Nonrelativistic conformal field theories in the large charge sector

We study the sector of large charge operators φ n (φ being the complexified scalar field) in the O(2) Wilson-Fisher fixed point in 4 − ǫ dimensions that emerges when the coupling takes the critical value g ∼ ǫ. We show that, in the limit g → 0, when the theory naively approaches the gaussian fixed point, the sector of operators with n → ∞ at fixed g n 2 ≡ λ remains non-trivial. Surprisingly, one can compute the exact 2-point function and thereby the non-trivial anomalous dimension of the operator φ n by a full resummation of Feynman diagrams. The same result can be reproduced from a saddle point approximation to the path integral, which partly explains the existence of the limit. Finally, we extend these results to the three-dimensional O(2)-symmetric theory with (φ φ) 3 potential.

Section: Introductionmentioning

confidence: 88%

The large charge limit of scalar field theories, and the Wilson-Fisher fixed point at 𝜖 = 0

Arias-Tamargo

Rodrı́guez-Gómez

Russo

2019

“…Another interesting direction would be to consider correlation functions of charged spinning operators in these NRCFTs. The universal scaling of the 3-point function and higher are all explicitly calculable within this EFT, as was done for scalar charged operators in [32]. In relativistic CFTs this was worked out in [9,13] for certain operators.…”

Section: Discussionmentioning

confidence: 99%

“…Via the state-operator correspondence of NRCFTs, this semi-classical calculation determines the dimension of a charged scalar operator to leading order in Q as ∆ Q = E Q ω . In particular, we have obtained [32]:…”

Section: The Set Up: Superfluid Hydrodynamics and Large Charge Nrcftmentioning

confidence: 99%

The spinful large charge sector of non-relativistic CFTs: from phonons to vortex crystals

Kravec

Pal

2019

Self Cite

We study operators in Schrödinger invariant field theories (non-relativistic conformal field theories or NRCFTs) with large charge (particle number) and spin. Via the state-operator correspondence for NRCFTs, such operators correspond to states of a superfluid in a harmonic trap with phonons or vortices. Using the effective field theory of the Goldstone mode, we compute the dimensions of operators to leading order in the angular momentum L and charge Q. We find a diverse set of scaling behaviors for NRCFTs in both d = 2 and d = 3.1 It is important to mention that Schrödinger symmetry is not simply the non-relativistic limit of the conformal symmetry but rather an entirely distinct algebra [15,16].2 It should be emphasized that this is not the only possibility. Ultimately the question "Given this NRCFT, what state of matter describes its large charge sector?" depends on the NRCFT, which we treat as UV physics. However we expect our results to be valid for a wide set of NRCFTs, including some of physical relevance such as unitary fermions [14].

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confidence: 99%

“…They admit a simple and universal effective field theory (EFT) description [21,22] which allows the computation of correlators in a perturbative expansion controlled by the charge density. The same strategy was recently applied also in the context of non-relativistic CFTs [23,24,25].As the angular momentum is increased, the superfluid starts rotating and vortices develop [26]. These can be included in the EFT as heavy topological defects [27,28,29].…”

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confidence: 99%

Superfluids, vortices and spinning charged operators in 4d CFT

Cuomo

2020

We include vortices in the superfluid EFT for four dimensional CFTs at large global charge. Using the state-operator correspondence, vortices are mapped to charged operators with large spin and we compute their scaling dimensions. Different regimes are identified: phonons, vortex rings, Kelvin waves, and vortex crystals. We also compute correlators with a Noether current insertion in between vortex states. Results for the scaling dimensions of traceless symmetric operators are given in arbitrary spacetime dimensions. * gabriel.cuomo@epfl.ch arXiv:1906.07283v2 [hep-th] 22 Jun 2019 1 IntroductionConformal field theories (CFTs) play a key role in particle and condensed matter physics. As fixed points of the renormalization group flow, they act as landmarks in the space of quantum field theories (QFTs). Through the AdS/CFT correspondence [1,2], they promise to shed light on quantum gravity. They also describe critical points for second order phase transitions. Finally, CFTs are also among the few examples of interacting QFTs where exact results are available without supersymmetry. Recently, the bootstrap program [3,4] achieved much progress in the study of CFTs, both through numerical [5,6] and analytical [7,8,9] techniques.Basic observables in CFTs are correlation functions of local operators in the vacuum. Despite this, sometimes one can make predictions for the CFT data defining the theory studying the dynamics of finite density states [10]. This is a consequence of the state/operator correspondence [11,12], which relates states in radial quantization to local operators with the same quantum numbers. So far, this idea has been mainly applied in the investigation of the superfluid phase in conformal field theories [10,13,14,15,16,17,18,19,20]. Indeed superfluids are the most natural candidates to describe states at large internal quantum numbers in CFTs. They admit a simple and universal effective field theory (EFT) description [21,22] which allows the computation of correlators in a perturbative expansion controlled by the charge density. The same strategy was recently applied also in the context of non-relativistic CFTs [23,24,25].As the angular momentum is increased, the superfluid starts rotating and vortices develop [26]. These can be included in the EFT as heavy topological defects [27,28,29]. In [30], this EFT was used to describe operators with large spin and large charge in three dimensional CFTs. In this work, we study the predictions of the vortex EFT for four dimensional CFTs.