<p>Fractonic matter with dipole symmetry can be coupled to a two-index symmetric tensor gauge field. In this work, we show that this symmetric tensor field, along with other related generalized Maxwell theories, can be consistently coupled to curved backgrounds in a covariant and gauge-invariant way by reformulating dipole symmetry using conventional vector gauge fields. We identify a family of curved geometries where global dipole symmetry is preserved and derive energy-momentum conservation laws as Ward identities associated with background diffeomorphisms. Our results pave the way for future extensions, including generalizations to higher-order multipole theories.</p>

Spain

Evangelos Afxonidis

Germany

Alessio Caddeo

Carlos Hoyos

Daniele Musso

Fracton gauge theories in curved spacetimes

We study the stability of fracton gravity, a variant of linearized gravity where the gauge symmetry is restricted to longitudinal diffeomorphisms. These transformations can be connected to a spacetime generalization of dipole symmetry, hence the tag fracton. We find that fracton gravity features an instability in the spin-1 sector corresponding to solutions with growing amplitude. This dynamical instability can be removed by tuning the couplings of the theory. Nonetheless, the Hamiltonian for the spin-1 modes remains always unbounded from below when evaluated on the classical solutions. We find no other sources of instability in the spin-2 or spin-0 sectors. We analyze in detail the canonical formulation and the constraints arguing that neither auxiliary fields nor gauge-fixing conditions can be employed to remove the problematic vector modes or stabilize them.

Analysis of fracton-gravity stability

Dipole charge conservation forces isolated charges to be immobile fractons. These couple naturally to spatial two-index symmetric tensor gauge fields that resemble a spatial metric. We propose a spacetime Lorentz-covariant version of dipole symmetry and study the theory of the associated gauge fields. In the presence of a suitable background field, these contain a massive antisymmetric and a massless symmetric two-index tensors. The latter transforms only under longitudinal diffeomorphisms, making the massless sector similar to linearized gravity, but with additional modes of lower spin. We show that the theory can be consistently coupled to a curved background metric and study its possible interaction terms with itself and with matter. In addition, we construct a map between solutions of linearized gravity in Kerr-Schild form and solutions of fracton gravity coupled to matter.

Fracton gravity from spacetime dipole symmetry

We study the concomitant breaking of spatial translations and dilatations in Ginzburg-Landau-like models, where the dynamics responsible for the symmetry breaking is described by an effective Mexican hat potential for spatial gradients. We show that there are fractonic modes with either subdimensional propagation or no propagation altogether, namely, immobility. Such a class of effective field theories encompasses instances of helical superfluids and metafluids, where fractons can be connected to an emergent symmetry under higher-moment charges, leading in turns to the trivialization of some elastic coefficients. The introduction of a finite-charge density alters the mobility properties of fractons and leads to a competition between the chemical potential and the superfluid velocity in determining the gap of the dilaton. The mobility of fractons can also be altered at zero density upon considering additional higher-derivative terms.

Belgium

Riccardo Argurio

Daniel Naegels

Fractons in effective field theories for spontaneously broken translations

We study a paradigmatic model in field theory where a global <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> 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 <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> Nambu-Goldstone mode and a light dilaton whose gap is determined by the chemical potential and corrected by the couplings. Even though <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> and scale symmetries commute, there is a mixing between the <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> 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.

Gapped dilatons in scale invariant superfluids

We study a massive real scalar field that breaks translation symmetry dynamically. Higher-gradient terms favor modulated configurations, and neither finite density nor temperature are needed. In the broken phase, the energy density depends on the spatial position and the linear fluctuations show phononic dispersion. We then study a related massless scalar model where the modulated vacua also break the field shift symmetry and give rise to an additional Nambu-Goldstone mode, the shifton. We discuss the independence of the shifton and the phonon and draw an analogy to rotons in superfluids. Proceeding from first principles, we reobtain and generalize some standard results for one-dimensional lattices. Eventually, we prove stability against geometric deformations extending existing analyses for elastic media to the higher-derivative cases.

