Holographic Description Research Articles

Phase transitions from the fifth dimension

We study the cosmological transition of 5D warped compactifications, from the high-temperature black-brane phase to the low-temperature Randall-Sundrum I phase. The transition proceeds via percolation of bubbles of IR-brane nucleating from the black-brane horizon. The violent bubble dynamics can be a powerful source of observable stochastic gravitational waves. While bubble nucleation is non-perturbative in 5D gravity, it is amenable to semiclassical treatment in terms of a “bounce” configuration interpolating between the two phases. We demonstrate how such a bounce configuration can be smooth enough to maintain 5D effective field theory control, and how a simple ansatz for it places a rigorous lower-bound on the transition rate in the thin-wall regime, and gives plausible estimates more generally. When applied to the Hierarchy Problem, the minimal Goldberger-Wise stabilization of the warped throat leads to a slow transition with significant supercooling. We demonstrate that a simple generalization of the Goldberger-Wise potential modifies the IR-brane dynamics so that the transition completes more promptly. Supercooling determines the dilution of any (dark) matter abundances generated before the transition, potentially at odds with data, while the prompter transition resolves such tensions. We discuss the impact of the different possibilities on the strength of the gravitational wave signals. Via AdS/CFT duality the warped transition gives a theoretically tractable holographic description of the 4D Composite Higgs (de)confinement transition. Our generalization of the Goldberger-Wise mechanism is dual to, and concretely models, our earlier proposal in which the composite dynamics is governed by separate UV and IR RG fixed points. The smooth 5D bounce configuration we introduce complements the 4D dilaton/radion dominance derivation presented in our earlier work.

Gauge/gravity dual dynamics for the strongly coupled sector of composite Higgs models

A holographic model of chiral symmetry breaking is used to study the dynamics plus the meson and baryon spectrum of the underlying strong dynamics in composite Higgs models. The model is inspired by top-down D-brane constructions. We introduce this model by applying it to Nf = 2 QCD. We compute meson masses, decay constants and the nucleon mass. The spectrum is improved by including higher dimensional operators to reflect the UV physics of QCD. Moving to composite Higgs models, we impose perturbative running for the anomalous dimension of the quark condensate in a variety of theories with varying number of colors and flavours. We compare our results in detail to lattice simulations for the following theories: SU(2) gauge theory with two Dirac fundamentals; Sp(4) gauge theory with fundamental and sextet matter; and SU(4) gauge theory with fundamental and sextet quarks. In each case, the holographic results are encouraging since they are close to lattice results for masses and decay constants. Moreover, our models allow us to compute additional observables not yet computed on the lattice, to relax the quenched approximation and move to the precise fermion content of more realistic composite Higgs models not possible on the lattice. We also provide a new holographic description of the top partners including their masses and structure functions. With the addition of higher dimension operators, we show the top Yukawa coupling can be made of order one, to generate the observed top mass. Finally, we predict the spectrum for the full set of models with top partners proposed by Ferretti and Karateev.

Holographic quark matter with color superconductivity and a stiff equation of state for compact stars

We present a holographic model of QCD with a first order chiral restoration phase transition with chemical potential, mu. The first order behaviour follows from allowing a discontinuity in the dual description as the quarks are integrated out below their constituent mass. The model predicts a deconfined yet massive quark phase at intermediate densities (350 MeV< mu <500 MeV), above the nuclear density phase, which has a very stiff equation of state and a speed of sound close to one. We also include a holographic description of a colour superconducting condensate in the chirally restored vacuum and study the resulting equation of state. They provides a well behaved first order transition from the deconfined massive quark phase at very high density (mu>500 MeV). We solve the Tolman-Oppenheimer-Volkoff equations with the resulting equations of state and find stable hybrid stars with quark cores. We compute the tidal deformability for these hybrid stars and show they are consistent with LIGO/Virgo data on a neutron star collision. Our holographic model shows that quark matter could be present at the core of such compact stars.

Erratum in “On the Holographic Principle Description for the Viscous Incompressible Fluids” and “The Mathematical Description of Homogeneous Turbulence for Incompressible Fluids

This note is to acknowledge errors made in previous article: “On the Holographic Principle Description for the Viscous Incompressible Fluids” due to the Laplacian of the Lagrangian fails to be zero as expected when a using G.I. Taylor's 2-D solution of the Navier-Stokes momentum equations. Unfortunately, the article “The Mathematical Description of Homogeneous Turbulence for Incompressible Fluids” was also affected due to the use of the Laplacian of the Lagrangian in order to obtain the power spectrum relationship of the pressure which obviously now is incorrect.

