Rainbow Nambu-Goldstone Modes under a Shear Flow

Minami, Yuki; Nakano, Hiroyoshi; Hidaka, Yoshimasa

doi:10.1103/physrevlett.126.141601

Cited by 6 publications

(3 citation statements)

References 35 publications

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“…Despite symmetries and NGMs are an old subject, there are still several open questions in particular when dissipative/open systems or out-of equilibrium setups are considered, e.g. [13][14][15], or non "standard" symmetries are spontaneously broken, e.g. [16].…”

Section: Jhep12(2022)113mentioning

confidence: 99%

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Pion dynamics in a soft-wall AdS-QCD model

Cao

Baggioli

Liu

et al. 2022

J. High Energ. Phys.

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Pseudo-Goldstone modes appear in many physical systems and display robust universal features. First, their mass m obeys the so-called Gell-Mann-Oakes-Renner (GMOR) relation f2m2 = $$ H\overline{\sigma} $$ H σ ¯ , with f the Goldstone stiffness, H the explicit breaking scale and $$ \overline{\sigma} $$ σ ¯ the spontaneous condensate. More recently, it has been shown that their damping Ω is constrained to follow the relation Ω = m2Dφ, where Dφ is the Goldstone diffusivity in the purely spontaneous phase. Pions are the most paradigmatic example of pseudo-Goldstone modes and they are related to chiral symmetry breaking in QCD. In this work, we consider a bottom-up soft-wall AdS-QCD model with broken SU(2)L × SU(2)R symmetry and we study the nature of the associated pseudo-Goldstone modes — the pions. In particular, we perform a detailed investigation of their dispersion relation in presence of dissipation, of the role of the explicit breaking induced by the quark masses and of the dynamics near the critical point. Taking advantage of the microscopic information provided by the holographic model, we give quantitative predictions for all the coefficients appearing in the effective description. In particular, we estimate the finite temperature behavior of the kinetic parameter $$ \mathfrak{r} $$ r 2 defined as the ratio between the Goldstone diffusivity Dφ and the pion attenuation constant DA. Interestingly, we observe important deviations from the value $$ \mathfrak{r} $$ r 2 = 3/4 computed in chiral perturbation theory in the limit of zero temperature.

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Section: Jhep12(2022)113mentioning

confidence: 99%

“…3.5 × 10 to the critical point T ≈ T c , {D ϕ (T = 163MeV) = 0.7269(Gev −1 ) , D Q (T = 163MeV) = 0.6815(Gev −1 )}. 15 We then move to the discussion of the pion velocity and attenuation constant, v 2 0 , D A (where the subfix 0 indicates the chiral limit). According to the definition of the sound velocity in eq.…”

Section: Jhep12(2022)113mentioning

confidence: 99%

Pion dynamics in a soft-wall AdS-QCD model

Cao

Baggioli

Liu

et al. 2022

J. High Energ. Phys.

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“…The behavior contrasts with equilibrium systems, for which the correlation length remains microscopic except near critical points. Another example of anomalous fluctuations is that external flow strongly suppresses long-wavelength fluctuations associated with equilibrium phase transitions, changing the universality class of critical phenomena [6][7][8][9][10][11][12][13]. The suppression of fluctuations is also observed in the polar phase of active matter [14][15][16][17][18][19].…”

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confidence: 99%

Emergence of surface long-range order under uniform shear flow

Nakano¹,

Minami²,

Haga³

et al. 2021

Preprint

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We study the two-dimensional surface long-range order in a non-equilibrium steady state under shear flow using the three-dimensional conserved O(N ) model. Whereas the correlation on the surface is enhanced by increasing interactions within the surface, the long-range order cannot be realized at equilibrium because of divergent thermal fluctuations associated with the low dimensionality of the surface. Here, the shear flow is applied parallel to the surface, on which the flow is set to zero. Despite the shear flow not affecting the order parameter on the surface directly, the fluctuations at the surface are strongly suppressed by the flow away from the surface, leading to the surface long-range order. We demonstrate these results through an exact analysis in the large-N limit, where non-linear fluctuations are self-consistently treated.

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The Schwinger-Keldysh coset construction

Akyuz,

Goon,

Penco

2024

J. High Energ. Phys.

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The coset construction is a tool for systematically building low energy effective actions for Nambu-Goldstone modes. This technique is typically used to compute time-ordered correlators appropriate for S-matrix computations for systems in their ground state. In this paper, we extend this technique to the Schwinger-Keldysh formalism, which enables one to calculate a wider variety of correlators and applies also to systems in a mixed state. We focus our attention on internal symmetries and demonstrate that, after identifying the appropriate symmetry breaking pattern, Schwinger-Keldysh effective actions for Nambu-Goldstone modes can be constructed using the standard rules of the coset construction. Particular emphasis is placed on the thermal state and ensuring that correlators satisfy the KMS relation. We also discuss explicitly the power counting scheme underlying our effective actions. We comment on the similarities and differences between our approach and others that have previously appeared in the literature. In particular, our prescription does not require the introduction of additional “diffusive” symmetries and retains the full non-linear structure generated by the coset construction. We conclude with a series of explicit examples, including a computation of the finite-temperature two-point functions of conserved spin currents in non-relativistic paramagnets, antiferromagnets, and ferromagnets. Along the way, we also clarify the discrete symmetries that set antiferromagnets apart from ferromagnets, and point out that the dynamical KMS symmetry must be implemented in different ways in these two systems.

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Rainbow Nambu-Goldstone Modes under a Shear Flow

Cited by 6 publications

References 35 publications

Pion dynamics in a soft-wall AdS-QCD model

Pion dynamics in a soft-wall AdS-QCD model

Emergence of surface long-range order under uniform shear flow

The Schwinger-Keldysh coset construction

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