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

We study a holographic model where translations are both spontaneously and explicitly broken, leading to the presence of (pseudo)-phonons in the spectrum. The weak explicit breaking is due to two independent mechanisms: a small source for the condensate itself and additional linearly space-dependent marginal operators. The low energy dynamics of the model is described by Wigner crystal hydrodynamics. In absence of a source for the condensate, the phonons remain gapless, but momentum is relaxed. Turning on a source for the condensate damps and pins the phonons. Finally, we verify that the universal relation between the phonon damping rate, mass and diffusivity reported in [1] continues to hold in this model for weak enough explicit breaking.

Italy

Andrea Amoretti

France

Daniel Areán

Blaise Goutéraux

Gapless and gapped holographic phonons

We study the emergence of Nambu–Goldstone modes due to broken translation symmetry in field theory. Purely spontaneous breaking yields a massless phonon which develops a mass upon introducing a perturbative explicit breaking. The pseudo-phonon mass agrees with Gell Mann-Oakes-Renner relations. We analyze the simplest possible theories featuring gradient Mexican hats and describing space-dependent order parameters. We comment on homogeneous translation breaking and the connections with holographic Q-lattices.

Simplest phonons and pseudo-phonons in field theory

We describe a strongly coupled layered system in 3+1 dimensions by means of a top-down D-brane construction. Adjoint matter is encoded in a large-N  c  stack of D3-branes, while fundamental matter is confined to (2 + 1)-dimensional defects introduced by a large-N  f  stack of smeared D5-branes. To the anisotropic Lifshitz-like background geometry, we add a single flavor D7-brane treated in the probe limit. Such bulk setup corresponds to a partially quenched approximation for the dual field theory. The holographic model sheds light on the anisotropic physics induced by the layered structure, allowing one to disentangle flavor physics along and orthogonal to the layers as well as identifying distinct scaling laws for various dynamical quantities. We study the thermodynamics and the fluctuation spectrum with varying valence quark mass or baryon chemical potential. We also focus on the density wave propagation in both the hydrodynamic and collisionless regimes where analytic methods complement the numerics, while the latter provides the only resource to address the intermediate transition regime.

Sweden

Ulf Gran

Finland

Niko Jokela

Alfonso Ramallo

Marcus Tornsö

Holographic fundamental matter in multilayered media

In this Letter, we uncover a universal relaxation mechanism of pinned density waves, combining gauge-gravity duality and effective field theory techniques. Upon breaking translations spontaneously, new gapless collective modes emerge, the Nambu-Goldstone bosons of broken translations. When translations are also weakly broken (e.g., by disorder or lattice effects), these phonons are pinned with a mass <math><mi>m</mi></math> and damped at a rate <math><mi>Ω</mi></math>, which we explicitly compute. This contribution to <math><mi>Ω</mi></math> is distinct from that of topological defects. We show that <math><mi>Ω</mi><mo>≃</mo><mi>G</mi><msup><mi>m</mi><mn>2</mn></msup><mi>Ξ</mi></math>, where <math><mi>G</mi></math> is the shear modulus and <math><mi>Ξ</mi></math> is related to a diffusivity of the purely spontaneous state. This result follows from the smallness of the bulk and shear moduli, as would be the case in a phase with fluctuating translational order. At low temperatures, the collective modes relax quickly into the heat current, so that late time transport is dominated by the thermal diffusivity. In this regime, the resistivity in our model is linear in temperature and the ac conductivity displays a significant rearranging of the degrees of freedom, as spectral weight is shifted from an off-axis, pinning peak to a Drude-like peak. These results could shed light on transport properties in cuprate high <math><msub><mi>T</mi><mi>c</mi></msub></math> superconductors, where quantum critical behavior and translational order occur over large parts of the phase diagram and transport shows qualitatively similar features.