Dual Gravity Description Research Articles

Excitations of bubbling geometries for line defects

The half-Bogomolny-Prasad-Sommerfield (BPS) Wilson line operators in the irreducible representations labeled by the Young diagrams for N=4 U(N) super Yang-Mills theory have gravity dual descriptions. When the number k of boxes of the diagram grows as k∼N2, the bubbling geometries emerge. We evaluate the spectra of quantum fluctuations on the particular bubbling geometry involving the largest degeneracy from the large N and large k limit of the supersymmetric indices decorated by the Wilson lines. The spectra of excitations over multiparticle 1/8- and 1/2-BPS states agree with the numbers of conjugacy classes of general linear group over finite fields while degeneracies of single particle BPS states are given by the general necklace polynomial. The bubbling geometry exhibits a new class of asymptotic degeneracy of states. Published by the American Physical Society 2024

Holographic odderon at TOTEM?

We consider the contribution of the Odderon to diffractive pp and pp¯ elastic scattering at large center of mass energy. We identify the Odderon and Pomeron with the Reggeized 1±− and 2++ glueballs in the bulk, respectively. We use for the gravity dual description the repulsive wall model, to account for the proper Gribov diffusion for off-forward scattering. The eikonalized and unitarized amplitudes exhibit a vanishingly small rho-parameter, and a slope parameter fixed by twice the closed string slope. The results for the differential and total cross sections are compared to the empirical results reported recently by the TOTEM collaboration. Published by the American Physical Society 2024

Applicability of holography in thermodynamic equilibrium

For a strongly coupled system that has a gravity dual description, we show that the standard holographic dictionary yields a non-negative susceptibility when the system is in thermodynamic equilibrium and the correlation function is absolutely integrable. When the system has no spontaneous condensation or has a spontaneous ${\mathbb{Z}}_{2}$-symmetry breaking, we find that the ``trace energy condition'' is violated in many cases. There is a normalized grand potential density that is monotonic as accessing to lower scales, providing a candidate $c$-function characterizing the number of effective degrees of freedom. Finally, we discuss a ``paradox'' raising by the negative susceptibility in holography and its resolution.

Holography, 1-form symmetries, and confinement

We study confinement in 4d $\mathcal{N}=1$ $SU(N)$ Super-Yang Mills (SYM) from a holographic point of view, focusing on the 1-form symmetry and its relation to chiral symmetry breaking. In the 5d supergravity dual, obtained by truncation of the Klebanov-Strassler solution, we identify the topological couplings that determine the 1-form symmetry and its 't Hooft anomalies. One such coupling is a mixed 0-form/1-form symmetry anomaly closely related to chiral symmetry breaking in gapped confining vacua. From the dual gravity description we also identify the infra-red (IR) 4d topological field theory (TQFT), which realises chiral symmetry breaking and matches the mixed anomaly. Finally, complementing this, we derive the chiral and mixed anomalies from the Little String Theory realization of pure SYM.

Path integral optimization from Hartle-Hawking wave function

We propose a gravity dual description of the path-integral optimization in conformal field theories arXiv:1703.00456, using Hartle-Hawking wave functions in anti-de Sitter spacetimes. We show that the maximization of the Hartle-Hawking wave function is equivalent to the path-integral optimization procedure. Namely, the variation of the wave function leads to a constraint, equivalent to the Neumann boundary condition on a bulk slice, whose classical solutions reproduce metrics from the path-integral optimization in conformal field theories. After taking the boundary limit of the semi-classical Hartle-Hawking wave function, we reproduce the path-integral complexity action in two dimensions as well as its higher and lower dimensional generalizations. We also discuss an emergence of holographic time from conformal field theory path-integrals.

Towards precision holography

A minimal requirement for any strongly coupled gauge field theory to have a classical dual bulk gravity description is that one should in principle be able to recover the full geometry as encoded on the asymptotics of the spacetime. Even this requirement cannot be fulfilled with arbitrary precision simply due to the fact that the boundary data is inherently noisy. We present a statistical approach to bulk reconstruction from entanglement entropy measurements, which handles the presence of noise in a natural way. Our approach therefore opens up a novel gateway for precision holography.

Qubit construction in 6D SCFTs

We consider a class of 6D superconformal field theories (SCFTs) which have a large N limit and a semi-classical gravity dual description. Using the quiver-like structure of 6D SCFTs we study a subsector of operators protected from large operator mixing. These operators are characterized by degrees of freedom in a one-dimensional spin chain, and the associated states are generically highly entangled. This provides a concrete realization of qubit-like states in a strongly coupled quantum field theory. Renormalization group flows triggered by deformations of 6D UV fixed points translate to specific deformations of these one-dimensional spin chains. We also present a conjectural spin chain Hamiltonian which tracks the evolution of these states as a function of renormalization group flow, and study qubit manipulation in this setting. Similar considerations hold for theories without AdS duals, such as 6D little string theories and 4D SCFTs obtained from compactification of the partial tensor branch theory on a T2.

