Dual Field Theory Research Articles

Establishing strongly-coupled 3D AdS quantum gravity with Ising dual using all-genus partition functions

We study 3D pure Einstein quantum gravity with negative cosmological constant, in the regime where the AdS radius l is of the order of the Planck scale. Specifically, when the Brown-Henneaux central charge c = 3l/2GN (GN is the 3D Newton constant) equals c = 1/2, we establish duality between 3D gravity and 2D Ising conformal field theory by matching gravity and conformal field theory partition functions for AdS spacetimes with general asymptotic boundaries. This duality was suggested by a genus-one calculation of Castro et al. [Phys. Rev. D85 (2012) 024032]. Extension beyond genus-one requires new mathematical results based on 3D Topological Quantum Field Theory; these turn out to uniquely select the c = 1/2 theory among all those with c < 1, extending the previous results of Castro et al. Previous work suggests the reduction of the calculation of the gravity partition function to a problem of summation over the orbits of the mapping class group action on a “vacuum seed”. But whether or not the summation is well-defined for the general case was unknown before this work. Amongst all theories with Brown-Henneaux central charge c < 1, the sum is finite and unique only when c = 1/2, corresponding to a dual Ising conformal field theory on the asymptotic boundary.

Reggeon field theory and self duality: making ends meet

Motivated by the question of unitarity of Reggeon Field Theory, we use the effective field theory philosophy to find possible Reggeon Field Theory Hamiltonians HRFT. We require that HRFT is self dual, reproduce all known limits (dilute-dense and dilute-dilute) and exhibits all the symmetries of the JIMWLK Hamiltonian. We find a family of Hamiltonians which satisfy all the above requirements. One of these is identical in form to the so called “diamond action” discussed in [67, 68]. However we show by explicit calculation that the so called “diamond condition” is not satisfied beyond leading perturbative order.

S-duality wall of SQCD from Toda braiding

Exact field theory dualities can be implemented by duality domain walls such that passing any operator through the interface maps it to the dual operator. This paper describes the S-duality wall of four-dimensional mathcal{N} = 2 SU(N) SQCD with 2N hypermultiplets in terms of fields on the defect, namely three-dimensional mathcal{N} = 2 SQCD with gauge group U(N − 1) and 2N flavours, with a monopole superpotential. The theory is self-dual under a duality found by Benini, Benvenuti and Pasquetti, in the same way that T[SU(N)] (the S-duality wall of mathcal{N} = 4 super Yang-Mills) is self-mirror. The domain-wall theory can also be realized as a limit of a USp(2N − 2) gauge theory; it reduces to known results for N = 2. The theory is found through the AGT correspondence by determining the braiding kernel of two semi-degenerate vertex operators in Toda CFT.

Fermionic dualities with axial gauge fields

The dualities that map hard-to-solve, interacting theories to free, non-interacting ones often trigger a deeper understanding of the systems to which they apply. However, simplifying assumptions such as Lorentz invariance, low dimensionality, or the absence of axial gauge fields, limit their application to a broad class of systems, including topological semimetals. Here we derive several axial field theory dualities in 2+1 and 3+1 dimensions by developing an axial slave-rotor approach capable of accounting for the axial anomaly. Our 2+1-dimensional duality suggests the existence of a dual, critical surface theory for strained three-dimensional non-symmorphic topological insulators. Our 3+1-dimensional duality maps free Dirac fermions to Dirac fermions coupled to emergent U(1) and Kalb-Ramond vector and axial gauge fields. Upon fixing an axial field configuration that breaks Lorentz invariance, this duality maps free to interacting Weyl semimetals, thereby suggesting that the quantization of the non-linear circular photogalvanic effect can be robust to certain interactions. Our work emphasizes how axial and Lorentz-breaking dualities improve our understanding of topological matter.

The dual of non-extremal area: differential entropy in higher dimensions

The Ryu-Takayanagi formula relates entanglement entropy in a field theory to the area of extremal surfaces anchored to the boundary of a dual AdS space. It is interesting to ask if there is also an information theoretic interpretation of the areas of non-extremal surfaces that are not necessarily boundary-anchored. In general, the physics outside such surfaces is associated to observers restricted to a time-strip in the dual boundary field theory. When the latter is two-dimensional, it is known that the differential entropy associated to the strip computes the length of the dual bulk curve, and has an interpretation in terms of the information cost in Bell pairs of restoring correlations inaccessible to observers in the strip. A general realization of this formalism in higher dimensions is unknown. We first prove a no-go theorem eliminating candidate expressions for higher dimensional differential entropy based on entropic c-theorems. Then we propose a new formula in terms of an integral of shape derivatives of the entanglement entropy of ball shaped regions. Our proposal stems from the physical requirement that differential entropy must be locally finite and conformally invariant. Demanding cancelation of the well-known UV divergences of entanglement entropy in field theory guides us to our conjecture, which we test for surfaces in AdS4. Our results suggest a candidate c-function for field theories in arbitrary dimensions.

