Independent Goldstone modes for translations and shift symmetry from a real modulated scalar

Musso, Daniele; Naegels, Daniel

doi:10.1103/physrevd.101.045016

Cited by 13 publications

(10 citation statements)

References 56 publications

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“…The standard formulation of spontaneous symmetry breaking (think, for example, about superconductivity) is done in terms of Ginzburg-Landau theory and the well-known double-well potential [39]. Despite attempts of this kind have been pursued for spacetime symmetries and phonons [40][41][42][43], the most successful framework in this case [44] appears slightly different. The main idea is rather simple.…”

Section: Effective Field Theories For Solids and Fluidsmentioning

confidence: 99%

Holographic axion model: A simple gravitational tool for quantum matter

Baggioli

Kim

et al. 2021

Sci. China Phys. Mech. Astron.

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This is a complete and exhaustive review on the so-called holographic axion model-a bottom-up holographic system characterized by the presence of a set of shift symmetric scalar bulk fields whose profiles are taken to be linear in the spatial coordinates. This simple model implements the breaking of translational invariance of the dual field theory by retaining the homogeneity of the background geometry and therefore allowing for controllable and fast computations. The usages of this model are very vast and they are a proof of the spectacular versatility of the framework. In this review, we touch upon all the up-to-date aspects of this model from its connection with massive gravity and effective field theories, to its role in modeling momentum dissipation and elastic properties ending with all the phenomenological features and its hydrodynamic description. In summary, this is a complete guide to one of the most used models in Applied Holography and a must-read for any researcher entering this field.

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Section: Effective Field Theories For Solids and Fluidsmentioning

confidence: 99%

Holographic axion model: A simple gravitational tool for quantum matter

Baggioli

Kim

et al. 2021

Sci. China Phys. Mech. Astron.

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“…The relevance of the question is threefold: it relates to the counting problem of NG modes for spacetime symmetries [9,16]; it concerns condensed matter systems where a critical scaling and the breaking of translations are intertwined 10 ; it provides insight regarding holographic models where scaling and translation symmetries are broken together [51][52][53][54]. 11 An example of inhomogeneous breaking of spatial translations in field theory was studied in [48]. Studying the cubic polynomial in ω 2 associated to (3.26), one can exclude the presence of complex solutions.…”

Section: Summary and Discussionmentioning

confidence: 99%

Gapped dilatons in scale invariant superfluids

et al. 2020

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We study a paradigmatic model in field theory where a global Uð1Þ and scale symmetries are jointly and spontaneously broken. At zero density the model has a noncompact flat direction, which at finite density needs to be slightly lifted. The resulting low-energy spectrum is composed by a standard gapless Uð1Þ Nambu-Goldstone mode and a light dilaton whose gap is determined by the chemical potential and corrected by the couplings. Even though Uð1Þ and scale symmetries commute, there is a mixing between the Uð1Þ Nambu-Goldstone and the dilaton that is crucial to recover the expected dynamics of a conformal fluid and leads to a phonon propagating at the speed of sound. The results rely solely on an accurate study of the Ward-Takahashi identities and are checked against standard fluctuation computations. We extend our results to a boosted superfluid, and comment the relevance of our findings to condensed matter applications.

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“…Of course, this should be qualified but it displays the tendency that even toy models are difficult theories. See for instance [99][100][101].…”

Section: Spacetime Symmetry Specificitiesmentioning

confidence: 99%

Goldstone Boson Physics and Effective Field Theories

Naegels¹

2022

Proceedings of Modave Summer School in Mathematical Physics — PoS(Modave2021)

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These lecture notes are based on a six-hour series of lectures given at the XVII Modave summer school in mathematical physics, aimed at Ph.D. students in high-energy theoretical physics.The manuscript starts by briefly stating Goldstone's theorem and emphasises the motivations behind Goldstone physics; the main asset being the universality of spontaneous symmetry breaking (SSB) which is the fundamental hypothesis of Goldstone's theorem. Once the different notions of SSB will be clarified/reviewed, Goldstone's theorem will be stated and proved. A prediction of this theorem is the existence of gapless particles, called Nambu-Goldstone modes (NG modes). From the discussion on Goldstone's results, some aspects of the NG modes will emerge. Besides to be gapless, they are systematically weakly coupled at low energy. Therefore, an effective field theory (EFT) building tool called "coset construction" will be presented to explicitly display these specific features of the NG modes. The coset construction suits our goal since it is mainly based on the symmetry realisation of the perturbed theory around the background inducing SSB. From the general obtained EFT, a counting rule for the NG modes will be derived. The limitations of this rule as well as the still ongoing generalisation will be discussed (e.g. spacetime symmetry breaking). The tools developed during this course will be illustrated with a concrete example in physics: ferromagnetism. The notes end with a brief state of the art of Goldstone physics. This provides some directions into which the interested reader could investigate to expand his knowledge on the subject. N.B. :No prerequisites are required beside the standard courses of a Master in theoretical physics.

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Independent Goldstone modes for translations and shift symmetry from a real modulated scalar

Cited by 13 publications

References 56 publications

Holographic axion model: A simple gravitational tool for quantum matter

Holographic axion model: A simple gravitational tool for quantum matter

Gapped dilatons in scale invariant superfluids

Goldstone Boson Physics and Effective Field Theories

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