Dual Field Theory Research Articles

Flat-space holography and correlators of Robinson–Trautman stress tensor

We propose a quasi-local stress tensor for the four-dimensional asymptotically flat Robinson–Trautman geometries by taking the flat-space limit from the corresponding asymptotically AdS solutions. This stress tensor results in the correct charges of the generators of BMS symmetry if we define conformal infinity by an anisotropic scaling of the metric components. Using flat-space holography this stress tensor is related to expectation values of the stress tensor in a dual field theory called BMS-invariant field theory (BMSFT). We also calculate the two and three point functions of the proposed stress tensor.

Evolution of holographic complexity near critical point

The holographic complexity has been studied in a background which includes a critical point in the dual field theory. We have examined how the complexity rate and the saturation time of dynamical variables in the theory behave as one moves towards the critical point. Two significant results of our analysis are that (i) it takes more time for the complexity in field theory dual to become time dependent as one moves away from the critical point and (ii) near the critical point the complexity starts evolving linearly in time sooner than the other points away from it. We also observe different behaviour for complexity rate in action and volume prescriptions. In action prescription we have used the time scales in theory to obtain the dynamical critical exponent and interestingly have observed that different time scales produce the same value up to very small error.

Novel color superconducting phases of mathcal{N} = 4 super Yang-Mills at strong coupling

We revisit the large-Nc phase diagram of mathcal{N} = 4 super Yang-Mills theory at finite R-charge density and strong coupling, by means of the AdS/CFT correspondence. We conjecture new phases that result from a black hole shedding some of its charge through the nucleation of probe color D3-branes that remain at a finite distance from the black hole when the dual field theory lives on a sphere. In the corresponding ground states the color group is partially Higgsed, so these phases can be identified as having a type of color superconductivity. The new phases would appear at intermediate values of the R-charge chemical potential and we expect them to be metastable but long-lived in the large-Nc limit.

Lattice construction of duality with non-Abelian gauge fields in 2+1D

The lattice construction of Euclidean path integrals has been a successful approach of deriving 2+1D field theory dualities with a U$(1)$ gauge field. In this work, we generalize this lattice construction to dualities with non-Abelian gauge fields. We construct the Euclidean spacetime lattice path integral for a theory with strongly-interacting $SO(3)$ vector bosons and Majorana fermions coupled to an $SO(3)$ gauge field and derive an exact duality between this theory and the theory of a free Majorana fermion on the spacetime lattice. We argue that this lattice duality implies the desired infrared duality between the field theory with an $SO(3)$ vector critical boson coupled to an $SO(3)_1$ Chern-Simons gauge theory, and a free massless Majorana fermion in 2+1D. We also generalize the lattice construction of dualities to models with $O(3)$ gauge fields.

On N-spike strings in conformal gauge with NS-NS fluxes

The AdS3 × S3 string sigma model supported both by NS-NS and R-R fluxes has become a well known integrable model, however a putative dual field theory description remains incomplete. We study the anomalous dimensions of twist operators in this theory via semiclassical string methods. We describe the construction of a multi-cusp closed string in conformal gauge moving in AdS3 with fluxes, which supposedly is dual to a general higher twist operator. After analyzing the string profiles and conserved charges for the string, we find the exact dispersion relation between the charges in the ‘long’ string limit. This dispersion relation in leading order turns out to be similar to the case of pure RR flux, with the coupling being scaled by a factor that depends on the amount of NS-NS flux turned on. We also analyse the case of pure NS flux, where the dispersion relation simplifies considerably. Furthermore, we discuss the implications of these results at length.

Geometry of mathcal{I} -extremization and black holes microstates

The entropy of a class of asymptotically AdS4 magnetically charged BPS black holes can be obtained by extremizing the topologically twisted index of the dual three-dimensional field theory. This principle is known as mathcal{I} -extremization. A gravitational dual of mathcal{I} -extremization for a class of theories obtained by twisted compactifications of M2-branes living at a Calabi-Yau four-fold has been recently proposed. In this paper we investigate the relation between the two extremization principles. We show that the two extremization procedures are equivalent for theories without baryonic symmetries, which include ABJM and the theory dual to the non-toric Sasaki-Einstein manifold V5,2. We then consider a class of quivers dual to M2-branes at toric Calabi-Yau four-folds for which the mathcal{I} -functional can be computed in the large N limit, and depends on three mesonic fluxes. We propose a gravitational dual for this construction, that we call mesonic twist, and we show that the gravitational extremization problem and mathcal{I} -extremization are equivalent. We comment on more general cases.

