Selected Publications

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.

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

We study some examples of Yang-Baxter deformations of the $AdS_5 \times S^5$ superstring with non-Abelian classical $r$-matrices which satisfy the homogeneous classical Yang-Baxter equation (CYBE). All of the resulting backgrounds satisfy the generalized type IIB supergravity equations. For some of them, we derive “T-dualized” backgrounds and show that these satisfy the usual type IIB supergravity equations. Remarkably, some of them are locally identical to undeformed $AdS_5 \times S^5$.
Journal of Physics A Highlight, 2016

We calculate the anomalous dimensions of operators with large global charge $J$ in certain strongly coupled conformal field theories in three dimensions, such as the $O(2)$ model and the supersymmetric fixed point with a single chiral superfield and a $W = \Phi^3$ superpotential. Working in a $1/J$ expansion, we find that the large-$J$ sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge $J$ is always a scalar operator whose dimension is $ \Delta(J) = a J^{3 / 2} + b J^{1 / 2} - 0.093$, up to corrections that vanish at large $J$.
In JHEP, 2015

Recent Publications

More Publications

. Near-Schrödinger dynamics at large charge. 2020.


. Selected Topics in the Large Quantum Number Expansion. 2020.


. Quantum crystals, Kagome lattice and plane partitions fermion-boson duality. 2020.


. S-duality and correlation functions at large R-charge. 2020.


. Charging the Conformal Window. 2020.


. Yang-Baxter deformations and generalized supergravity - A short summary. 2019.


Selected Talks

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

Introduction to the large charge expansion
Fri, 16 Oct, 2020
Solving the large charge expansion with integrability
Thu, 24 Sep, 2020
Introduction to the large charge expansion
Tue, 15 Sep, 2020
Introduction to the large charge expansion
Wed, 17 Jun, 2020
Introduction to the large charge expansion
Thu, 19 Mar, 2020
Introduction to the large charge expansion
Tue, 14 Jan, 2020