Bulk reconstruction of metrics with a compact space asymptotically

Holographic duality implies that the geometric properties of the gravitational bulk theory should be encoded in the dual field theory. These naturally include the metric on dimensions that become compact near the conformal boundary, as is the case for any asymptotically locally AdSn × mathbbm{S} k spacetime. Almost all previous work on metric reconstruction ignores these dimensions and would thus at most apply to dimensionally-reduced metrics. In this work, we generalize the approach to bulk reconstruction using light-cone cuts and propose a prescription to obtain the full higher-dimensional metric of generic spacetimes up to an overall conformal factor. We first extend the definition of light-cone cuts to include information about the asymptotic compact dimensions, and show that the full conformal metric can be recovered from these extended cuts. We then give a prescription for obtaining these extended cuts from the dual field theory. The location of the usual cuts can still be obtained from bulk-point singularities of correlators, and the new information in the extended cut can be extracted by using appropriate combinations of operators dual to Kaluza-Klein modes of the higher-dimensional bulk fields.

Resonating AdS soliton

The AdS soliton is a nonsingular spacetime that has a flat conformal boundary with a compact S1 direction. We find a horizonless cohomogeneity-1 metric that describes nonlinear gravitational oscillations of the AdS soliton in five dimensions. We call this spacetime the resonating AdS soliton. This solution is obtained as the nonlinear extension of normal modes of the AdS soliton dual to spin-2 glueball excitations. The boundary energy momentum tensor of the resonating AdS soliton has time periodic components, and it is interpreted as a coherently excited state in the dual field theory. Physical quantities of the resonating AdS soliton are multivalued at a fixed energy, suggesting a transition between different frequency solutions. The energy of the resonating AdS soliton is higher than that of the undeformed AdS soliton, in accordance with the positive energy conjecture proposed by Horowitz and Myers.

Cosmological singularities and 2-dimensional dilaton gravity

We study Big-Bang or -Crunch cosmological singularities in 2-dimensional dilaton-gravity-scalar theories, in general obtained by dimensional reduction of higher dimensional theories. The dilaton potential encodes information about the asymptotic data defining the theories, and encompasses various families such as flat space, AdS, conformally AdS as arising from nonconformal branes, and more general nonrelativistic theories. We find a kind of universal near singularity behaviour independent of the dilaton potential, giving universal interrelations between the exponents defining the time behaviour near the cosmological singularity. More detailed analysis using a scaling ansatz enables finding various classes of cosmological backgrounds, recovering known examples such as the AdS Kasner singularity as well finding as new ones. We give some comments on the dual field theory from this point of view.

More on Schr\xf6dinger holography

We find explicit solutions for giant magnons and spiky strings living on the Schrödinger space Schr5 × T1,1 and compute dispersion relations. The holographic dual field theory is conjectured to be a non-local dipole-deformed CFT at strong coupling. We find that the dependence between conserved charges in the dispersion relations is transcen- dental, which is quite different from the most symmetric case of spherical internal space. Keeping the squashing parameter b general allows us to take some limits and to compare our results to known cases.

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.

Renormalized holographic subregion complexity under relevant perturbations

We construct renormalized holographic entanglement entropy (HEE) and subregion complexity (HSC) in the CV conjecture for asymptotically AdS4 and AdS5 geometries under relevant perturbations. Using the holographic renormalization method developed in the gauge/gravity duality, we obtain counter terms which are invariant under coordinate choices. We explicitly define different forms of renormalized HEE and HSC, according to conformal dimensions of relevant operators in the d = 3 and d = 4 dual field theories. We use a general embedding for arbitrary entangling subregions and showed that any choice of the coordinate system gives the same form of the counter terms, since they are written in terms of curvature invariants and scalar fields on the boundaries. We show an explicit example of our general procedure. Intriguingly, we find that a divergent term of the HSC in the asymptotically AdS5 geometry under relevant perturbations with operators of conformal dimensions in the range 0 < ∆ < frac{1}{2} and frac{7}{2} < ∆ < 4 cannot be cancelled out by adding any coordinate invariant counter term. This implies that the HSCs in these ranges of the conformal dimensions are not renormalizable covariantly. We also write the plot of the renormalization procedure in the case of asymptotically AdSd+1 geometries, with d > 4.

