Quantum field theories with exact but spontaneously broken conformal invariance have an intriguing feature: their vacuum energy (cosmological constant) is equal to zero. Up to now, the only known ultraviolet complete theories where conformal symmetry can be spontaneously broken were associated with supersymmetry (SUSY), with the most prominent example being the $\mathcal N$=4 SUSY Yang-Mills. In this Letter we show that the recently proposed conformal "fishnet" theory supports at the classical level a rich set of flat directions (moduli) along which conformal symmetry is spontaneously broken. We demonstrate that, at least perturbatively, some of these vacua survive in the full quantum theory (in the planar limit, at the leading order of $1/N_c$ expansion) without any fine tuning. The vacuum energy is equal to zero along these flat directions, providing the first non-SUSY example of a four-dimensional quantum field theory with "natural" breaking of conformal symmetry.
We compute explicitly the two-dimensional version of Basso-Dixon type integrals for the planar four-point correlation functions given by conformal fishnet Feynman graphs. These diagrams are represented by a fragment of a regular square lattice of power-like propagators, arising in the recently proposed integrable bi-scalar fishnet CFT. The formula is derived from first principles, using the formalism of separated variables in integrable SL(2,C) spin chain. It is generalized to anisotropic fishnet, with different powers for propagators in two directions of the lattice.
I will discuss spontaneous conformal symmetry breaking in the strongly $γ$-deformed limit of the $\mathcal N=4$ supersymmetric Yang-Mills theory known as~\emph{Fishnet Conformal Field Theory}.
We study the Feynman graph structure and compute certain exact four-point correlation functions in chiral CFT$_4$ proposed by Ö.Gürdoğan and one of the authors as a double scaling limit of $γ$-deformed $\mathcal{N}=4$ SYM theory. We give full description of bulk behavior of large Feynman graphs: it shows a generalized "dynamical fishnet" structure, with a dynamical exchange of bosonic and Yukawa couplings. We compute certain four-point correlators in the full chiral CFT$_4$, generalizing recent results for a particular one-coupling version of this theory -- the bi-scalar "fishnet" CFT. We sum …
The major simplification in a number of quantum integrable systems is the existence of special coordinates in which the eigenstates take a factorised form. Despite many years of studies, the basis realising the separation of variables (SoV) remains unknown in N=4 SYM and similar models, even though it is widely believed they are integrable. In this paper we initiate the SoV approach for observables with nontrivial coupling dependence in a close cousin of N=4 SYM - the fishnet 4D CFT. We develop the functional SoV formalism in this theory, which allows us to compute non-perturbatively some nont…
Integrability and the spectrum of two-dimensional fishnet CFT
King’s College London（伦敦国王学院）；Uppsala University（乌普萨拉大学）；Centre for Mathematical Science, City St George’s, University of London（伦敦大学城市圣乔治学院数学科学中心）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器研究所）
We review the quantum spectral curve (QSC) formalism for anomalous dimensions of planar ${\cal\ N}=4$ SYM, including its $γ$-deformation. Leaving aside its derivation, we concentrate on formulation of the "final product" in its most general form: a minimal set of assumptions about the algebraic structure and the analyticity of the $Q$-system -- the full system of Baxter $Q$-functions of the underlying integrable model. The algebraic structure of the $Q$-system is entirely based on (super)symmetry of the model and is efficiently described by Wronskian formulas for $Q$-functions organized into t…
We present the TBA equations and the Y-system for the exact spectrum of general multi-magnon local operators in the $D$-dimensional anisotropic version of the bi-scalar fishnet CFT. The mixing matrix of such operators is given in terms of fishnet planar graphs of multi-wheel and multi-spiral type. These graphs probe the two main building blocks of the TBA approach that are the magnon dispersion relation and the magnon scattering matrix and which we both obtain by diagonalising suitable graph-building operators. We also obtain the dual version of the TBA equations, which relates, in the continu…
We investigate properties of four point colour ordered scattering amplitudes in D=6 fishnet CFT. We show that such amplitudes are related via very simple relation to their D=4 counterparts considered previously in the literature. Exploiting this relation we obtain closed expression for such amplitudes and investigate its behaviour at weak and strong coupling. As by product of this investigation we also obtain generating function for on-shell D=6 Box ladder diagrams with l rungs.
