Spontaneous breaking of non-relativistic scale symmetry

Arav, Igal; Hason, Itamar; Oz, Yaron

doi:10.1007/jhep10(2017)063

Cited by 12 publications

(10 citation statements)

References 45 publications

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“…As also pointed out in [26], if the U(1) of particle number is broken then, as a consequence of the algebraic relation,…”

Section: The Missing Goldstonesmentioning

confidence: 96%

“…As mentioned in the introduction, consequences of spontaneous breaking of conformal invariance in non-relativistic systems is unique as the non-relativistic kinetic term for the dilaton appears to be in tension with boost invariance [26]. As such, we will study systems for which the broken symmetries are dilatations (D), special conformal transformations (C) and boosts (K i ).…”

Section: The Stability Of Goldstone Boson Mass Under Renormalizationmentioning

confidence: 99%

“…The authors of [26] point out that given that the dilaton σ transforms under Galilean boosts as σ(x, t) → σ(x − vt, t) (1.10)…”

Section: The Missing Goldstonesmentioning

confidence: 99%

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Symmetry realization via a dynamical inverse Higgs mechanism

Rothstein

Shrivastava

2018

J. High Energ. Phys.

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Abstract:The Ward identities associated with spontaneously broken symmetries can be saturated by Goldstone bosons. However, when space-time symmetries are broken, the number of Goldstone bosons necessary to non-linearly realize the symmetry can be less than the number of broken generators. The loss of Goldstones may be due to a redundancy or the generation of a gap. In either case the associated Goldstone may be removed from the spectrum. This phenomena is called an Inverse Higgs Mechanism (IHM) and its appearance has a well defined mathematical condition. However, there are cases when a Goldstone boson associated with a broken generator does not appear in the low energy theory despite the lack of the existence of an associated IHM. In this paper we will show that in such cases the relevant broken symmetry can be realized, without the aid of an associated Goldstone, if there exists a proper set of operator constraints, which we call a Dynamical Inverse Higgs Mechanism (DIHM). We consider the spontaneous breaking of boosts, rotations and conformal transformations in the context of Fermi liquids, finding three possible paths to symmetry realization: pure Goldstones, no Goldstones and DIHM, or some mixture thereof. We show that in the two dimensional degenerate electron system the DIHM route is the only consistent way to realize spontaneously broken boosts and dilatations, while in three dimensions these symmetries could just as well be realized via the inclusion of non-derivatively coupled Goldstone bosons. We present the action, including the leading order non-linearities, for the rotational Goldstone (angulon), and discuss the constraint associated with the possible DIHM that would need to be imposed to remove it from the spectrum. Finally we discuss the conditions under which Goldstone bosons are non-derivatively coupled, a necessary condition for the existence of a Dynamical Inverse Higgs Constraint (DIHC), generalizing the results for Vishwanath and Wantanabe.

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“…As also pointed out in [26], if the U(1) of particle number is broken then, as a consequence of the algebraic relation,…”

Section: The Missing Goldstonesmentioning

confidence: 96%

Section: The Stability Of Goldstone Boson Mass Under Renormalizationmentioning

confidence: 99%

See 1 more Smart Citation

Symmetry realization via a dynamical inverse Higgs mechanism

Rothstein

Shrivastava

2018

J. High Energ. Phys.

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“…(11.2). It is known that the non-linearly realized Schrödinger symmetry forbids time derivatives in the kinetic term for π [158]. This should not be a source of concern, however, since our model should be thought of as a non-relativistic effective theory which ultimately admits some relativistic UV completion.…”

Section: Particle Model Buildingmentioning

confidence: 99%

Emergence of the mass discrepancy-acceleration relation from dark matter-baryon interactions