Time evolution of entanglement entropy in holographic FLRW cosmologies

To understand the time-dependent quantum correlation in expanding universes, we study the time-dependent entanglement entropy in the braneworld model. If we take into account a generalized string cloud geometry caused by uniformly distributed open strings, cosmologies on the braneworld result in the standard Friedmann-Lema\^{i}tre-Robertson-Walker cosmologies with various matter contents. On the dual field theory side, open strings are reinterpreted as a fundamental matter, while the black hole mass corresponds to the excitation energy of massless gauge bosons. In this work, we show how the string cloud geometry is matched to various braneworld cosmologie,s for example, eternal inflation, radiation-, and matter-dominated universes. Then, we investigate how the entanglement entropy evolves in those expanding universes.

Scalarization of asymptotically anti–de Sitter black holes with applications to holographic phase transitions

We study the spontaneous scalarization of spherically symmetric, static and asymptotically Anti-de Sitter (aAdS) black holes in a scalar-tensor gravity model with non-mininal coupling of the form $\phi^2\left(\alpha{\cal R} + \gamma {\cal G}\right)$, where $\alpha$ and $\gamma$ are constants, while ${\cal R}$ and ${\cal G}$ are the Ricci scalar and Gauss-Bonnet term, respectively. Since these terms act as an effective ``mass'' for the scalar field, non-trivial values of the scalar field in the black hole space-time are possible for {\it a priori} vanishing scalar field mass. In particular, we demonstrate that the scalarization of an aAdS black hole requires the curvature invariant $-\left(\alpha{\cal R} + \gamma {\cal G}\right)$ to drop below the Breitenlohner-Freedman bound close to the black hole horizon, while it asymptotes to a value well above the bound. The dimension of the dual operator on the AdS boundary depends on the parameters $\alpha$ and $\gamma$ and we demonstrate that -- for fixed operator dimension -- the expectation value of this dual operator increases with decreasing temperature of the black hole, i.e. of the dual field theory. When taking backreaction of the space-time into account, we find that the scalarization of the black hole is the dual description of a phase transition in a strongly coupled quantum system, i.e. corresponds to a holographic phase transition. A possible application are liquid-gas quantum phase transitions, e.g. in $^4$He. Finally, we demonstrate that extremal black holes with $AdS_2\times S^2$ near-horizon geometry {\it cannot support regular scalar fields on the horizon} in the scalar-tensor model studied here.

Probing the holographic dilaton

Many strongly coupled field theories admit a spectrum of gauge-invariant bound states that includes scalar particles with the same quantum numbers as the vacuum. The challenge naturally arises of how to characterise them. In particular, how can a dilaton — the pseudo-Nambu-Goldstone boson associated with approximate scale invariance — be distinguished from other generic light scalars with the same quantum numbers? We address this problem within the context of gauge-gravity dualities, by analysing the fluctuations of the higher-dimensional gravitational theory. The diagnostic test that we propose consists of comparing the results of the complete calculation, performed by using gauge-invariant fluctuations in the bulk, with the results obtained in the probe approximation. While the former captures the mixing between scalar and metric degrees of freedom, the latter removes by hand the fluctuations that source the dilatation operator of the boundary field- theory. Hence, the probe approximation cannot capture a possible light dilaton, while it should fare well for other scalar particles. We test this idea on a number of holographic models, among which are some of the best known, complete gravity backgrounds constructed within the top-down approach to gauge-gravity dualities. We compute the spectra of scalar and tensor fluctuations, that are interpreted as bound states (glueballs) of the dual field theory, and we highlight those cases in which the probe approximation yields results close to the correct physical ones, as well as those cases where significant discrepancies emerge. We interpret the latter occurrence as an indication that identifying one of the lightest scalar states with the dilaton is legitimate, at least as a leading-order approximation.

Holographic computation of Wilson loops in a background with broken conformal invariance and finite chemical potential