Various classes of fishnet Feynman graphs are shown to feature a Yangian symmetry over the conformal algebra. We explicitly discuss scalar graphs in three, four and six spacetime dimensions as well as the inclusion of fermions in four dimensions. The Yangian symmetry results in novel differential equations for these families of largely unsolved Feynman integrals. Notably, the considered fishnet graphs in three and four dimensions dominate the correlation functions and scattering amplitudes in specific double scaling limits of planar, gamma-twisted N=4 super Yang-Mills or ABJM theory. Consequen…
Recently, infinite families of massive Feynman integrals were found to feature an unexpected Yangian symmetry. In the massless case, similar integrability properties are understood via the interpretation of individual Feynman integrals as correlators in the massless fishnet theory introduced by Gürdoğan and Kazakov. Here we seek for an analogous interpretation of the integrability of massive Feynman integrals. We contrast two approaches to define simple massive quantum field theories in four dimensions. First, we discuss spontaneous symmetry breaking in the massless bi-scalar fishnet theory. W…
We compute exactly various 4-point correlation functions of shortest scalar operators in bi-scalar planar four-dimensional "fishnet" CFT. We apply the OPE to extract from these functions the exact expressions for the scaling dimensions and the structure constants of all exchanged operators with an arbitrary Lorentz spin. In particular, we determine the conformal data of the simplest unprotected two-magnon operator analogous to the Konishi operator, as well as of the one-magnon operator. We show that at weak coupling 4-point correlation functions can be systematically expanded in terms of harmo…
We propose a $D$-dimensional generalization of $4D$ bi-scalar conformal quantum field theory recently introduced by Gürdogan and one of the authors as a strong-twist double scaling limit of $γ$-deformed $\mathcal{N}=4$ SYM theory. Similarly to the $4D$ case, this D-dimensional CFT is also dominated by "fishnet" Feynman graphs and is integrable in the planar limit. The dynamics of these graphs is described by the integrable conformal $SO(D+1,1)$ spin chain. In $2D$ it is the analogue of L. Lipatov's $SL(2,\mathbb{C})$ spin chain for the Regge limit of $QCD$, but with the spins $s=1/4$ instead o…
In this paper we study a wide class of planar single-trace four point correlators in the chiral conformal field theory ($χ$CFT$_4$) arising as a double scaling limit of the $γ$-deformed $\mathcal{N}=4$ SYM theory. In the planar (t'Hooft) limit, each of such correlators is described by a single Feynman integral having the bulk topology of a square lattice "fishnet" and/or of an honeycomb lattice of Yukawa vertices. The computation of this class of Feynmann integrals at any loop is achieved by means of an exactly-solvable spin chain magnet with $SO(1,5)$ symmetry. In this paper we explain in det…
Conformal Field Theories (CFTs) have rich dynamics in heavy states. We describe the constraints due to spontaneously broken boost and dilatation symmetries in such states. The spontaneously broken boost symmetries require the existence of new low-lying primaries whose scaling dimension gap, we argue, scales as $O(1)$. We demonstrate these ideas in various states, including fluid, superfluid, mean field theory, and Fermi surface states. We end with some remarks about the large charge limit in 2d and discuss a theory of a single compact boson with an arbitrary conformal anomaly.
We analyze, in the framework of AdS/CFT correspondence, the gauge theory phase structure that are supposed to be dual to the recently found non-supersymmetric dilatonic deformations to AdS_5 X S^5 in type IIB string theory. Analyzing the probe D7-brane dynamics in the backgrounds of our interest, which corresponds to the fundamental N=2 hypermultiplet, we show that the chiral bi-fermion condensation responsible for spontaneous chiral symmetry breaking is not logically related to the phenomenon of confinement.