Scattering length in holographic confining theories

The low-energy effective theory description of a confining theory, such as QCD, is constructed including local interactions between hadrons organized in a derivative expansion. This kind of approach also applies more generically to theories with a mass gap, once the relevant low energy degrees of freedom are identified. The strength of local interactions in the effective theory is determined by the low momentum expansion of scattering amplitudes, with the scattering length capturing the leading order. We compute the main contribution to the scattering length between two spin-zero particles in strongly coupled theories using the gauge/gravity duality. We study two different theories with a mass gap: a massive deformation of ${\cal N}=4$ super Yang-Mills theory (${\cal N}=1^*$) and a non-supersymmetric five-dimensional theory compactified on a circle. These cases have a different realization of the mass gap in the dual gravity description: the former is the well-known GPPZ singular solution and the latter a smooth $AdS_6$ soliton geometry. Despite disparate gravity duals, we find that the scattering lengths have strikingly similar functional dependences on the masses of the particles and on the conformal dimension of the operators that create them. This evinces universal behavior in the effective description of gapped strongly coupled theories beyond what is expected from symmetry considerations alone.

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.

On non-supersymmetric conformal manifolds: field theory and holography

We discuss the constraints that a conformal field theory should enjoy to admit exactly marginal deformations, i.e. to be part of a conformal manifold. In particular, using tools from conformal perturbation theory, we derive a sum rule from which one can extract restrictions on the spectrum of low spin operators and on the behavior of OPE coefficients involving nearly marginal operators. We then focus on conformal field theories admitting a gravity dual description, and as such a large-N expansion. We discuss the relation between conformal perturbation theory and loop expansion in the bulk, and show how such connection could help in the search for conformal manifolds beyond the planar limit. Our results do not rely on supersymmetry, and therefore apply also outside the realm of superconformal field theories.

A construction of quarter BPS coherent states and Brauer algebras

BPS coherent states closely resemble semiclassical states and they have gravity dual descriptions in terms of semiclassical geometries. The half BPS coherent states have been well studied, however less is known about quarter BPS coherent states. Here we provide a construction of quarter BPS coherent states. They are coherent states built with two matrix fields, generalizing the half BPS case. These states are both the eigenstates of annihilation operators and in the kernel of dilatation operator. Another useful labeling of quarter BPS states is by representations of Brauer algebras and their projection onto a subalgebra $\mathbb{C}[S_n\times S_m]$. Here, the Schur-Weyl duality for the Walled Brauer algebra plays an important role in organizing the operators. One interesting subclass of these Brauer states are labeled by representations involving two Young tableaux. We obtain the overlap between quarter BPS Brauer states and quarter BPS coherent states, where the Schur polynomials are used. We also derive superposition formulas transforming a truncated version of quarter BPS coherent states to quarter BPS Brauer states. The entanglement entropy of Brauer states as well as the overlap between Brauer states and squeezed states are also computed.

Towards timelike singularity via AdS dual

It is well known that Kasner geometry with spacelike singularity can be extended to bulk AdS-like geometry, furthermore, one can study field theory on this Kasner space via its gravity dual. In this paper, we show that there exists a Kasner-like geometry with timelike singularity for which one can construct a dual gravity description. We then study various extremal surfaces including spacelike geodesics in the dual gravity description. Finally, we compute correlators of highly massive operators in the boundary field theory with a geodesic approximation.

Conformal Janus on Euclidean sphere

We interpret Janus as an interface in a conformal field theory and study its properties. The Janus is created by an exactly marginal operator and we study its effect on the interface conformal field theory on the Janus. We do this by utilizing the AdS/CFT correspondence. We compute the interface free energy both from leading correction to the Euclidean action in the dual gravity description and from conformal perturbation theory in the conformal field theory. We find that the two results agree each other and that the interface free energy scales precisely as expected from the conformal invariance of the Janus interface.

Physical effects of the gravitational Θ-parameter

We describe the effect of the gravitational [Formula: see text]-parameter on the behavior of the stretched horizon of a black hole in [Formula: see text]-dimensions. The gravitational [Formula: see text]-term is a total derivative, however, it affects the transport properties of the horizon. In particular, the horizon acquires a third-order parity violating, dimensionless transport coefficient which affects the way localized perturbations scramble on the horizon. In the context of the gauge/gravity duality, the [Formula: see text]-term induces a nontrivial contact term in the energy–momentum tensor of a [Formula: see text]-dimensional large-N gauge theory, which admits a dual gravity description. As a consequence, the dual gauge theory in the presence of the [Formula: see text]-term acquires the same third-order parity violating transport coefficient.