Integrability and holographic aspects of six-dimensional mathcal{N}=left(1, 0right) superconformal field theories

In the framework of six-dimensional conformal field theories with mathcal{N}=left(1, 0right) supersymmetry we develop the map between the holographic description, the field theoretical description and the associated Hanany-Witten set-ups. General expressions that calculate various observables are presented. The study of string solitons singles out a special background of Massive IIA on which we show (by explicitly finding a Lax pair) that the Neveu-Schwarz part of the string sigma model is classically integrable. We study the particular dual conformal field theory and compute some of its observables.

Holographic signatures of resolved cosmological singularities

The classical gravity approximation is often employed in AdS/CFT to study the dual field theory, as it allows for many computations. A drawback is however the generic presence of singularities in classical gravity, which limits the applicability of AdS/CFT to regimes where the singularities are avoided by bulk probes, or some other form of regularisation is applicable. At the same time, quantum gravity is expected to resolve those singularities and thus to extend the range of applicability of AdS/CFT also in classically singular regimes. This paper exemplifies such a computation. We use an effective quantum corrected Kasner-AdS metric inspired by results from non-perturbative canonical quantum gravity to compute the 2-point correlator in the geodesic approximation for a negative Kasner exponent. The correlator derived in the classical gravity approximation has previously been shown to contain a pole at finite distance as a signature of the singularity. Using the quantum corrected metric, we show explicitly how the pole is resolved and that a new subdominant long-distance contribution to the correlator emerges, caused by geodesics passing arbitrarily close to the resolved classical singularity. In order to compute analytically in this paper, two key simplifications in the quantum corrected metric are necessary. They are lifted in a companion paper using numerical techniques, leading to the same qualitative results.

Toric geometry and the dual of \u2110-extremization

We consider d = 3, mathcal{N}=2 gauge theories arising on membranes sitting at the apex of an arbitrary toric Calabi-Yau 4-fold cone singularity that are then further compactified on a Riemann surface, Σg , with a topological twist that preserves two supersymmetries. If the theories flow to a superconformal quantum mechanics in the infrared, then they have a D = 11 supergravity dual of the form AdS2 × Y9, with electric four-form flux and where Y9 is topologically a fibration of a Sasakian Y7 over Σg . These D = 11 solutions are also expected to arise as the near horizon limit of magnetically charged black holes in AdS4 × Y7, with a Sasaki-Einstein metric on Y7. We show that an off-shell entropy function for the dual AdS2 solutions may be computed using the toric data and Kähler class parameters of the Calabi-Yau 4-fold, that are encoded in a master volume, as well as a set of integers that determine the fibration of Y7 over Σg and a Kähler class parameter for Σg . We also discuss the class of supersymmetric AdS3 × Y7 solutions of type IIB supergravity with five-form flux only in the case that Y7 is toric, and show how the off-shell central charge of the dual field theory can be obtained from the toric data. We illustrate with several examples, finding agreement both with explicit supergravity solutions as well as with some known field theory results concerning ℐ-extremization.

Adventure in Topological Phase Transitions in 3+1 -D: Non-Abelian Deconfined Quantum Criticalities and a Possible Duality

Continuous quantum phase transitions beyond the conventional paradigm of fluctuations of a symmetry-breaking order parameter are challenging for theory. These phase transitions often involve emergent deconfined gauge fields at the critical points as demonstrated in phase transitions between different broken-symmetry states of 2+1-dimensional quantum magnets, as well as those between symmetry-protected topological (SPT) phases. In this paper, we present several examples of deconfined quantum critical points between SPT phases in 3+1-D for both bosonic and fermionic systems. These critical theories can be formulated as non-Abelian gauge theories either in the infrared-free regime or in the conformal window when they flow to the Banks-Zaks fixed points. We explicitly demonstrate several interesting quantum critical phenomena. We describe situations in which the same phase transition allows for multiple universality classes controlled by distinct fixed points. We exhibit the possibility—which we dub “unnecessary quantum critical points”—of stable generic continuous phase transitions within the same phase. We present examples of interaction-driven, band-theory-forbidden, continuous phase transitions between two distinct band insulators. The understanding we develop leads us to suggest an interesting possible 3+1-D field theory duality between SU(2) gauge theory coupled to one massless adjoint Dirac fermion and the theory of a single massless Dirac fermion augmented by a decoupled topological field theory.3 MoreReceived 2 January 2019Revised 2 April 2019DOI:https://doi.org/10.1103/PhysRevX.9.021034Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCritical phenomenaDualities in field theoryNon-Abelian gauge theoriesSymmetry protected topological statesTopological insulatorsTopological phase transitionCondensed Matter, Materials & Applied PhysicsParticles & Fields

