We discuss phases of gauge theories in the holographic context, and formulate a criterion for the existence of a Higgs phase, where the gauge redundancy is "spontaneously broken", in purely bulk language. This condition, the existence of a finite tension solitonic string representing a narrow magnetic flux tube, is necessary for a bulk theory to be interpreted as a Higgs phase of a boundary gauge theory. We demonstrate the existence of such solitons in both top-down and bottom-up examples of holographic theories. In particular, we numerically construct new solitonic solutions in AdS black hole background, for various values of the boundary gauge coupling, which are used to demonstrate that the bulk theory models a superconductor, rather than a superfluid. The criterion we find is expected to be useful in finding holographic duals of color superconducting phases of gauge theories at finite density.
We consider the holographic abelian Higgs model and show that, in the absence of the scale symmetry breaking effect, chiral symmetry breaking gives linear confinement where the slope is given by the value of the chiral condensation. The model can be considered either as the theory of superconductivity or as the axial sector of QCD depending on the interpretation of the charge. We also provided a few models with linear confinement.
The holographic approach to double diffractive Higgs production is presented for the AdS graviton/Pomeron. The goal is to provide a predictive phenomenology for the strong coupling expansion of QCD. This is the first step to set up the framework for the double diffractive Higgs production in anticipation of experimental observations at the LHC. Comparisons are made with the weak coupling approach based on the BFKL Pomeron models and soft Regge parameterizations.
In a recently proposed scenario for primordial inflation, where the Standard Model (SM) Higgs boson plays a role of the inflation field, an effective field theory (EFT) approach is the most convenient for working out the consequences of breaking of perturbative unitarity, caused by the strong coupling of the Higgs field to the Ricci scalar. The domain of validity of the EFT approach is given by the ultraviolet (UV) cutoff, which, roughly speaking, should always exceed the Hubble parameter in the course of inflation. On the other hand, applying the trusted principles of quantum gravity to a loc…
I review the holographic techniques used to efficiently study models with Gauge-Higgs Unification (GHU) in one extra dimension. The general features of GHU models in flat extra dimensions are then reviewed, emphasizing the aspects related to electroweak symmetry breaking. Two potentially realistic models, based on SU(3) and SO(5) electroweak gauge groups, respectively, are constructed.
We study collective excitations of cold (2+1)-dimensional fundamental matter living on a defect of the four-dimensional N=4 super Yang-Mills theory in the Higgs branch. This system is realized holographically as a D3-D5 brane intersection, in which the D5-brane is treated as a probe with a non-zero gauge flux across the internal part of its worldvolume. We study the holographic zero sound mode in the collisionless regime at low temperature and find a simple analytic result for its dispersion relation. We also find the diffusion constant of the system in the hydrodynamic regime at higher temper…
In the minimal composite Higgs model (MCHM), the size of the Higgs mass and vacuum expectation value is determined, via the Higgs potential, by the size of operators that violate the global SO(5) symmetry. In 5D holographic realisations of this model, this translates into the inclusion of brane localised operators. However, the inclusion of all such operators results in a large and under-constrained parameter space. In this paper we study the level of fine-tuning involved in such a parameter space, focusing on the MCHM${}_5$. It is demonstrated that the gauge contribution to the Higgs potentia…
We reassess employing the holographic technique to the description of 4D minimal composite Higgs model with $SO(5)\to SO(4)$ global symmetry breaking pattern. The particular 5D bottom-up holographic treatment is inspired by previous work in the context of QCD and it allows to study spin one and spin zero resonances. The resulting spectrum consists of the states transforming under the unbroken $SO(4)$ subgroup and those with quantum numbers in the $SO(5)/SO(4)$ coset. The spin one states are arranged in linear radial trajectories, and the states from the broken subgroup are generally heavier. T…
We study strongly-coupled, approximately scale-invariant gauge theories, which develop a mass gap in the infrared. We argue that a large number of fermion flavours is most suitable to provide an ultraviolet completion for the composite Higgs scenario. The holographic approach allows to describe the qualitative features of the non-perturbative dynamics in the Veneziano limit. We introduce new bottom-up holographic models, which incorporate the backreaction of flavour on the geometry, and show that this can correlate the mass gap to the scale of flavour-symmetry breaking. We compute the mass spe…