We prove the instability of $d$-dimensional conformal field theories (CFTs) having in the operator-product expansion of two fundamental fields a primary operator of scaling dimension $h=d/2+i r$, with non-vanishing $ r\in\mathbb{R}$. From an AdS/CFT point of view, this corresponds to a well-known tachyonic instability, associated to a violation of the Breitenlohner-Freedman bound in AdS${}_{d+1}$; we derive it here directly for generic $d$-dimensional CFTs that can be obtained as limits of multiscalar quantum field theories, by applying the harmonic analysis for the Euclidean conformal group t…
We study the gravity duals of symmetry-breaking deformations of superconformal field theories, AdS/CFT dual to Type IIB string theory on AdS_5 x Y where Y is a Sasaki-Einstein manifold. In these vacua both conformal invariance and baryonic symmetries are spontaneously broken. We present a detailed discussion of the supergravity moduli space, which involves flat form fields on asymptotically conical Calabi-Yau manifolds, and match this to the gauge theory vacuum moduli space. We discuss certain linearised fluctuations of the moduli, identifying the Goldstone bosons associated with spontaneous b…
In our previous paper we derived the holographic dual of the planar fishnet CFT in four dimensions. The dual model becomes classical in the strongly coupled regime of the CFT and takes the form of an integrable chain of particles in five dimensions. Here we study the theory at the quantum level. By applying the canonical quantization procedure with constraints, we show that the model describes a quantum chain of particles propagating in $AdS_5$. We prove the duality at the full quantum level in the ${\mathfrak u}(1)$ sector and reproduce exactly the spectrum for the cases when it is known anal…
We consider the 6d (1,0) SCFT on a stack of $N$ M5-branes probing a $\mathbb C^2/\mathbb Z_2$ singularity. In particular, we study its compactifications to four dimensions on a smooth genus-$g$ Riemann surface with non-trivial flavor flux, yielding a family of 4d CFTs. By tracking the M-theory origin of the global symmetries of the 4d CFTs, we detect the emergence of an accidental symmetry and the spontaneous symmetry breaking of a $U(1)$ generator. These effects are visible from geometric considerations and not apparent from the point of view of the compactification of the 6d field theory. Th…
We propose a new approach to solve conformal field theories and apply it to Chern-Simons Matter theories and three-dimensional bosonization duality. All three-point correlation functions of single-trace operators are obtained in the large-$N$ as a simple application. The idea is to construct, as an effective weakly-coupled theory, a nonlinear realization of the conformal algebra in terms of physical, gauge-invariant, operators. The efficiency of the method is also in the use of an analog of the light-cone gauge and of the momentum-space on the CFT side. AdS/CFT is used as a convenient regulato…
We study the semiclassical decay of macroscopic spinning strings in AdS_5 x S^5 through spontaneous splitting of the folded string worldsheet. Based on similar considerations in flat space this decay channel is expected to dominate the full quantum computation. The outgoing strings are uniquely specified by an infinite set of conserved (local) charges with a regular expansion in inverse powers of the initial angular momentum. We compute these charges and determine functional relations between them. Finally, a preliminary discussion of the corresponding calculation in the non-planar sector of t…
Celestial holography proposes a duality between gravitational scattering in asymptotically flat space-time and a conformal field theory living on the celestial sphere. Its dictionary relates the infinite dimensional space-time symmetry group to Ward identities of the CFT. The spontaneous breaking of these asymptotic symmetries governs the dynamics of the soft sector in the CFT. Here we show that this sector encodes non-trivial backreaction effects that exhibit characteristics of maximal quantum chaos. A key element in the derivation is the identification of the Hilbert space of celestial CFT, …
Utilizing AdS/CFT correspondence in M-theory, an example of interacting d=3 conformal field theories and renormalization group flow between them is presented. Near-horizon geometry of N coincident M2-branes located on a conical singularity on eight-dimensional hyperkähler manifold or manifold with Spin(7) holonomy is, in large-N limit, AdS4*X7, where X7 is seven-sphere with squashing. Deformation from round $§_7$ to squashed one is known to lead to spontaneous breaking of N=8 local supersymmetry in gauged AdS4 supergravity to N=1, 0. Via AdS/CFT correspondence, it is interpreted as renormaliza…
We show that minimal massive 3d gravity (MMG), as well as the topological massive gravity, are particular cases of a more general `minimal massive gravity' theory (with a single massive propagating mode) arising upon spontaneous breaking of a local symmetry in a Chern-Simons gravity based on a Hietarinta or Maxwell algebra. Similar to the MMG case, the requirements that the propagating massive mode is neither tachyon nor ghost and that the central charges of an asymptotic algebra associated with a boundary CFT are positive, impose restrictions on the range of the parameters of the theory.
