Abelian scalar theory at large global charge

As a sequel to previous work, we extend the study of the ground state configuration of the D = 3, Wilson-Fisher conformal O(4) model. In this work, we prove that for generic ratios of two charge densities, ρ 1 /ρ 2 , the ground-state configuration is inhomogeneous and that the inhomogeneity expresses itself towards longer spatial periods. This is the direct extension of the similar statements we previously made for ρ 1 /ρ 2 1. We also compute, at fixed set of charges, ρ 1 , ρ 2 , the ground state energy and the two-point function(s) associated with this inhomogeneous configuration on the torus. The ground state energy was found to scale (ρ 1 + ρ 2 ) 3/2 , as dictated by dimensional analysis and similarly to the case of the O(2) model. Unlike the case of the O(2) model, the ground also strongly violates cluster decomposition in the large-volume, fixed-density limit, with a two-point function that is negative definite at antipodal points of the torus at leading order at large charge.

Section: Conformal Sigma Model From Linear Sigma Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A note on inhomogeneous ground states at large global charge

Hellerman

Kobayashi

Maeda

et al. 2019

“…Additional references about the large charge expansion of general conformal field theories and inAdS/CFT context may be found in[31][32][33][34][35][36][37][38][39][40][41][42].…”

mentioning

confidence: 99%

On the large R-charge $$ \mathcal{N} $$ = 2 chiral correlators and the Toda equation

Beccaria

2019

We consider N = 2 SU (N ) SQCD in four dimensions and a weak-coupling regime with large R-charge recently discussed in arXiv:1803.00580. If ϕ denotes the adjoint scalar in the N = 2 vector multiplet, it has been shown that the 2-point functions in the sector of chiral primaries (Trϕ 2 ) n admit a finite limit when g YM → 0 with large R-charge growing like ∼ 1/g 2 YM . The correction with respect to N = 4 correlators is a non-trivial function F (λ; N ) of the fixed coupling λ = n g 2 YM and the gauge algebra rank N . We show how to exploit the Toda equation following from the tt * equations in order to control the R-charge dependence. This allows to determine F (λ; N ) at order O(λ 10 ) for generic N , greatly extending previous results and placing on a firmer ground a conjecture proposed for the SU (2) case. We show that a similar Toda equation, discussed in the past, may indeed be used for the additional sector (Trϕ 2 ) n Trϕ 3 due to the special mixing properties of these composite operators on the 4-sphere. We discuss the large R-limit in this second case and compute the associated scaling function F at order O(λ 7 ) and generic N . Large N factorization is also illustrated as a check of the computation.

“…From (C.3), the coset is written as Ω = e iy a Pa e iσD e iη i J 0i e iξ n J n3 e iχQ . (C. 15) One can compute the MC one form as before Ω −1 D µ Ω = iE a µ P a + ∇ a σD + ∇ a χQ + ∇ a η i J 0i + ∇ a ξ n J n3 + Ω 12 a J 12 ; (C. 16) with…”

Section: C2 3+1 Dimensionsmentioning

confidence: 99%

“…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.…”

mentioning

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.