Symmetries and currents of the ideal and unitary Fermi gases

Bekaert, Xavier; Meunier, Elisa; Moroz, Sergej

doi:10.1007/jhep02(2012)113

Cited by 22 publications

(25 citation statements)

References 91 publications

(370 reference statements)

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“…Unfortunately, non-relativistic conformal invariance seems to have little to say about the OPE in the physically important case of operators with vanishing particle number, for example conserved currents and the stress tensor. The reason is that the Hilbert space interpretation of operators in the oscillator frame, which played a crucial role in our analysis, breaks down in the sector of operators with N O = 0, as explained in [49]. However, our results open the possibility of constraining the charged sector of NRCFTs, i.e.…”

Section: Discussionmentioning

confidence: 84%

“…Several explicit examples, analyzed in section 4.2, provide consistency checks of our results. Unfortunately, our general results only apply in the sector of operators with N O = 0, since the decomposition of operators in terms of primaries and descendants, which is crucial to our analysis, is known to break down for the case N O = 0, see [49].…”

Section: Jhep12(2015)048mentioning

confidence: 99%

“…It is important to note that the representation structure just described only makes sense for operators with nonzero particle number [49,55]. In the sector with N O = 0, the Galilean algebra implies [K i , P j ] = 0, and the decomposition of operators into primaries and JHEP12(2015)048 descendants breaks down: in particular, if O(0) is a primary operator, so is the descendant [P i , O(0)].…”

Section: Jhep12(2015)048mentioning

confidence: 99%

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OPE convergence in non-relativistic conformal field theories

Goldberger

Khandker

Prabhu

2015

J. High Energ. Phys.

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Motivated by applications to the study of ultracold atomic gases near the unitarity limit, we investigate the structure of the operator product expansion (OPE) in non-relativistic conformal field theories (NRCFTs). The main tool used in our analysis is the representation theory of charged (i.e. non-zero particle number) operators in the NR-CFT, in particular the mapping between operators and states in a non-relativistic "radial quantization" Hilbert space. Our results include: a determination of the OPE coefficients of descendant operators in terms of those of the underlying primary state, a demonstration of convergence of the (imaginary time) OPE in certain kinematic limits, and an estimate of the decay rate of the OPE tail inside matrix elements which, as in relativistic CFTs, depends exponentially on operator dimensions. To illustrate our results we consider several examples, including a strongly interacting field theory of bosons tuned to the unitarity limit, as well as a class of holographic models. Given the similarity with known statements about the OPE in SO(2, d) invariant field theories, our results suggest the existence of a bootstrap approach to constraining NRCFTs, with applications to bound state spectra and interactions. We briefly comment on a possible implementation of this non-relativistic conformal bootstrap program.

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Section: Discussionmentioning

confidence: 84%

Section: Jhep12(2015)048mentioning

confidence: 99%

Section: Jhep12(2015)048mentioning

confidence: 99%

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OPE convergence in non-relativistic conformal field theories

Goldberger

Khandker

Prabhu

2015

J. High Energ. Phys.

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“…The SO(D − 1) isotropy of the background implies that g xy will not couple to any other modes. We hence write the perturbation to the metric as 37) and find the differential equation governing h xy . We do this computation in appendix B, and here quote the leading order answer (at finite Ω):…”

Section: Viscositymentioning

confidence: 99%

“…As Lifshitz invariance is a much weaker requirement than conformal invariance [37][38][39], it is not clear that holographic models can capture the dynamics of generic Lifshitz theories. Nonetheless, we will be able to demonstrate a generalization of (1.3) in at least one class of interacting Lifshitz theories, and although our specific results for A and B are not generic, we expect that the qualitative features of this model are more robust.…”

Section: Bulk Modelmentioning

confidence: 99%

Quantum critical response: from conformal perturbation theory to holography

Lucas¹,

Sierens²,

Witczak-Krempa³

2017

J. High Energ. Phys.

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We discuss dynamical response functions near quantum critical points, allowing for both a finite temperature and detuning by a relevant operator. When the quantum critical point is described by a conformal field theory (CFT), conformal perturbation theory and the operator product expansion can be used to fix the first few leading terms at high frequencies. Knowledge of the high frequency response allows us then to derive nonperturbative sum rules. We show, via explicit computations, how holography recovers the general results of conformal field theory, and the associated sum rules, for any holographic field theory with a conformal UV completion -regardless of any possible new ordering and/or scaling physics in the IR. We numerically obtain holographic response functions at all frequencies, allowing us to probe the breakdown of the asymptotic high-frequency regime. Finally, we show that high frequency response functions in holographic Lifshitz theories are quite similar to their conformal counterparts, even though they are not strongly constrained by symmetry.

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Higher-Spin Theory and Space-Time Metamorphoses

Vasiliev

2014

Lecture Notes in Physics

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Introductory lectures on higher-spin gauge theory given at 7 Aegean workshop on non-Einstein theories of gravity. The emphasis is on qualitative features of the higher-spin gauge theory and peculiarities of its space-time interpretation. In particular, it is explained that Riemannian geometry cannot play a fundamental role in the higher-spin gauge theory. The higher-spin symmetries are argued to occur at ultra high energy scales beyond the Planck scale. This suggests that the higher-spin gauge theory can help to understand Quantum Gravity. Various types of higher-spin dualities are briefly discussed.Comment: 37 pages, no figures; V2: references adde

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Symmetries and currents of the ideal and unitary Fermi gases

Cited by 22 publications

References 91 publications

OPE convergence in non-relativistic conformal field theories

OPE convergence in non-relativistic conformal field theories

Quantum critical response: from conformal perturbation theory to holography

Higher-Spin Theory and Space-Time Metamorphoses

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