We study a 5D bottom-up holographic model that is expected to describe the dynamics of the minimal composite Higgs model characterized by a $SO(5)\to SO(4)$ global symmetry breaking pattern. We assume that the fundamental degrees of freedom are scalars transforming under some representation of $SO(5)$ and subject to some unspecified strong interactions. The holographic description presented here is inspired by previous studies performed in the context of QCD and it allows for the consideration of spin one and spin zero resonances. The resulting spectrum leads in a natural way to a variety of r…
We use holography to study (3+1)-dimensional N=4 supersymmetric Yang-Mills theory with gauge group SU(Nc), in the large-Nc and large-coupling limits, coupled to a single massless (n+1)-dimensional hypermultiplet in the fundamental representation of SU(Nc), with n=3,2,1. In particular, we study zero-temperature states with a nonzero baryon number charge density, which we call holographic matter. We demonstrate that a moduli space of such states exists in these theories, specifically a Higgs branch parameterized by the expectation values of scalar operators bilinear in the hypermultiplet scalars…
We introduce a scenario of lepton mixing in holographic composite Higgs models based on non-abelian discrete symmetries of the form G_f=X x Z_N, broken to Z_2 x Z_2 x Z_N in the elementary sector and to Z_N^(D) in the composite sector with Z_N^(D) being the diagonal subgroup of a Z_N contained in X and the external Z_N. By choosing X = Delta(96) or Delta(384), a non-vanishing theta_{13} of order 0.1 is naturally obtained. We apply our considerations to a 5D model in warped space for the particular cases of X = S_4, A_5, Delta(96) and Delta(384) and N=3 or 5. Lepton flavour violating processes …
We study leptons in holographic composite Higgs models, namely in models possibly admitting a weakly coupled description in terms of five-dimensional (5D) theories. We introduce two scenarios leading to Majorana or Dirac neutrinos, based on the non-abelian discrete group $S_4\times \Z_3$ which is responsible for nearly tri-bimaximal lepton mixing. The smallness of neutrino masses is naturally explained and normal/inverted mass ordering can be accommodated. We analyze two specific 5D gauge-Higgs unification models in warped space as concrete examples of our framework. Both models pass the curre…
We revisit the construction of the composite Higgs models in a context of the bottom-up holographic approach. The soft wall framework is under consideration imposing the translation of the $4D$ global symmetry breaking characteristic to the new strongly interacting sector in the $5D$ bulk. The focus stays on the minimal $SO(5)\to SO(4)$ breaking pattern. The $5D$ model has a specific form inspired by the effective models of QCD, representing a generalized sigma model coupled both to the composite resonances and to the SM gauge bosons. The latter are treated as external $4D$ sources and concept…
We find solutions of a gravity-Yang-Mills-Higgs theory in four dimensions that represent asymptotic anti-de Sitter charged black holes with partial/full gauge symmetry breaking. We then apply the AdS/CFT correspondence to study the strong coupling regime of a $2+1$ quantum field theory at temperature $T$ and finite chemical potential, which undergoes transitions to phases exhibiting the condensation of a composite charged vector operator below a critical temperature $T_c$, presumably describing $p+ip/p$-wave superconductors. In the case of $p+ip$-wave superconductors the transitions are always…
Within the context of top-down holography, we study a one-parameter family of regular background solutions of maximal gauged supergravity in seven dimensions, dimensionally reduced on a 2-torus. The dual, four-dimensional confining field theory realises the global (spontaneous as well as explicit) symmetry breaking pattern SO(5)->SO(4). We compute the complete mass spectrum for the fluctuations of the 128 bosonic degrees of freedom of the five-dimensional gravity theory, which correspond to scalar, pseudoscalar, vector, axial-vector, and tensor bound states of the dual field theory, and includ…
We investigate nonlinear extensions of the holographic soft wall model proposed by Karch, Katz, Son and Stephanov \cite{Karch:2006pv} with a positive quadratic dilaton. We consider a Higgs potential for the tachyonic field that brings a more natural realisation of chiral symmetry breaking in the infrared regime. Utilising the AdS/CFT dictionary and holographic renormalisation we find the chiral condensate as a function of the quark mass. The nonlinearity of the Higgs potential leads to a nonlinear relation between the chiral condensate and the quark mass. Solving the effective Schrödinger equa…
