Observables in inhomogeneous ground states at large global charge

Hellerman, Simeon; Kobayashi, Nozomu; Maeda, Shunsuke; Watanabe, Masataka

doi:10.1007/jhep08(2021)079

Cited by 13 publications

(19 citation statements)

References 35 publications

(56 reference statements)

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“…Before discussing the details of the general computation, it is instructive to discuss the solution of (29) for small λn. Namely, we compute the function Γ −1 (λn) in (21) to order O λ 2 n 2 /(4π) 4 and we check that the result agrees with (27). As we work at first order in the coupling, in what follows we will take λ 0 = λ.…”

Section: Semiclassics At Small Fixed λNmentioning

confidence: 78%

“…Another direction to explore, concerns Wilson-Fisher fixed points in models with non-abelian symmetry, like the O(n) model. That will allow to study the patterns of symmetry breaking induced by the choice of the Cartan charges, again illuminating the more general, but abstract, work in refs [7,20,21] While most of the above are low hanging fruits, there are also structural questions whose study is possibly more technically involved. One concerns the spectrum of nearby operators with the same charge.…”

Section: Discussionmentioning

confidence: 97%

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The epsilon expansion meets semiclassics

Badel

Cuomo

Monin

et al. 2019

J. High Energ. Phys.

159

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We study the scaling dimension ∆ φ n of the operator φ n where φ is the fundamental complex field of the U (1) model at the Wilson-Fisher fixed point in d = 4 − ε. Even for a perturbatively small fixed point coupling λ * , standard perturbation theory breaks down for sufficiently large λ * n. Treating λ * n as fixed for small λ * we show that ∆ φ n can be successfully computed through a semiclassical expansion around a non-trivial trajectory, resulting in We explicitly compute the first two orders in the expansion, ∆ −1 (λ * n) and ∆ 0 (λ * n). The result, when expanded at small λ * n, perfectly agrees with all available diagrammatic computations. The asymptotic at large λ * n reproduces instead the systematic large charge expansion, recently derived in CFT. Comparison with Monte Carlo simulations in d = 3 is compatible with the obvious limitations of taking ε = 1, but encouraging.

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Section: Semiclassics At Small Fixed λNmentioning

confidence: 78%

Section: Discussionmentioning

confidence: 97%

The epsilon expansion meets semiclassics

Badel

Cuomo

Monin

et al. 2019

J. High Energ. Phys.

159

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“…One can study two-point functions of powers O n ∆ of the generator, and use analytic methods to estimate the behavior of the two-point function when the total R-charge J = n∆ of the operator insertion O n ∆ is large. In [3][4][5] we used a supersymmetric version of the previously developed large-charge expansion 2 [28][29][30][31][32][33][34][35][36][37][38][39][40] (see [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60] for more recent developments) to determine the leading behavior of the correlation function at large n, and then used supersymmetric recursion relations [61][62][63] to derive the higher 1 n corrections from the leading terms. All this analysis uses only large J as a control parameter; the analysis does not require any weak-coupling limit of a marginal parameter of the CFT, or for that matter any marginal parameter at all.…”

Section: Introductionmentioning

confidence: 99%

Large R-charge EFT correlators in N=2 SQCD

Hellerman,

Orlando

2021

Preprint

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We consider large-R-charge Coulomb branch correlation functions in N = 2 superconformal QCD in D=4 dimensions, with gauge group G = SU (2) and N F = 4 hypermultiplets in the fundamental representation. Using information from supersymmetric recursion relations, S−duality, and matching of EFT parameters with the doublescaling limit, we give an exact formula for the massless Coulomb branch EFT contribution to the correlation function two-point functions of the n th power of the chiral ring generator, G τ ] , with A[τ ] and B[τ ] given as explicit functions of the coupling constant τ in closed form. We note the precise agreement of the EFT formula with supersymmetric localization even at low values of n, and discuss aspects of the post-EFT remainder contributed by the macroscopic virtual propagation of massive particles.

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“…This is the case for free massless theories and N = 2 superconformal field theories, where the large R-charge expansion is organized differently [75,76,77]. In [78,79] the possibility of a semiclassical but inhomogeneous phase in the O(4) model was also explored.…”

Section: Discussionmentioning

confidence: 99%

Superfluids, vortices and spinning charged operators in 4d CFT

Cuomo

2020

J. High Energ. Phys.

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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.

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Observables in inhomogeneous ground states at large global charge

Cited by 13 publications

References 35 publications

The epsilon expansion meets semiclassics

The epsilon expansion meets semiclassics

Large R-charge EFT correlators in N=2 SQCD

Superfluids, vortices and spinning charged operators in 4d CFT

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