Are there Goldstone bosons in d≤z+1{d\leq z+1} ?

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 (quantum field theoretically) and yes (holographically). With field theory tools, we show that symmetry breaking is indeed prevented by large quantum fluctuations when $d\leq z+1$, 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.Comment: 18 pages. v2: a few clarifying comments added, matches published versio

Symmetry breaking in holographic theories with Lifshitz scaling

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 study 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.Comment: 39 pages, 3 figures. v2: a few clarifying comments added, matches published versio

A Note on Holographic Non-Relativistic Goldstone Bosons

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.Comment: 13+7 pages, no figures; v2: added clarification on vanishing chemical potential, version to appear in journa

Holographic Ward identities for symmetry breaking in two dimensions

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 current 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.Comment: 20 pages. v2 comments added. Version to appear in JHE

Gapped dilatons in scale invariant superfluids

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 noncompact flat direction, which at finite density needs to be slightly lifted. The resulting 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 applicationsR. A. and D. N. acknowledge support by IISNBelgium (convention 4.4503.15) and by the F. R. S.-FNRS under the “Excellence of Science" EOS be.h Project No. 30820817. R. A. is supported as a Research Director of the F. R. S.-FNRS (Belgium). C. H. has been partially supported by the Spanish Ministerio de Ciencia, Innovacion y Universidades Grant No. PGC2018-096894-B-100 and by the Principado de Asturias through Grant No. GRUPIN-IDI/2018/000174S

Perturbative and holographic study of symmetry breaking in non-relativistic theories

This thesis lies in the framework of the spontaneous symmetry breaking mechanism. When such a mechanism occurs, Goldstone's theorem predicts the existence of massless modes, called Nambu-Goldstone modes (NG modes). The current knowledge on NG modes is classified following the types of symmetries involved in the considered breaking pattern. Spacetime symmetries are the ones for which most of the analysis remains to be done. From a perturbative approach, we separately and concomitantly study the breaking of dilatation symmetry and of spatial translation symmetry. It allows us to comment on the present-day conjectures concerning the counting of NG modes associated to breaking patterns involving spacetime symmetries. Moreover, we get closer to standard laboratory conditions by investigating the situation in presence of a chemical potential. The considered Landau-Ginzburg's like models constitute plausible effective field theories to describe superfluids. The higher derivative terms required to spontaneously break translations lead to emergent subsystem symmetries. A connection between NG modes and fractonic modes, i.e. excitations with reduced mobility, is then made. Non-relativistic systems are less constrained by the symmetries compared to Lorentz invariant systems which make the former more general. Even for non-spacetime symmetries, some uncertainties on the physics of NG modes remain when dealing with non-relativistic models. One of them is the critical dimension of Minkowski spacetime under which no spontaneous symmetry breaking can occur. This dimension has been conjectured and we propose an explicit computation in order to attest this conjecture. However, through a holographic analysis, we discuss some way out for large N field theories. All along the dissertation, concrete future research perspectives on the above-mentioned discussions are provided.Cette thèse porte sur le mécanisme de la brisure spontanée de symétrie. Lorsqu’un tel mécanisme se produit, le théorème de Goldstone prédit l’existence de modes non-massifs, appelés modes de Nambu-Goldstone (modes NG). Nos connaissances actuelles sur les modes NG sont classifiées suivant le type de symétries impliquées dans le motif de brisure considéré. Les symétries d’espace-temps sont les symétries pour lesquelles la majorité de l’analyse reste encore à faire. A travers une approche perturbative, nous étudions séparément et de façon concomitante la brisure de la symétrie de dilatation et la brisure de la symétrie de translation spatiale. Cela nous permet de commenter les conjectures actuelles portant sur le comptage des modes NG associés au motif de brisure faisant intervenir des symétries d’espace-temps. De plus, nous nous rapprochons des conditions expérimentales en investiguant la situation en présence d’un potentiel chimique. Les modèles de type Landau-Ginzburg considérés constituent des théories effectives plausibles pour la description de superfluides. Les termes de dérivées supérieures nécessaires à la brisure des translations mènent à l’émergence de symétries de sous-systèmes. Un lien entre les modes NG et les modes fractoniques, c-à-d. des excitations à mobilité réduite, est alors établi.Les systèmes non-relativistes sont moins contraints par les symétries comparés aux systèmes invariants de Lorentz, ce qui rend les premiers plus généraux. Ainsi, même pour des symétries qui ne sont pas d’espace-temps, certaines incertitudes sur la physique des modes NG subsistent lorsque nous considérons des modèles non-relativistes. L’une d’entre elles est la dimension critique de l’espace-temps de Minkowski en-dessous de laquelle aucune brisure spontanée de symétrie ne peut se produire. Cette dimension a été conjecturée et nous proposons un calcul explicite en vue de valider cette conjecture. Cependant, à travers une analyse holographique, nous discutons d’une échappatoire concernant les théories de champs à grand N.Tout au long de ce travail, de futures perspectives concrètes de recherche portant sur les discussions mentionnées ci-dessus sont proposées.Doctorat en Sciencesinfo:eu-repo/semantics/nonPublishe

Goldstone Boson Physics and Effective Field Theories

These lecture notes are based on a six-hour series of lectures given at the XVII Modave summer school inmathematical physics, aimed at Ph.D. students in high-energy theoretical physics. The manuscript starts by briefly stating Goldstone's theorem and emphasises the motivations behind Goldstone physics; the main asset being the universality of spontaneous symmetry breaking (SSB) which is the fundamental hypothesis of Goldstone's theorem. Once the different notions of SSB will be clarified/reviewed, Goldstone's theorem will be stated and proved. A prediction of this theorem is the existence of gapless particles, called Nambu-Goldstone modes (NG modes). From the discussion on Goldstone's results, some aspects of the NG modes will emerge. Besides to be gapless, they are systematically weakly coupled at low energy. Therefore, an effective field theory (EFT) building tool called ''coset construction'' will be presented to explicitly display these specific features of the NG modes. The coset construction suits our goal since it is mainly based on the symmetry realisation of the perturbed theory around the background inducing SSB. From the general obtained EFT, a counting rule for the NG modes will be derived. The limitations of this rule as well as the still ongoing generalisation will be discussed (e.g. spacetime symmetry breaking). The tools developed during this course will be illustrated with a concrete example in physics: ferromagnetism. The notes end with a brief state of the art of Goldstone physics. This provides some directions into which the interested reader could investigate to expand his knowledge on the subject.N.B. No prerequisites are required beside the standard courses of a Master in theoretical physics.info:eu-repo/semantics/inPres

Fractons in effective field theories for spontaneously broken translations

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.Comment: 47 pages, 5 figures and 2 table

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

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.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Omeprazole and fundic gland polyps [13]

SCOPUS: le.jinfo:eu-repo/semantics/publishe