We study the SU(3)-invariant relevant deformation of D=4 N=4 SU(N) gauge theory at large N using the AdS/CFT correspondence. At low energies, we obtain a nonsupersymmetric gauge theory with three left-handed quarks in the adjoint of SU(N). In terms of the five dimensional gauged supergravity, there is an unstable critical point in the scalar potential for fluctuations of some fields in a nontrivial representation of the symmetry group SU(3). On the field theory side, this corresponds to dynamical breaking of the SU(3) chiral symmetry down to SO(3). We compute the condensate of the quark biline…
Using the AdS/CFT correspondence we study vacua of N=4 SYM for which part of the gauge symmetry is broken by expectation values of scalar fields. A specific subclass of such vacua can be analyzed with gauged supergravity and the corresponding domain wall solutions lift to continuous distributions of D3-branes in type IIB string theory. Due to the non-trivial expectation value of the scalars, the SO(6) R-symmetry is spontaneously broken and field theory predicts the existence of Goldstone bosons. We explicitly show that, in the dual supergravity description, these emerge as massless poles in th…
We discuss fermionic higher spin gauge symmetry breaking in AdS space from a holographic perspective. Analogously to the recently discussed bosonic case, the higher spin Goldstino mode responsible for the symmetry breaking has a non-vanishing mass in the limit in which the gauge symmetry is restored. This result is precisely in agreement with the AdS/CFT correspondence, which implies that N=4 SYM at vanishing coupling constant is dual to a theory in AdS which exhibits higher spin gauge symmetry enhancement. When the SYM coupling is non-zero, the current conservation condition becomes anomalous…
We consider generalizations of the AdS/CFT correspondence in which probe branes are embedded in gravity backgrounds dual to either conformal or confining gauge theories. These correspond to defect conformal field theories (dCFT) or QCD-like theories with fundamental matter, respectively. Computing the quark condensate and the meson spectrum for a non-supersymmetric QCD-like theory from supergravity, we find spontaneous U(1) chiral symmetry breaking as well as the associated Goldstone boson. For another example at finite temperature, we observe a phase transition corresponding to a geometrical …
We review the applications of the Quantum Spectral Curve (QSC) method to the Regge (BFKL) limit in N=4 supersymmetric Yang-Mills theory. QSC, based on quantum integrability of the AdS$_5$/CFT$_4$ duality, was initially developed as a tool for the study of the spectrum of anomalous dimensions of local operators in the N=4 SYM in the planar, $N_c\to\infty$ limit. We explain how to apply the QSC for the BFKL limit, which requires non-trivial analytic continuation in spin $S$ and extends the initial construction to non-local light-ray operators. We give a brief review of high precision non-perturb…
We study the transition of a scalar field in a fixed $AdS_{d+1}$ background between an extremum and a minimum of a potential. We first prove that two conditions must be met for the solution to exist. First, the potential involved cannot be generic, i.e. a fine-tuning of their parameters is mandatory. Second, at least in some region its second derivative must have a negative upper limit which depends only on the dimensionality $d$. We then calculate the boundary propagator for small momenta in two different ways: first in a WKB approximation, and second with the usual matching method, generaliz…
We propose an effective conformal field theory (CFT) description of steady state incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We derive a KPZ-type equation for the anomalous scaling of the longitudinal velocity structure functions and relate the intermittency parameter to the boundary Euler (A-type) conformal anomaly coefficient. The proposed theory consists of a mean field CFT that exhibits Kolmogorov linear scaling (K41 theory) coupled to a dilaton. The dilaton is a Nambu-Goldstone gapless mode that arises from a spontaneous breaking du…
We show that any conformal field theory in d-dimensional Minkowski space, in a phase with spontaneously broken conformal symmetry and with the dilaton among its fields, can be rewritten in terms of the static gauge (d-1)-brane on AdS_(d+1) by means of an invertible change of variables. This nonlinear holographic transformation maps the Minkowski space coordinates onto the brane worldvolume ones and the dilaton onto the transverse AdS brane coordinate. One of the consequences of the existence of this map is that any (d-1)-brane worldvolume action on AdS_(d+1)\times X^m (with X^m standing for th…
For an effective AdS theory, we present a simple prescription to compute the renormalization of its dual boundary field theory. In particular, we define anomalous dimension holographically as the dependence of the wave-function renormalization factor on the radial cutoff in the Poincare patch of AdS. With this definition, the anomalous dimensions of both single- and double- trace operators are calculated. Three different dualities are considered with the field theory being CFT, CFT with a double-trace deformation and spontaneously broken CFT. For the second dual pair, we compute scaling correc…
Extreme and very-near-extreme spin J Kerr black holes have been conjectured to be holographically dual to two-dimensional (2D) conformal field theories (CFTs) with left and right central charges c_L=c_R=12J. In this paper it is observed that the 2D conformal symmetry of the scalar wave equation at low frequencies persists for generic non-extreme values of the mass M. Interestingly, this conformal symmetry is not derived from a conformal symmetry of the spacetime geometry except in the extreme limit. The periodic identification of the azimuthal angle is shown to correspond to a spontaneous brea…
A field theoretic understanding of how the radial direction in the AdS/CFT Correspondence plays the role of a gauge invariant measure of energy scale has long been missing. In SU(N) Yang-Mills, a realization of a gauge invariant cutoff has been achieved by embedding the theory in spontaneously broken SU(N|N) gauge theory. With the recent discovery of ghost D-branes an AdS/CFT Correspondence version of this scheme is now possible. We show that a very simple construction precisely ties the two pictures together providing a concrete understanding of the radial RG flow on the field theory side.
