first principles. We focus on the Wilson–Fisher point in three dimensions. We compute conformal dimensions and energies on generic Riemann surfaces at zero and finite temperature, at fixed charge Q in the regime 1 ≪ N ≪ Q. Our approach places the earlier effective field theory treatment on firm ground and extends its predictions.

We compute conformal dimensions and other physical quantities for strongly coupled conformal field theories in three dimensions with global symmetries. We show how in sectors of large global charge $Q$, the charge acts as a controlling parameter and physical quantities can be explicitly computed in a $1/Q$ perturbative expansion. In the case of the $O(2)$ model we show how the predictions of this approach are in very good agreement with lattice measurements.

I discuss a general proof of the following two facts regarding two-dimensional local quantum field theories with non-vanishing gravitational anomaly: 1. these theories do not admit a lattice regularization (this generalizes the renowned Nielsen-Ninomiya theorem); 2. their Hilbert space does not factorize into Hilbert spaces in complementary regions. Fact 2 implies in particular that, in the presence of a non-vanishing gravitational anomaly, the usual definitions of quantum entanglement break down.

Recent & Upcoming Talks

More Talks

N=2 SUSY at large R-charge
Fri, 25 Mar, 2022
Vector models at large charge (and some supersymmetry)
Thu, 18 Nov, 2021
The large N effective potential from large charge
Thu, 14 Oct, 2021
Introduction to the large charge expansion
Thu, 5 Aug, 2021
The O(N) vector model at large charge: EFT, large N and resurgence
Tue, 6 Apr, 2021