Far-from-equilibrium dynamics of a strongly coupled non-Abelian plasma with non-zero charge density or external magnetic field

Using holography, we study the evolution of a spatially homogeneous, far from equilibrium, strongly coupled $$ \mathcal{N}=4 $$ supersymmetric Yang-Mills plasma with a non-zero charge density or a background magnetic field. This gauge theory problem corresponds, in the dual gravity description, to an initial value problem in Einstein-Maxwell theory with homogeneous but anisotropic initial conditions. We explore the dependence of the equilibration process on different aspects of the initial departure from equilibrium and, while controlling for these dependencies, examine how the equilibration dynamics are affected by the presence of a non-vanishing charge density or an external magnetic field. The equilibration dynamics are remarkably insensitive to the addition of even large chemical potentials or magnetic fields; the equilibration time is set primarily by the form of the initial departure from equilibrium. For initial deviations from equilibrium which are well localized in scale, we formulate a simple model for equilibration times which agrees quite well with our results.

Holographic thermalization with a chemical potential from Born-Infeld electrodynamics

The problem of holographic thermalization in the framework of Einstein gravity coupled to Born-Infeld nonlinear electrodynamics is investigated. We use equal time two-point correlation functions and expectation values of Wilson loop operators in the boundary quantum field theory as probes of thermalization, which have dual gravity descriptions in terms of geodesic lengths and minimal area surfaces in the bulk spacetime. The full range of values of the chemical potential per temperature ratio μ/T on the boundary is explored. The numerical results show that the effect of the charge on the thermalization time is similar to the one obtained with Maxwell electrodynamics, namely the larger the charge the later thermalization occurs. The Born-Infeld parameter, on the other hand, has the opposite effect: the more nonlinear the theory is, the sooner it thermalizes. We also study the thermalization velocity and how the parameters affect the phase transition point separating the thermalization process into an accelerating phase and a decelerating phase.

The [formula omitted] gravity function of the Linde quintessence

We calculate the f(R) gravity function in the dual gravity description of the quintessence model with a quadratic (Linde) scalar potential and a positive cosmological constant. We find that in the large curvature regime relevant to chaotic inflation in Early Universe, the dual f(R) gravity is well approximated by the (matter) loop-corrected Starobinsky inflationary model. In the small curvature regime relevant to dark energy in the Present Universe, the f(R) gravity function reduces to the Einstein–Hilbert one with a positive cosmological constant.

Skewness dependence of generalized parton distributions, conformal OPE, and the AdS/CFT correspondence

The traditional idea of the Pomeron/Reggeon description for hadron scattering is now being given theoretical foundation in gravity dual descriptions, where Pomeron corresponds to an exchange of spin-$j\ensuremath{\in}2\mathbb{Z}$ states in the graviton trajectory. Deeply virtual Compton scattering (DVCS) is essentially a two-to-two scattering process of a hadron and a photon, and hence one should be able to study nonperturbative aspects (the generalized parton distribution [GPD]) of this process by the Pomeron/Reggeon process in gravity dual. We find, however, that even one of the most developed formulations of gravity dual, Pomeron [Brower-Polchinski-Strassler-Tan (BPST), 2006], is not able to capture skewness dependence of GPD properly. Therefore, we compute Reggeon wave functions on ${\mathrm{AdS}}_{5}$ so that the formalism of BPST can be generalized. These wave functions are used to determine the DVCS amplitude, bring it to the form of conformal operator product expansion/collinear factorization, and extract a holographic model of GPD, which naturally fits into the framework known as ``dual parametrization,'' or the ``(conformal) collinear factorization approach.''

Deconfinement transition as black hole formation by the condensation of QCD strings

We argue that the deconfinement transition of large-$N$ Yang-Mills theory is the condensation of very long and self-intersecting chromo-electric flux strings (QCD string), which is analogous to the formation of a black hole in string theory. We do this by using lattice gauge theory and matrix models. As evidence, we derive an analytic formula for the deconfinement temperature in the strong coupling limit and confirm it numerically. Dual gravity descriptions interpreted in this manner should make it possible to understand the details of the formation of black holes in terms of fundamental strings. We argue that very simple matrix models capture the essence of the formation of black holes.

Universality of Abrupt Holographic Quenches

We make an analytic investigation of rapid quenches of relevant operators in d-dimensional holographic conformal field theories, which admit a dual gravity description. We uncover a universal scaling behavior in the response of the system, which depends only on the conformal dimension of the quenched operator in the vicinity of the ultraviolet fixed point of the theory. Unless the amplitude of the quench is scaled appropriately, the work done on a system during the quench diverges in the limit of abrupt quenches for operators with dimension (d/2)≤Δ<d.