Holographic Description of the Early Universe

The holographic principle is applied to a description of the Universe in the early stage of its evolution. As an example, we examine a cosmological model with a bounce with subsequent transition to the early stage of inflation. We investigate cosmological models based on a viscous liquid with a generalized equation of state in terms of the holographic cutoff proposed by Nojiri and Odintsov. Within the framework of these models, we have calculated the infrared radius in terms of the particle horizon or the event horizon. Energy conservation laws are obtained from the holographic point of view. The viscous liquid describing the bounce and the early Universe is presented as a generalization of holographic energy.

Effective field theory in AdS: Continuum regime, soft bombs, and IR emergence

We consider a scalar field in a slice of Lorentzian five-dimensional AdS at arbitrary energies. We show that the presence of bulk interactions separates the behavior of the theory into two different regimes: Kaluza-Klein and continuum. We determine the transition scale between these regimes and show that UV-brane correlation functions are independent of IR-brane-localized operators for four-momenta beyond this transition scale. The same bulk interactions that induce the transition also give rise to cascade decays. We study these cascade decays for the case of a cubic self-interaction in the continuum regime. We find that the cascade decay progresses slowly towards the IR region and gives rise to soft spherical final states, in accordance with former results from both gravity and CFT. We identify a recursion relation between integrated squared amplitudes of different leg numbers and thus evaluate the total rate. We find that cascade decays in the continuum regime are exponentially suppressed. This feature completes the picture of the IR brane as an emergent sector as seen from the UV brane. We briefly discuss consistency with the holographic dual description of glueballs and some implications for dark sector models.

Virasoro Hair and Entropy for Axisymmetric Killing Horizons.

We show that the gravitational phase space for the near-horizon region of a bifurcate, axisymmetric Killing horizon in any dimension admits a 2D conformal symmetry algebra with central charges proportional to the area. This extends the construction of Haco et. al. [J. High Energy Phys. 12 (2018) 098JHEPFG1029-847910.1007/JHEP12(2018)098] to generic Killing horizons appearing in solutions of Einstein's equations and motivates a holographic description in terms of a 2D conformal field theory. The Cardy entropy in such a field theory agrees with the Bekenstein-Hawking entropy of the horizon, suggesting a microscopic interpretation. A set of appendixes is included in the Supplemental Material that provides examples and further details of the calculations presented in the main text.

Instability of AdS black holes with lattices * *Supported by Natural Science Foundation of China (11875053)

Anti-de Sitter (AdS) black holes with lattices are essential for optical conductivity studies in the holographic approach. We investigate the instability of these black holes that can result in the holographic description of charge density waves. In the presence of homogeneous axion fields, we show that the instability of AdS-Reissner-Nordström (AdS-RN) black holes is always suppressed. However, in the presence of Q-lattices, we find that the unstable region becomes the smallest in the vicinity of the critical region for the metal/insulator phase transition. This novel phenomenon is reminiscent of the behavior of the holographic entanglement entropy during quantum phase transitions.

Quantum BMS transformations in conformally flat space-times and holography

We define and study asymptotic Killing and conformal Killing vectors in d-dimensional Minkowski, (A)dS, ℝ × Sd−1 and AdS2× Sd−2. We construct the associated quantum charges for an arbitrary CFT and show they satisfy a closed algebra that includes the BMS as a sub-algebra (i.e. supertranslations and superrotations) plus a novel transformation we call ‘superdilations’. We study representations of this algebra in the Hilbert space of the CFT, as well as the action of the finite transformations obtained by exponentiating the charges. In the context of the AdS/CFT correspondence, we propose a bulk holographic description in semi-classical gravity that reproduces the results obtained from CFT computations. We discuss the implications of our results regarding quantum hairs of asymptotically flat (near-)extremal black holes.

On a gravity dual to flavored topological quantum mechanics

In this paper, we propose a generalization of the AdS2/CFT1 correspondence constructed by Mezei, Pufu and Wang in [1], which is the duality between 2d Yang-Mills theory with higher derivatives in the AdS2 background, and 1d topological quantum mechanics of two adjoint and two fundamental U(N ) fields, governing certain protected sector of operators in 3d ABJM theory at the Chern-Simons level k = 1. We construct a holographic dual to a flavored generalization of the 1d quantum mechanics considered in [1], which arises as the effective field theory living on the intersection of stacks of N D2-branes and k D6-branes in the Ω-background in Type IIA string theory, and describes the dynamics of the protected sector of operators in mathcal{N} = 4 theory with k fundamental hypermultiplets, having a holographic description as M-theory in the AdS4× S7/ℤk background. We compute the structure constants of the bulk theory gauge group, and construct a map between the observables of the boundary theory and the fields of the bulk theory.

Holographic Wilsonian renormalization of a heavy quark moving through a strongly coupled plasma

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 action 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.

