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.
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.
We study the viability of spontaneous breaking of continuous symmetries in theories with Lifshitz scaling, according to the number of space-time dimensions $d$ and the dynamical scaling $z$. Then, the answer to the question in the title is no (quantu
m field theoretically) and yes (holographically). With field theory tools, we show that symmetry breaking is indeed prevented by large quantum fluctuations when $dleq z+1$, as expected from scaling arguments. With holographic tools, on the other hand, we find nothing that prevents the existence of a vacuum expectation value. This difference is made possible by the large $N$ limit of holography. An important subtlety in this last framework is that in order to get a proper description of a conserved current, renormalization of the temporal mode of the bulk vector requires an alternative quantization. We also comment on the implications of turning on temperature.
We study holographically Lifshitz-scaling theories with broken symmetries. In order to do this, we set up a bulk action with a complex scalar and a massless vector on a background which consists in a Lifshitz metric and a massive vector. We first stu
dy separately the complex scalar and the massless vector, finding a similar pattern in the two-point functions that we can compute analytically. By coupling the probe complex scalar to the background massive vector we can construct probe actions that are more general than the usual Klein--Gordon action. Some of these actions have Galilean boost symmetry. Finally, in the presence of a symmetry breaking scalar profile in the bulk, we reproduce the expected Ward identities of a Lifshitz-scaling theory with a broken global continuous symmetry. In the spontaneous case, the latter imply the presence of a gapless mode, the Goldstone boson, which will have dispersion relations dictated by the Lifshitz scaling.
We investigate symmetry breaking in two-dimensional field theories which have a holographic gravity dual. Being at large N, the Coleman theorem does not hold and Goldstone bosons are expected. We consider the minimal setup to describe a conserved cur
rent and a charged operator, and we perform holographic renormalization in order to find the correct Ward identities describing symmetry breaking. This involves some subtleties related to the different boundary conditions that a vector can have in the three-dimensional bulk. We establish which is the correct prescription that yields, after renormalization, the same Ward identities as in higher dimensions.
We consider the interplay between explicit and spontaneous symmetry breaking in strongly coupled field theories. Some well-known statements, such as the Gell-Mann-Oakes-Renner relation, descend directly from the Ward identities and have thus a genera
l relevance. Such Ward identities are recovered in gauge/gravity dual setups through holographic renormalization. In a simple paradigmatic three dimensional toy-model, we find analytic expressions for the two-point correlators which match all the quantum field theoretical expectations. Moreover, we have access to the full spectrum, which is reminiscent of linear confinement.
We consider a holographic set-up where relativistic invariance is broken by a chemical potential, and a non-abelian internal symmetry is broken spontaneously. We use the tool of holographic renormalization in order to infer what can be learned purely
by analytic boundary considerations. We find that the expected Ward identities are correctly reproduced. In particular, we obtain the identity which implies the non-commutation of a pair of broken charges, which leads to the presence of Goldstone bosons with quadratic dispersion relations.
We investigate the collider signatures of the multiple goldstini scenario in the framework of gauge mediation. This class of models is characterized by a visible sector (e.g. the MSSM or any extension) coupled by gauge interactions to more than one S
USY breaking sector. The spectrum consists of a light gravitino LSP, behaving as a goldstino, and a number of neutral fermions (the pseudo-goldstini) with a mass between that of the LSP and that of the lightest particle of the observable sector (LOSP). We consider the two situations where the LOSP is either a gaugino-like neutralino or a stau and we assume only one pseudo-goldstino of a mass of O(100) GeV. The coupling of the LOSP to the pseudo-goldstino can be enhanced with respect to those of the gravitino giving rise to characteristic signatures. We show that the decay modes of the LOSP into a SM particle and a pseudo-goldstino can be significant. For both LOSP scenarios we analyze (pseudo)-goldstini production at colliders. Compared to standard gauge mediation the final state spectrum is softer and more structured.