Black hole microstate counting in Type IIB from 5d SCFTs

We use recently established AdS6/CFT5 dualities to count the microstates of magnetically charged AdS6 × S2 × Σ black holes in Type IIB. The near-horizon limit is described by solutions with AdS2 × {varSigma}_{{mathfrak{g}}_1} × {varSigma}_{{mathfrak{g}}_2} × S2 × Σ geometry, where {varSigma}_{{mathfrak{g}}_i} are Riemann surfaces of constant curvature and Σ is a further Riemann surface over which the geometry is warped. Our results show that the topologically twisted indices of the proposed dual superconformal field theories precisely reproduce the Bekenstein-Hawking entropy of this class of black holes. This provides further support for a prescription to compute fivedimensional topologically twisted indices put forth recently, and for the proposed dualities. We confirm the N4 scaling found in the sphere partition functions and extend previous matches of sphere partition functions to AdS6 solutions with monodromy.

Transplanckian axion monodromy!?

We show that warped throats of the Klebanov-Strassler kind, regarded as 5d flux compactifications on Sasaki-Einstein manifolds X5, describe fully backreacted solutions of transplanckian axion monodromy. We show that the asymptotic Klebanov-Tseytlin solution features a 5d axion physically rolling through its dependence on an spatial coordinate, and traversing arbitrarily large distances in field space. The solution includes the backreaction on the breathing mode of the compactification space and on the vacuum energy, which yields a novel form of flattening. We establish the description of the system in terms of an effective 5d theory for the axion, and verify its validity in transplanckian regimes. In this context, rolling axion monodromy configurations with limited field space range would correspond, in the holographic dual field theory, to duality walls, which admit no embedding in string theory so far. We present an identical realization of transplanckian axion monodromy in 4d in fluxed version of AdS4 × X7. We speculate that similar models in which the axion rolls in the time direction naturally correspond to embedding the same mechanism in de Sitter vacua, thus providing a natural arena for large field inflation, and potentially linking the swampland de Sitter and distance conjectures.

Holographic Schwinger-Keldysh effective field theories

We construct a holographic dual of the Schwinger-Keldysh effective action for the dissipative low-energy dynamics of relativistic charged matter at strong coupling in a fixed thermal background. To do so, we use a mixed signature bulk spacetime whereby an eternal asymptotically anti-de Sitter black hole is glued to its Euclidean counterpart along an initial time slice in a way to match the desired double-time contour of the dual field theory. Our results are consistent with existing literature and can be regarded as a fully-ab initio derivation of a Schwinger-Keldysh effective action. In addition, we provide a simple infrared effective action for the near horizon region that drives all the dissipation and can be viewed as an alternative to the membrane paradigm approximation.

WdW-patches in AdS3 and complexity change under conformal transformations II

We study the null-boundaries of Wheeler-de Witt (WdW) patches in three dimensional Poincaré-AdS, when the selected boundary timeslice is an arbitrary (non-constant) function, presenting some useful analytic statements about them. Special attention will be given to the piecewise smooth nature of the null-boundaries, due to the emergence of caustics and null-null joint curves. This is then applied, in the spirit of one of our previous papers, to the problem of how the complexity of the CFT2 groundstate changes under a small local conformal transformation according to the action (CA) proposal. In stark contrast to the volume (CV) proposal, where this change is only proportional to the second order in the infinitesimal expansion parameter σ, we show that in the CA case we obtain terms of order σ and even σ log(σ). This has strong implications for the possible field-theory duals of the CA proposal, ruling out an entire class of them.

Holographic entanglement negativity conjecture for adjacent intervals in AdS3/CFT2

We propose a holographic entanglement negativity conjecture involving the bulk geometry, for mixed states of adjacent intervals in (1+1)-dimensional dual conformal field theories through the AdS/CFT correspondence. The holographic entanglement negativity is obtained from a specific algebraic sum of the geodesics anchored on respective intervals on the boundary which reduces to the holographic mutual information between them. Utilizing our conjecture we obtain the entanglement negativity of adjacent intervals in zero and finite temperature (1+1)-dimensional holographic conformal field theories dual to the bulk AdS3 vacuum and the Euclidean BTZ black hole respectively. Our holographic conjecture exactly reproduces the conformal field theory results obtained through the replica technique, in the large central charge limit. We briefly elucidate the corresponding issue for the AdSd+1/CFTd scenario.