Modular Hamiltonians in flat holography and (W)AdS/WCFT

We study several aspects of holographic entanglement in two models known as flat3/BMSFT and (W)AdS3/WCFT. These are two examples of holography beyond AdS/CFT where the boundary field theories are not Lorentz invariant but still feature an infinite set of local symmetries. In the first example, BMS-invariant field theories (BMSFTs) are conjectured to provide a holographic description of quantum gravity in asymptotically flat three-dimensional spacetimes; while in the second example, warped conformal field theories (WCFTs) are proposed to describe quantum gravity in warped AdS3 or AdS3 backgrounds with Dirichlet-Neumann boundary conditions. In particular, we derive the modular Hamiltonian for single intervals in both BMSFTs and WCFTs and find the holographic duals in the bulk using the covariant formulation of gravitational charges. We also extend the first law of entanglement entropy to these models of non-AdS holography and discuss the bound on “modular chaos” introduced recently in the context of the AdS/CFT correspondence.

Towards reconciling the holographic and lattice descriptions of radially excited hadrons

Within the framework of AdS/QCD models, the spectra of radially excited hadrons are identified with towers of Kaluza–Klein (KK) states in a putative dual theory. The infinite number of KK states is indispensable to provide correct high energy asymptotics of correlation functions in QCD. It is known, however, that the KK modes of dual theory must be qualitatively different from real hadrons. And what is more important, the radially excited states appear in lattice calculations not as ”excitations” of some ground state, but rather as independent states coupled to higher dimensional QCD operators – the larger is a basis of interpolating operators, the larger set of states can be resolved. A question arises whether is it possible to reconcile the holographic and lattice descriptions of radially excited hadrons? We propose a new phenomenological ”consistency test” for bottom-up holographic models: If the KK spectrum of massive 5D fields dual to higher dimensional operators in QCD coincides with the conventional radial KK spectrum, then the holographic KK states can be identified with real excited mesons in the large-N_c limit of QCD. We demonstrate that the Soft Wall holographic model passes this test while the Hard Wall model does not.

Geometric encoding of renormalization group β -functions in an emergent holographic dual description

First, we reformulate RG transformations in a recursive way with introduction of an order-parameter field. As a result, we manifest the RG flow of an effective field theory through the emergence of an extra dimensional space, where both RG $\beta-$functions of coupling functions and RG flow equation of the order-parameter field appear in the resulting effective action explicitly through the extra dimensional space. Second, we consider an effective dual holographic description derived recently, where the classical gravity theory of the large $N$ limit takes into account quantum corrections in the all-loop order. This non-perturbative nature turns out to originate from an intertwined renormalization structure between both RG flow equations of coupling functions and order-parameter fields in the emergent extra-dimensional space, where the IR boundary condition of the order-parameter field gives rise to a mean-field equation with fully renormalized interaction coefficients. Third, comparing the RG-reformulated effective field theory with this effective dual holographic description, we obtain term-by-term matching conditions in the level of an effective action. As a result, we express all RG coefficients of fields and interaction vertices in terms of the metric tensor of the dual holographic theory. Through this metric reformulation for the RG analysis, we propose a prescription on how to find RG $\beta-$functions of interaction coefficients in a non-perturbative way beyond the perturbative RG analysis. In particular, we claim that the present prescription of the RG flow generalizes the holographic RG flow of the holographic duality conjecture towards the absence of conformal symmetry, where the emergent holographic dual effective field theory has been derived from the first principle, thus being applicable even away from quantum criticality.

Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS7 \xd7 S4

Surface operators in the 6d (2,0) theory at large N have a holographic description in terms of M2 branes probing the AdS7×S4 M-theory background. The most symmetric, 1/2-BPS, operator is defined over a planar or spherical surface, and it preserves a 2d superconformal group. This includes, in particular, an SO(2, 2) subgroup of d conformal transformations, so that the surface operator may be viewed as a conformal defect in the 6d theory. The dual M2 brane has an AdS3 induced geometry, reflecting the 2d conformal symmetry. Here we use the holographic description to extract the defect CFT data associated to the surface operator. The spectrum of transverse fluctuations of the M2 brane is found to be in one-to-one correspondence with a protected multiplet of operator insertions on the surface, which includes the displacement operator. We compute the one-loop determinants of fluctuations of the M2 brane, and extract the conformal anomaly coefficient of the spherical surface to order N0. We also briefly discuss the RG flow from the non-supersymmetric to the 1/2-BPS defect operator, and its consistency with a “b-theorem” for the defect CFT. Starting with the M2 brane action, we then use AdS3 Witten diagrams to compute the 4-point functions of the elementary bosonic insertions on the surface operator, and extract some of the defect CFT data from the OPE. The 4-point function is shown to satisfy superconformal Ward identities, and we discuss a related sub- sector of “twisted” scalar insertions, whose correlation functions are constrained by the residual superconformal symmetry.