We continue our study of strongly-coupled, approximately scale-invariant gauge theories with a large number of flavours, which provide a suitable ultraviolet completion of the composite-Higgs scenario. We identify the requisite operators to realise partial compositeness of the Standard-Model fermions. In order to compute the spectrum of composite fermionic states, we extend the bottom-up holographic models, which we previously introduced to capture the main features of the non-perturbative dynamics in the Veneziano limit, by adding fermion fields in the bulk. We identify regions in parameter s…
The entanglement exhibits extremal or singular behavior near quantum critical points (QCPs) in many condensed matter models. These intriguing phenomena, however, still call for a widely accepted understanding. In this letter we study this issue in holographic framework. We investigate the connection between the holographic entanglement entropy (HEE) and the quantum phase transition (QPT) in a lattice-deformed Einstein-Maxwell-Dilaton theory. Novel backgrounds exhibiting metal-insulator transitions (MIT) have been constructed in which both metallic phase and insulating phase have vanishing entr…
Holographic screens are the generalization of the event horizon of a black hole in entropic force scheme, which are defined by setting Newton potential $ϕ$ constant, \textit{i. e.} $e^{2ϕ}=c=$const. By demonstrating that the integrated first law of thermodynamics is equivalent to the ($r-r$) component of Einstein equations, We strengthen the correspondence between thermodynamics and gravity. We show that there are not only the first law of thermodynamics, but also kinds of phase transitions of holographic screens. These phase transitions are characterized by the discontinuity of their heat cap…
We study the holographic entanglement entropy in metal/superconductor phase transition with exponential nonlinear electrodynamics (ENE) in four and five dimensional spacetimes. We find that the holographic entanglement entropy is powerful tool in studying the properties of the holographic phase transition. For the operator $\langle\mathcal{O}_{+}\rangle$, we observe that the entanglement entropy in 4-dimensional spacetime decreases in metal phase but changes non-monotonously in superconducting phase with the increase of the ENE parameter. Interestingly, the change of the entanglement entropy i…
We employ the variational method for the Sturm-Liouville eigenvalue problem to analytically study the phase transition between the holographic insulator and superconductor in the Gauss-Bonnet gravity. By investigating the s-wave and p-wave holographic insulator/superconductor models, we find that this analytic method is more effective to obtain the analytic results on the condensation and the critical phenomena in the AdS soliton background in Gauss-Bonnet gravity. Our analytic result can be used to back up the numerical computations in the AdS soliton with Gauss-Bonnet correction.
The phase transition of Reissner-Nordstrom AdS_4 interacting with a massive charged scalar field has been further revisited. We found exactly one stable and one unstable quasinormal mode regions for the scalar field. The two of them are separated by the first marginally stable solution.
We describe a numerical method to compute the action of Euclidean saddlepoints for the partition function of a two-dimensional holographic CFT on a Riemann surface of arbitrary genus, with constant curvature metric. We explicitly evaluate the action for the saddles for genus two and map out the phase structure of dominant bulk saddles in a two-dimensional subspace of the moduli space. We discuss spontaneous breaking of discrete symmetries, and show that the handlebody bulk saddles always dominate over certain non-handlebody solutions.
Applying the "Complexity=Action" conjecture, we study the holographic complexity close to crossover/phase transition in a holographic QCD model proposed by Gubser et al. This model can realize three types of phase transition, crossover or first and second order, depending on the parameters of the dilaton potential. The re-scaled late-time growth rate of holographic complexity density for the three cases is calculated. Our results show that it experiences a fast drop/jump close to the critical point while approaching constants far beyond the critical temperature. Moreover, close to the critical…
In this work we aim at discussing the effects of higher order corrections to curvature on the Lovelock AdS black holes quasinormal spectrum and, in the context of gauge/gravity correspondence, their consequences for the formation of holographic superconductors. We also explore the hydrodynamic limit of the $U(1)$ gauge field perturbations in $d$ dimensions.