We investigate dispersion relation of Nambu-Goldstone modes in a dissipative system realized by the AdS/CFT correspondence. We employ the D3/D7 model which represents ${\cal N} = 4$ supersymmetric Yang-Mills theory coupled to ${\cal N = 2}$ flavor fields. If we consider massless quarks in the presence of an external magnetic field, the system exhibits the phase transition associated with the spontaneous symmetry breaking of the chiral symmetry. We find that the Nambu-Goldstone modes shows a diffusive behavior in the dispersion relation, which agrees with that found with the effective field the…
We numerically construct asymptotically AdS black brane solutions of $D=4$ Einstein-Maxwell theory coupled to a pseudoscalar. The solutions are holographically dual to $d=3$ CFTs at finite chemical potential and in a constant magnetic field, which spontaneously break translation invariance leading to the spontaneous formation of abelian and momentum magnetisation currents flowing around the plaquettes of a periodic Bravais lattice. We analyse the three-dimensional moduli space of lattice solutions, which are generically oblique, and show, for a specific value of the magnetic field, that the fr…
In this thesis we investigate the effective actions for massive Kaluza-Klein states, focusing on the massive modes of spin-3/2 and spin-2 fields. To this end we determine the spontaneously broken gauge symmetries associated to these `higher spin' states and construct the unbroken phase of the Kaluza-Klein theory. We show that for the particular background AdS_3 x S*3 x S*3 a consistent coupling of the first massive spin-3/2 multiplet requires an enhancement of local supersymmetry, which in turn will be spontaneously broken in the Kaluza-Klein vacuum. The corresponding action is constructed as …
Holographic CFTs and holographic RG flows on space-time manifolds which are $d$-dimensional products of spheres are investigated. On the gravity side, this corresponds to Einstein-dilaton gravity on an asymptotically $AdS_{d+1}$ geometry, foliated by a product of spheres. We focus on holographic theories on $S^2\times S^2$, we show that the only regular five-dimensional bulk geometries have an IR endpoint where one of the sphere shrinks to zero size, while the other remains finite. In the $Z_2$-symmetric limit, where the two spheres have the same UV radii, we show the existence of a infinite d…
In the first part of this thesis we study baryonic U(1) symmetries dual to Betti multiplets in the AdS_4/CFT_3 correspondence for M2 branes at Calabi-Yau 4-fold singularities. We begin by focusing on isolated toric singularities without vanishing 6-cycles, which we classify, and propose for them field theory duals. We then study in detail the cone over Q^111 and find agreement between the spectrum of baryonic operators in this theory and M5 branes wrapping 5-cycles in the Q^111 space. The physics of vacua in which these symmetries are spontaneously broken precisely matches a dual gravity analy…
4D cylindrical gravitational waves with aligned polarizations (Einstein-Rosen waves) are shown to be described by a weight 1/2 massive free field on the double cover of AdS_2. Thorn's C-energy is one of the sl(2,R) generators, the reconstruction from the (timelike) symmetry axis is the CFT_1 holography. Classically the phase space is also invariant under a O(1,1) group action on the metric coefficients that is a remnant of the original 4D diffeomorphism invariance. In the quantum theory this symmetry is found to be spontaneously broken while the AdS_2 conformal invariance remains intact.