Vacuum structure of large N QCD3 from holography

We study the vacuum structure of three-dimensional SU(N ) gauge theory coupled to a Chern-Simons term at level k and to F fundamental Dirac fermions. We use a large N holographic description based on a D3/D7 system in type IIB string theory compactified on a supersymmetry breaking circle. The multiple vacua of the theory and the transitions between them are nicely captured by the dual holographic background. The resulting phase diagram, which we derive both at leading and first subleading orders in the 1/N expansion, shows a rich structure where topological field theories, non-linear sigma models and first-order phase transitions appear.

Gravitational anomalies in nAdS2/nCFT1

We revisit the holographic description of the near horizon geometry of the BTZ black hole in AdS3 gravity, with a gravitational Chern–Simons term included. After a dimensional reduction of the three dimensional theory, we use the framework of nAdS2/nCFT1 to describe the near horizon physics. This setup allows us to contrast the role of the gravitational and conformal anomaly inherited from AdS3/CFT2 in the symmetry breaking mechanism of nAdS2/nCFT1. Our results display how boundary conditions in the 3D spacetime, combined with the gravitational anomaly, affect the holographic description of the near horizon of the black hole relative to the physics near the AdS3 boundary.

Studies of boundary entropy in AdS/BCFT

In this paper we review the AdS/BCFT proposal of Takayanagi for holographic description of systems with boundaries, in particular, boundary conformal field theories (BCFTs). Motivated by better understanding of the proposed duality we employ entanglement entropy as a probe of familiar properties of impurities and defects. Using the dual gravity description, we check that in two spacetime dimensions the impurity entropy does not depend on a particular state of the theory, which is a well-known CFT result. In three dimensions different, and not necessarily equivalent, definitions of the defect entropy can be given. We compute the entanglement entropy of a line defect at finite temperature and compare it with earlier calculations of the thermodynamical entropy. The results indicate that the entanglement entropy flows to the definition of the entropy as the Bekenstein–Hawking entropy associated to a portion of the black horizon, which we call impurity ‘shadow’. Geometric configurations, which we discuss, provide examples of RG flows of the defect entropies. We outline the connection between the geometric picture of the RG flows and examples of lattice calculations. We also discuss some new generalizations of the AdS/BCFT geometries.

Any room left for technicolor? Holographic studies of NJL assisted technicolor

We use a holographic description of technicolor dynamics to study gauge theories that only break chiral symmetry when aided by a strong four fermion interaction. These Nambu-Jona-Lasinio (NJL) assisted technicolor models provide examples of different dynamics from walking technicolor which can, by tuning, generate a light higgs like $\sigma$ meson. We compute the vector meson ($\rho$) and axial vector meson (A) spectrum for a variety of models with techni-quarks in the fundamental representation, enlarging the available parameter space over a previous analysis of walking theories. These predictions determine the parameter space of a low energy effective description where LHC constraints from dilepton channels have already been applied. Many of the models with low numbers of electroweak doublets still lie beyond current constraints and motivate exploration of new signatures beyond dilepton for LHC and a 100 TeV proton collider.

Non-Abelian anomalies in multi-Weyl semimetals

We construct the effective field theory for time-reversal symmetry breaking multi-Weyl semimetals (mWSMs), composed of a single pair of Weyl nodes of (anti-)monopole charge $n$, with $n=1,2,3$ in crystalline environment. From both the continuum and lattice models, we show that a mWSM with $n>1$ can be constructed by placing $n$ flavors of linearly dispersing simple Weyl fermions (with $n=1$) in a bath of an $SU(2)$ non-Abelian static background gauge field. Such an $SU(2)$ field preserves certain crystalline symmetry (four-fold rotational or $C_4$ in our construction), but breaks the Lorentz symmetry, resulting in nonlinear band spectra (namely, $E \sim (p^2_x + p^2_y)^{n/2}$, but $E \sim |p_z|$, for example, where momenta ${\bf p}$ is measured from the Weyl nodes). Consequently, the effective field theory displays $U(1) \times SU(2)$ non-Abelian anomaly, yielding anomalous Hall effect, its non-Abelian generalization, and various chiral conductivities. The anomalous violation of conservation laws is determined by the monopole charge $n$ and a specific algebraic property of the $SU(2)$ Lie group, which we further substantiate by numerically computing the regular and "isospin" densities from the lattice models of mWSMs. These predictions are also supported from a strongly coupled (holographic) description of mWSMs. Altogether our findings unify the field theoretic descriptions of mWSMs of arbitrary monopole charge $n$ (featuring $n$ copies of the Fermi arc surface states), predict signatures of non-Abelian anomaly in table-top experiments, and pave the route to explore anomaly structures for multi-fold fermions, transforming under arbitrary half-integer or integer spin representations.