Famaey

Khoury

Penco

2018

J. Cosmol. Astropart. Phys.

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The observed tightness of the mass discrepancy-acceleration relation (MDAR) poses a finetuning challenge to current models of galaxy formation. We propose that this relation could arise from collisional interactions between baryons and dark matter (DM) particles, without the need for modification of gravity or ad hoc feedback processes. We assume that these interactions satisfy the following three conditions: (i) the relaxation time of DM particles is comparable to the dynamical time in disk galaxies; (ii) DM exchanges energy with baryons due to elastic collisions; (iii) the product between the baryon-DM cross section and the typical energy exchanged in a collision is inversely proportional to the DM number density. As a proof of principle, we present an example of a particle physics model that gives a DM-baryon cross section with the desired density and velocity dependence. For consistency with direct detection constraints, our DM particles must be either very light (m m b ) or very heavy (m m b ), corresponding respectively to heating and cooling of DM by baryons. In both cases, our mechanism applies and an equilibrium configuration can in principle be reached. In this exploratory paper, we focus on the heavy DM/cooling case because it is technically simpler, since the average energy exchanged turns out to be approximately constant throughout galaxies. Under these assumptions, we find that rotationally-supported disk galaxies could naturally settle to equilibrium configurations satisfying a MDAR at all radii without invoking finely tuned feedback processes. We also discuss issues related to the small scale clumpiness of baryons, as well as predictions for pressuresupported systems. We argue in particular that galaxy clusters do not follow the MDAR despite being DM-dominated because they have not reached their equilibrium configuration. Finally, we revisit existing phenomenological, astrophysical and cosmological constraints on baryon-DM interactions in light of the unusual density dependence of the cross section of DM particles.The presence of mass discrepancies from the scales of dwarf galaxies to the largest scales in the Universe is nowadays backed by a plethora of astronomical data. After first hints for these mass discrepancies about 85 years ago (e.g., [1,2]), the problem became manifest with the discovery of the asymptotic flatness of the rotation curves of disk galaxies [3][4][5]. Since then, numerous cosmological observations [6-9] have confirmed the need for missing mass, dubbed dark matter (DM), on larger scales. In the present-day standard ΛCDM cosmological model, the missing mass is made of cold dark matter (CDM) particles, which are non-relativistic at decoupling and interact with each other and with baryons almost exclusively through gravity. In this context, the fluid of DM particles can be assumed to obey the collisionless Boltzmann equation, which is the fundamental equation of Galactic Dynamics for stars and DM particles. In the present contribution, we argue that, in order to explain certain...

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“…Since these theories are intrinsically (d þ 1)-dimensional, the use of Newton-Cartan geometry is not a natural choice. It would also be interesting to understand the dispersion relation of Goldstone bosons, arising from spontaneous breaking of z ≠ 2 scale symmetry; the z ¼ 2 case has been studied in [43]. …”

Section: Discussionmentioning

confidence: 99%

Existence and construction of Galilean invariant z≠2 theories

Grinstein

Pal

2018

Phys. Rev. D

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We prove a no-go theorem for the construction of a Galilean boost invariant and z ≠ 2 anisotropic scale invariant field theory with a finite dimensional basis of fields. Two point correlators in such theories, we show, grow unboundedly with spatial separation. Correlators of theories with an infinite dimensional basis of fields, for example, labeled by a continuous parameter, do not necessarily exhibit this bad behavior. Hence, such theories behave effectively as if in one extra dimension. Embedding the symmetry algebra into the conformal algebra of one higher dimension also reveals the existence of an internal continuous parameter. Consideration of isometries shows that the nonrelativistic holographic picture assumes a canonical form, where the bulk gravitational theory lives in a space-time with one extra dimension. This can be contrasted with the original proposal by Balasubramanian and McGreevy, and by Son, where the metric of a (d þ 2)-dimensional space-time is proposed to be dual of a d-dimensional field theory. We provide explicit examples of theories living at fixed point with anisotropic scaling exponent z ¼ 2l lþ1 , l ∈ Z.

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Spontaneous breaking of non-relativistic scale symmetry

Cited by 12 publications

References 45 publications

Symmetry realization via a dynamical inverse Higgs mechanism

Symmetry realization via a dynamical inverse Higgs mechanism

Emergence of the mass discrepancy-acceleration relation from dark matter-baryon interactions

Existence and construction of Galilean invariant z≠2 theories

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