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 class of effective field theories encompasses instances of helical superfluids and meta-fluids, 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.
A pair of complex-conjugate fixed points that lie close to the real axis generates a large mass hierarchy in the real renormalization group flow that passes in between them. We show that pairs of complex fixed points that are close to the real axis a
nd to one another generate multiple hierarchies, some of which can be parametrically enhanced. We illustrate this effect at weak coupling with field-theory examples, and at strong coupling using holography. We also construct complex flows between complex fixed points, including flows that violate the $c$-theorem.
Low-energy dynamics of many-body fracton excitations necessary to describe topological defects should be governed by a novel type of hydrodynamic theory. We use a Poisson bracket approach to systematically derive hydrodynamic equations from conservat
ion laws of scalar theories with fracton excitations. We study two classes of theories. In the first class we introduce a general action for a scalar with a shift symmetry linear in the spatial coordinates, while the second class serves as a toy model for disclinations and dislocations propagating along the Burgers vector. We apply our construction to study hydrodynamic fluctuations around equilibrium states and derive the dispersion relations of hydrodynamic modes.
Energy conditions, especially the null energy condition (NEC), are generically imposed on solutions to retain a physically sensible classical field theory and they also play an important role in the AdS/CFT duality. Using this duality, we study non-t
rivially deformed strongly coupled quantum field theories at large-$N_c$. The corresponding dual classical gravity constructions entail the use of radially non-monotonic D-brane distributions. The gravity backgrounds are supersymmetric and hence perturbatively stable, and do not possess curvature singularities. There are no short-cuts through the bulk spacetime for signal propagation which assures that the field theory duals are causal. Nevertheless, some of our solutions violate the NEC in the gravity dual. In these cases the non-monotonicity of the D-brane distributions is reflected in the properties of the renormalization group flow: none of the $c$-functions proposed in the literature are monotonic. This further suggests that the non-monotonic behavior of the $c$-functions within previously known anisotropic backgrounds does not originate from the breaking of Lorentz invariance. We surmise that NEC violations induced by quantum corrections also need to be considered in holographic duals, but can be studied already at the classical level.
We investigate first order phase transitions in a holographic setting of five-dimensional Einstein gravity coupled to a scalar field, constructing phase diagrams of the dual field theory at finite temperature. We scan over the two-dimensional paramet
er space of a simple bottom-up model and map out important quantities for the phase transition: the region where first order phase transitions take place; the latent heat, the transition strength parameter $alpha$, and the stiffness. We find that $alpha$ is generically in the range 0.1 to 0.3, and is strongly correlated with the stiffness (the square of the sound speed in a barotropic fluid). Using the LISA Cosmology Working Group gravitational wave power spectrum model corrected for kinetic energy suppression at large $alpha$ and non-conformal stiffness, we outline the observational prospects at the future space-based detectors LISA and TianQin. A TeV-scale hidden sector with a phase transition described by the model could be observable at both detectors.
A heavy quark moving through a strongly coupled deconfined plasma has a holographic dual description as a string moving in a black brane geometry. We apply the holographic Wilsonian renormalization method to derive a holographic effective string acti
on dual to the heavy quark. The effective action only depends on the geometry between the black brane horizon and a cutoff localized in the radial direction, corresponding to the IR of the dual theory. We derive RG flow equations for the coefficients in the effective action and show that the force acting on the heavy quark is independent of the position of the cutoff. All the information about the UV is hidden in integration constants of the RG flow equations. This type of approach could be used to improve semi-holographic models where the UV is described by perturbative QCD and the IR by a holographic model.
We present a study of Hall transport in semi-Dirac critical phases. The construction is based on a covariant formulation of relativistic systems with spatial anisotropy. Geometric data together with external electromagnetic fields is used to devise a
n expansion procedure that leads to a low-energy effective action consistent with the discrete $PT$ symmetry that we impose. We use the action to discuss terms contributing to the Hall transport and extract the coefficients. We also discuss the associated scaling symmetry.
We study a paradigmatic model in field theory where a global $U(1)$ and scale symmetries are jointly and spontaneously broken. At zero density the model has a non-compact flat direction, which at finite density needs to be slightly lifted. The result
ing low-energy spectrum is composed by a standard gapless $U(1)$ Nambu-Goldstone mode and a light dilaton whose gap is determined by the chemical potential and corrected by the couplings. Even though $U(1)$ and scale symmetries commute, there is a mixing between the $U(1)$ 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.
Motivated by the possible presence of deconfined quark matter in neutron stars and their mergers and the important role of transport phenomena in these systems, we perform the first-ever systematic study of different viscosities and conductivities of
dense quark matter using the gauge/gravity duality. Utilizing the V-QCD model, we arrive at results that are in qualitative disagreement with the predictions of perturbation theory, which highlights the differing transport properties of the system at weak and strong coupling and calls for caution in the use of the perturbative results in neutron-star applications.
The low-energy effective theory description of a confining theory, such as QCD, is constructed including local interactions between hadrons organized in a derivative expansion. This kind of approach also applies more generically to theories with a ma
ss gap, once the relevant low energy degrees of freedom are identified. The strength of local interactions in the effective theory is determined by the low momentum expansion of scattering amplitudes, with the scattering length capturing the leading order. We compute the main contribution to the scattering length between two spin-zero particles in strongly coupled theories using the gauge/gravity duality. We study two different theories with a mass gap: a massive deformation of ${cal N}=4$ super Yang-Mills theory (${cal N}=1^*$) and a non-supersymmetric five-dimensional theory compactified on a circle. These cases have a different realization of the mass gap in the dual gravity description: the former is the well-known GPPZ singular solution and the latter a smooth $AdS_6$ soliton geometry. Despite disparate gravity duals, we find that the scattering lengths have strikingly similar functional dependences on the masses of the particles and on the conformal dimension of the operators that create them. This evinces universal behavior in the effective description of gapped strongly coupled theories beyond what is expected from symmetry considerations alone.
