# Compensating strong coupling with large charge

@article{AlvarezGaum2016CompensatingSC, title={Compensating strong coupling with large charge}, author={Lu{\'i}s Alvarez-Gaum{\'e} and Orestis Loukas and Domenico Orlando and Susanne Reffert}, journal={Journal of High Energy Physics}, year={2016}, volume={2017}, pages={1-21} }

A bstractWe study some (conformal) field theories with global symmetries in the sector where the value of the global charge Q is large. We find (as expected) that the low energy excitations of this sector are described by the general form of Goldstone’s theorem in the non-relativistic regime. We also derive the unexpected result, first presented in [1], that the effective field theory describing such sector of fixed Q contains effective couplings λeff ∼ λb/Qa, where λ is the original coupling…

## 91 Citations

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We extend and clarify the large-charge expansion of the conformal dimension ∆ Q of the lowest operator of charge Q in nonrelativistic conformal ﬁeld theories using the state-operator correspondence.…

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### The large charge expansion at large N

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A bstractThe scaling dimensions of charged operators in conformal field theory have recently been predicted to exhibit universal behavior in the large charge limit. We verify this behavior in the 2+1…

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A bstractWe consider unitary CFTs with continuous global symmetries in d > 2. We consider a state created by the lightest operator of large charge Q ≫ 1 and analyze the correlator of two light…

### Feynman diagrams and the large charge expansion in 3 − ε dimensions

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We elaborate on Abelian complex scalar models, which are dictated by natural actions (all couplings are of order one), at fixed and large global U(1) charge in an arbitrary number of dimensions. The…

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- Physics
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This thesis explores the application of semiclassical methods in the study of states with large quantum numbers for theories invariant under internal symmetries. In the first part of the thesis, we…

### A safe CFT at large charge

- PhysicsJournal of High Energy Physics
- 2019

Abstract
We apply the large-charge limit to the first known example of a four-dimensional gauge-Yukawa theory featuring an ultraviolet interacting fixed point in all couplings. We determine the…

## References

SHOWING 1-10 OF 17 REFERENCES

### Implications of relativity on nonrelativistic Goldstone theorems: gapped excitations at finite charge density.

- PhysicsPhysical review letters
- 2013

This work adapts the Goldstone theorem to study spontaneous symmetry breaking in relativistic theories at finite charge density and derives exact nonperturbative expressions for gaps, in terms of the chemical potential and of the symmetry algebra.

### On the integration of fields and quanta in time dependent backgrounds

- Physics
- 2014

A bstractField theories with global continuous symmetries may admit configurations in which time translation invariance is broken by the movement of homogeneous background fields evolving along the…

### Spontaneous symmetry probing

- Physics
- 2012

A bstractFor relativistic quantum field theories, we consider Lorentz breaking, spatially homogeneous field configurations or states that evolve in time along a symmetry direction. We dub this…

### Massive Nambu-Goldstone bosons.

- PhysicsPhysical review letters
- 2013

It is shown that the phenomenon is much more general than anticipated and the presence of Nambu-Goldstone-like modes in a number of systems from (anti)ferromagnets in a magnetic field to superfluid phases of quantum chromodynamics.

### On the CFT operator spectrum at large global charge

- Physics
- 2015

A bstractWe 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…

### Bootstrapping the O(N) archipelago

- Mathematics
- 2015

A bstractWe study 3d CFTs with an O(N) global symmetry using the conformal bootstrap for a system of mixed correlators. Specifically, we consider all nonvanishing scalar four-point functions…

### Spontaneous Symmetry Breaking and Nambu-Goldstone Bosons in Quantum Many-Body Systems

- PhysicsSymmetry
- 2010

This work focuses on manifestations of spontaneously broken symmetries in systems that are not Lorentz invariant, which include both nonrelativistic systems as well as relativistic system at nonzero density, providing a self-contained review of the properties of spontaneously break symmetry specific to such theories.

### Conformal Bootstrap Dashing Hopes of Emergent Symmetry

- Physics
- 2016

We use the conformal bootstrap program to derive necessary conditions for emergent symmetry enhancement from discrete symmetry (e.g. Zn) to continuous symmetry (e.g. U(1)) under the renormalization…

### Anisotropic perturbations in three-dimensional O(N)-symmetric vector models

- Physics
- 2011

We investigate the effects of anisotropic perturbations in three-dimensional O(N)-symmetric vector models. In order to assess their relevance for the critical behavior, we determine the…