Generalised global symmetries in holography: magnetohydrodynamic waves in a strongly interacting plasma

We begin the exploration of holographic duals to theories with generalised global (higher-form) symmetries. In particular, we focus on the case of magnetohydrodynamics (MHD) in strongly coupled plasmas by constructing and analysing a holographic dual to a recent, generalised global symmetry-based formulation of dissipative MHD. The simplest holographic dual to the effective theory of MHD that was proposed as a description of plasmas with any equation of state and transport coefficients contains dynamical graviton and two-form gauge field fluctuations in a magnetised black brane background. The dual field theory, which is closely related to the large-Nc, mathcal{N} = 4 supersymmetric Yang-Mills theory at (infinitely) strong coupling, is, as we argue, in our setup coupled to a dynamical U(1) gauge field with a renormalisation condition-dependent electromagnetic coupling. After constructing the holographic dictionary for gauge-gravity duals of field theories with higher-form symmetries, we compute the dual equation of state and transport coefficients, and for the first time analyse phenomenology of MHD waves in a strongly interacting, dense plasma with a (holographic) microscopic description. From weak to extremely strong magnetic fields, several predictions for the behaviour of Alfvén and magnetosonic waves are discussed.

Adding new branches to the \u201cChristmas tree\u201d of the quasinormal spectrum of black branes

In holography, quasinormal spectra of black branes coincide with the poles of retarded finite-temperature correlation functions of a dual quantum field theory in the limit of infinite number of relevant degrees of freedom such as colours. For asymptotically antide Sitter backgrounds, the spectra form a characteristic pattern in the complex frequency plane, colloquially known as the “Christmas tree”. At infinite coupling, the tree has only one pair of branches. At large but finite coupling, the branches become more dense and lift up towards the real axis, consistent with the expectation of forming a branch cut in the limit of zero coupling. However, it is known that at zero coupling, the corresponding correlators generically have not one but multiple branch cuts separated by intervals proportional to the Matsubara frequency. This suggests the existence of multiple branches of the “Christmas tree” spectrum in dual gravity. In this note, we show numerically how these additional branches of the spectrum can emerge from the dual gravitational action with higher-derivative terms. This phenomenon appears to be robust, yet, reproducing the expected weak coupling behaviour of the correlators quantitatively implies the existence of certain constraints on the coefficients of the higher-derivative terms of the dual gravity theory.

Holographic fermionic spectrum with Weyl correction

We study the fermionic spectrum with Weyl correction, which exhibits the non-Fermi liquid behavior. Also, we find that both the height of the peak of the fermionic spectrum and the dispersion relation exhibit a nonlinearity with the variety of the Weyl coupling parameter [Formula: see text], which means that such nonlinearity may be ascribed to one of the Maxwell field. Another important property of this system is that for [Formula: see text], the degree of the deviation from Fermi liquid is heavier than that for [Formula: see text]. It indicates that there is a transition of coupling strength in the dual boundary field theory.

CLASSICAL AND QUANTUM INTEGRABLE SIGMA MODELS. RICCI FLOW, “ NICE DUALITY” AND PERTURBED RATIONAL CONFORMAL FIELD THEORIES

We consider classical and quantum integrable sigma models and their relations with the solutions of renormalization group equations. We say that an integrable sigma model possesses the nice duality property if the dual quantum field theory has the weak coupling region. As an example, we consider the deformed $CP(n-1)$ sigma model with additional quantum degrees of freedom. We formulate the dual integrable field theory and use perturbed conformal field theory, perturbation theory, $S$-matrix, Bethe Ansatz and renormalization group methods to show that this field theory has the nice duality property. We consider also an alternative approach to the analysis of sigma models on the deformed symmetric spaces, based on the perturbed rational conformal field theories.

Nonlinear perturbation of black branes at large D

The Einstein equations describing the black brane dynamics both in Minkowski and AdS background were recently recast in the form of coupled diffusion equations in the large‐D(imension) limit. Using such results in the literature, we formulate a higher‐order perturbation theory of black branes in time domain and present the general form of solutions for arbitrary initial conditions. For illustrative purposes, the solutions up to the first or second order are explicitly written down for several kind of initial conditions, such as a Gaussian wave packet, shock wave, and rather general superposed sinusoidal waves. These could be the first examples describing the nontrivial evolution of black brane horizons in the time domain. In particular, we learn some interesting aspects of black brane dynamics, such as the Gregory–Laflamme (GL) instability and nonequilibrium steady state (NESS). The formalism presented here would be applicable to the analysis of various black branes and their holographically dual field theories.