We present an exactly solvable model of a scalar field in an AdS$_{d+1}$ like background interpolating between a $Z_2$ preserving and a $Z_2$ breaking minima of the potential. We define its holographic dual through the AdS/CFT dictionary and argue that at zero temperature the $d-$dimensional strongly coupled system on the boundary of AdS$_{d+1}$ exhibits a phase with a spontaneously broken discrete symmetry. In the presence of a black hole in the bulk ($T\neq 0$) we find that, although the metastable phase is present, the discrete symmetry gets restored. We compute exactly the lowest order bou…
We show that for a certain low frequency limit the wave equation of a generic massive scalar field in the background of the spacelike warped AdS_3 black hole can be written as the Casimir of an SL(2,R) symmetry. Two sets of SL(2,R) generators are found which uncover the hidden SL(2,R)\times SL(2,R) symmetry of the solution. This symmetry is only locally defined and is spontaneously broken to U(1)\times U(1) by a periodic identification of the ϕcoordinate. By using the generator of the identification we read the left and right temperatures (T_L,T_R) of the proposed dual conformal field theory w…
We derive positivity bounds on EFT coefficients in theories where boosts are spontaneously broken. We employ the analytic properties of the retarded Green's function of conserved currents (or of the stress-energy tensor) and assume the theory becomes conformal in the UV. The method is general and applicable to both cosmology and condensed matter systems. As a concrete example, we look at the EFT of conformal superfluids which describes the universal low-energy dynamics of CFT's at large chemical potential and we derive inequalities on the coefficients of the operators, in three dimensions, at …
The theory of scalar gravity proposed by Nordström, and refined by Einstein and Fokker, provides a striking analogy to general relativity. In its modern form, scalar gravity appears as the low-energy effective field theory of the spontaneous breaking of conformal symmetry within a CFT, and is AdS/CFT dual to the original Randall-Sundrum I model, but without a UV brane. Scalar gravity faithfully exhibits several qualitative features of the cosmological constant problem of standard gravity coupled to quantum matter, and the Weinberg no-go theorem can be extended to this case as well. Remarkably,…
Upon compactification on a circle, SU(N) gauge theory with all fields in the adjoint representation acquires a $Z_N$ global symmetry because the center of the gauge group is $Z_N$. For N=4 super Yang-Mills theory, we show how this $Z_N$ "topological symmetry" arises in the context of the AdS/CFT correspondence, and why the symmetry group is $Z_N$ rather than U(1). This provides a test of the AdS/CFT correspondence for finite N. If the theory is formulated on $R^3 \times S^1$ with anti-periodic boundary conditions for fermions around the $S^1$, the topological symmetry is spontaneously broken; …
The D3/D7 holographic model aims at a better approximation to QCD by adding to N=4 SYM theory N_f of N=2 supersymmetric hypermultiplets in the fundamental representation of SU(N_c) -- the "flavor fields" representing the quarks. Motivated by a recent observation of the importance of the Wess-Zumino-like (WZ) term for realizing the chiral magnetic effect within this model, we revisit the phase diagram of the finite temperature, massless D3/D7 model in the presence of external electric/magnetic fields and at finite chemical potential. We point out that the A-V-V triangle anomaly represented by t…
We make an exact field theoretical computation of the conformal anomaly for two-dimensional submanifold observables. By including a scalar field in the definition for the Wilson surface, as appropriate for a spontaneously broken A_1 theory, we get a conformal anomaly which is such that N times it is equal to the anomaly that was computed in hep-th/9901021 in the large N limit and which relied on the AdS-CFT correspondence. We also show how the spherical surface observable can be expressed as a conformal anomaly.
We review recent progress towards the understanding of higher spin gauge symmetry breaking in AdS space from a holographic vantage point. According to the AdS/CFT correspondence, N=4 SYM theory at vanishing coupling constant should be dual to a theory in AdS which exhibits higher spin gauge symmetry enhancement. When the SYM coupling is non-zero, all but a handful of HS currents are violated by anomalies, and correspondingly local higher spin symmetry in the bulk gets spontaneously broken. In agreement with previous results and holographic expectations, we find that, barring one notable except…