Using a simple analytic approach, we study the universal properties of second-order phase transition in holographic superconductor models. We explore a general model in arbitrary dimensions in which the condensation occurs via the Stückelberg spontaneous symmetry breaking mechanism. All the possible second-order phase transitions and their universal characteristics can be identified analytically. The relationship between the critical temperature and charge density is generic, and the critical exponents can be greater than the typical mean field value 1/2. In addition, the related numerical fac…
The phase structure of holographic entanglement entropy is studied in massive gravity for the quantum systems with finite and infinite volumes, which in the bulk is dual to calculate the minimal surface area for a black hole and black brane respectively. In the entanglement entropy$-$temperature plane, we find for both the black hole and black brane there is a Van der Waals-like phase transition as the case in thermal entropy$-$temperature plane. That is, there is a first order phase transition for the small charge and a second order phase transition at the critical charge. For the first order…
We investigate the behavior of entanglement entropy in the holographic QCD model proposed by Gubser et al. By choosing suitable parameters of the scalar self-interaction potential, this model can exhibit various types of phase structures: crossover, first order and second order phase transitions. We use entanglement entropy to probe the crossover/phase transition, and find that it drops quickly/suddenly when the temperature approaches the critical point which can be seen as a signal of confinement. Moreover, the critical behavior of the entanglement entropy suggests that we may use it to chara…
In this note we study the symmetry-breaking phases of 3D gravity coupled to matter. In particular, we consider black holes with scalar hair as a model of symmetry-breaking phases of a strongly coupled 1+1 dimensional CFT. In the case of a discrete symmetry, we show that these theories admit metastable phases of broken symmetry and study the thermodynamics of these phases. We also demonstrate that the 3D Einstein-Maxwell theory shows continuous symmetry breaking at low temperature. The apparent contradiction with the Coleman-Mermin-Wagner theorem is discussed.
The Holographic Naturalness (HN) is a new paradigm towards an explanation of the Cosmological Constant (CC) and the Higgs Hierarchy (HH) in the Universe. Motivated by the Holographic Principle, and inspired by the (A)dS/CFT correspondence, we elaborate on the possibility and on the cosmological consequences of a fundamental intrinsic disorder and temperature in "vacuo". We postulate that the zero vacuum entropy is provided by a large number of quantum hair fields, the "hairons". The quantum hairon gas in space-time induces an effective decoherence effect to the Standard Model (SM) particle sec…
In this paper, phase transition of AdS black holes in lorentz breaking massive gravity has been studied in the framework of holography. We find that there is a first order phase transition(FPT) and second order phase transition(SPT) both in Bekenstein-Hawking entropy(BHE)-temperature plane and holographic entanglement entropy(HEE)-temperature plane. Furthermore, for the FPT, the equal area law is checked and for the SPT, the critical exponent of the heat capacity is also computed. Our results confirm that the phase structure of HEE is similar to that of BHE in lorentz breaking massive gravity,…
In this paper we review some results on the generalization of the gauge/gravity duality to include fundamental matter by means of probe branes. We compute the meson spectrum of maximally supersymmetric gauge theories in several dimensions, both in the Coulomb and Higgs branch. We also study the addition of flavor and compute the meson spectrum for non-commutative theories. Additionally, we present a thorough search of supersymmetric embeddings of probe branes in the Klebanov-Witten model.
We consider a holographic superconductor with homogeneous impurities added. We start with the holographic Abelian-Higgs model for s-wave superconductivity, and turn on a coupling between the gauge field and a new massive gauge field that is introduced for impurities, whose effect is examined in the probe limit. We find that the condensation of the massive gauge field is induced in the superconducting phase. When the coupling is sufficiently large, the mass gap in the optical conductivity disappears. A resonance peak is found in the conductivity for the massive vector field.
We consider a holographic model constructed from the intersecting brane configuration D4-$\bar{\rm{D4}}$/D4 in noncritical string theory. We study the chiral phase diagram of this holographic QCD-like model with a finite baryon chemical potential through the supergravity dual approximation.
We show how Higgs phases at non-zero density can be described using a simple analytic method for gauge theories possessing a holographic dual. We introduce co-dimension one branes in a bottom-up gravity dual that are sources of form flux, such that the effective curvature radius is changed when the brane is crossed. This mimics the expected flow produced by color branes nucleating in a top-down model.
The dynamical stability of a Julia-Zee solution in the AdS background in a four dimensional Einstein-Yang-Mills-Higgs theory is studied. We find that the model with a vanishing scalar field develops a non-zero value for the field at a certain critical temperature which corresponds to a topological dyon in the bulk and a topological phase transition at the boundary.
We study the holographic entanglement measures such as the holographic mutual information, HMI, and the holographic entanglement of purification, EoP, in a holographic QCD model at finite temperature and zero chemical potential. This model can realize various types of phase transitions including crossover, first order and second order phase transitions. We use the HMI and EoP to probe the phase structure of this model and we find that at the critical temperature they can characterize the phase structure of the model. Moreover we obtain the critical exponent using the HMI and EoP.
In this paper, we study the holographic s+p model in 5-dimensional bulk gravity with the Gauss-Bonnet term. We work in the probe limit and give the $Δ$-T phase diagrams at three different values of the Gauss-Bonnet coefficient to show the effect of the Gauss-Bonnet term. We also construct the P-T phase diagrams for the holographic system using two different definitions of the pressure and compare the results.
We investigate the holographic entanglement entropy (HEE) of a strip geometry in four dimensional Q-lattice backgrounds, which exhibit metal-insulator transitions in the dual field theory. Remarkably, we find that the HEE always displays a peak in the vicinity of the quantum critical points. Our model provides the first direct evidence that the HEE can be used to characterize the quantum phase transition (QPT). We also conjecture that the maximization behavior of HEE at quantum critical points would be universal in general holographic models.
We investigate the behavior of entanglement entropy across the holographic p-wave superconductor phase transition in an Einstein-Yang-Mills theory with a negative cosmological constant. The holographic entanglement entropy is calculated for a strip geometry at AdS boundary. It is found that the entanglement entropy undergoes a dramatic change as we tune the ratio of the gravitational constant to the Yang-Mills coupling, and that the entanglement entropy does behave as the thermal entropy of the background black holes. That is, the entanglement entropy will show the feature of the second order …
We construct a dyon solution for a Yang-Mills-Higgs theory in a 4 dimensional Schwarzschild-anti-de Sitter black hole background with temperature T. We then apply the AdS/CFT correspondence to describe the strong coupling regime of a 2+1 quantum field theory which undergoes a phase transition exhibiting the condensation of a composite charge operator below a critical temperature $T_c$.
We use the matching method to investigate the first-order phase transition in holographic superconductor and superfluid. We first use the simple holographic superconductor model to describe the matching method and mention how to see the first-order phase transition. Next, we study the holographic superconductor with Stückelberg term and see that the analytic results indicate the existence of first-order phase transition. Finally, we study the holographic superfluid and show that the first-order phase transition can be found for some values of parameters. We determine the critical value analyti…
The notion of a holographic entropy cone has recently been introduced and it has been proven that this cone is polyhedral. However, the original definition was fully geometric and did not strictly require a holographic duality. We introduce a new definition of the cone, insisting that the geometries used for its construction should be dual to states of a CFT. As a result, the polyhedrality of this holographic cone does not immediately follow. A numerical evaluation of the Euclidean action for the geometries that realize extremal rays of the original cone indicates that these are subdominant bu…
We study how to engineer holographic models with features of a high temperature superconductor phase diagram. We introduce a field in the bulk which provides a tunable "doping" parameter in the boundary theory. By designing how this field changes the effective masses of other order parameter fields, desired phase diagrams can be engineered. We give examples of generating phase diagrams with phase boundaries similar to a superconducting dome and an anti-ferromagnetic phase by including two order parameter fields. We also explore whether the pseudo gap phase can be described without adding anoth…
We investigate the effect of order parameter fluctuations in the holographic superconductor. In particular, using a fully backreacted bulk geometry, the intrinsic spectral functions of the order parameter in both the normal and the superconducting phase are computed. We also present a vector-like large-$N$ version of the Ginzburg-Landau model that accurately describes our long-wavelength results in both phases. The large-$N$ limit of the latter model explains why the Higgs mode and the second-sound mode are not present in the spectral functions. Our results indicate that the holographic superc…
Using a five dimensional AdS soliton in an Einstein-Yang-Mills theory with SU(2) gauge group we study p-wave holographic insulator/superconductor phase transition. To explore the phase structure of the model we consider the system in the probe limit as well as fully back reacted solutions. We will also study zero temperature limit of the p-wave holographic superconductor in four dimensions.