In this paper, we follow a `bottom-up' AdS/QCD approach to holographically probe the dynamics of a moving $q\bar{q}$ pair inside a strongly coupled plasma at the boundary. We consider a deformed AdS-Reissner Nordstr\"om metric in the bulk in order to introduce nonconformality and finite quark density in the dual field theory. By boosting the gravity solution in a specific direction we consider two extreme cases of orientation, parallel and perpendicular, for the Wilson loop which in turn fixes the relative position of the $q\bar{q}$ pair with respect to the direction of boost in the plasma. By utilizing this set-up, we holographically compute the vacuum expectation value of the time-like Wilson loop in order to obtain real part of the $q\bar{q}$ potential and the effects of nonconformality (deformation parameter $c$), chemical potential $\mu$ and rapidity $\beta$ are observed on this potential. We then compute the in-medium energy loss of the moving parton (jet quenching parameter $q_m$) by setting $\beta\rightarrow\infty$ which in turn makes the Wilson loop light-like. We also use the jet quenching as an order parameter to probe the strongly-coupled domain of the dual field theory. Finally, we compute the imaginary part of the $q\bar{q}$ potential ($\mathrm{Im}(V_{q\bar{q}})$) by considering the thermal fluctuation (arbitrary long wavelength) of the string world-sheet. It is observed that for fixed values of the chemical potential and rapidity, increase in the nonconformality parameter leads to an increase in the real and imaginary potentials as well as the jet quenching parameter.

Weyl connections and their role in holography

It is a well-known property of holographic theories that diffeomorphism invariance in the bulk space-time implies Weyl invariance of the dual holographic field theory in the sense that the field theory couples to a conformal class of background metrics. The usual Fefferman-Graham formalism, which provides us with a holographic dictionary between the two theories, breaks explicitly this symmetry by choosing a specific boundary metric and a corresponding specific metric ansatz in the bulk. In this paper, we show that a simple extension of the Fefferman-Graham formalism allows us to sidestep this explicit breaking; one finds that the geometry of the boundary includes an induced metric and an induced connection on the tangent bundle of the boundary that is a Weyl connection (rather than the more familiar Levi-Civita connection uniquely determined by the induced metric). Properly invoking this boundary geometry has far-reaching consequences: the holographic dictionary extends and naturally encodes Weyl-covariant geometrical data, and, most importantly, the Weyl anomaly gains a clearer geometrical interpretation, cohomologically relating two Weyl-transformed volumes. The boundary theory is enhanced due to the presence of the Weyl current, which participates with the stress tensor in the boundary Ward identity.

Non-Abelian mirror symmetry beyond the chiral ring

Mirror symmetry is a type of infrared duality in 3D quantum field theory that relates the low-energy dynamics of two distinct ultraviolet descriptions. Though first discovered in the supersymmetric context, it has far-reaching implications for understanding nonperturbative physics in general 3D quantum field theories. We study mirror symmetry in 3D $\mathcal{N}=4$ supersymmetric field theories whose Higgs or Coulomb branches realize $D$- and $E$-type Kleinian singularities in the $ADE$ classification, generalizing previous work on the $A$-type case. Such theories include the $SU(2)$ gauge theory coupled to fundamental matter in the $D$-type case and non-Lagrangian generalizations thereof in the $E$-type case. In these cases, the mirror description is given by a quiver gauge theory of affine $D$- or $E$-type. We investigate the mirror map at the level of the recently identified 1D protected subsector described by topological quantum mechanics, which implements a deformation quantization of the corresponding $ADE$ singularity. We give an explicit dictionary between the monopole operators and their dual mesonic operators in the $D$-type case. Along the way, we extract various operator product expansion (OPE) coefficients for the quantized Higgs and Coulomb branches. We conclude by offering some perspectives on how the topological subsectors of the $E$-type quivers might shed light on their non-Lagrangian duals.

Range of novel black hole phase transitions via massive gravity: Triple points and N -fold reentrant phase transitions

Massive gravities in anti-de Sitter spacetime can be viewed as effective dual field theories of different phases of condensed matter systems with broken translational symmetry such as solids, (perfect) fluids, and liquid crystals. Motivated by this fact, we explore the black hole chemistry (BHC) of these theories and find a new range of novel phase transitions close to realistic ones in ordinary physical systems. We find that the equation of state of topological black holes (TBHs) at their inflection point(s) in $d$-dimensional spacetime reduces to a polynomial equation of degree $(d-4)$, which yields up to $n=(d-4)$ critical points. As a result, for (neutral) TBHs, we observe triple-point phenomena with the associated first-order phase transitions (in $d \ge 7$), and a new phenomenon we call an $N$-fold reentrant phase transition, in which several ($N$) regions of thermodynamic phase space exhibit distinct reentrant phase transitions, with associated virtual triple points and zeroth-order phase transitions (in $d \ge 8$), as well as Van der Waals transitions (in $d \ge 5$) and reentrant (in $d \ge 6$) behavior. We conclude that BHC in higher-dimensional massive gravity is very likely to offer further new surprises.

Holographic description of M-branes via AdS2

We study AdS2× S4× S2× Σ2 solutions in type IIB string theory arising from D1-D3-NS5 brane intersections. These backgrounds enjoy sixteen supercharges and the corresponding internal geometry is non-compact due to the specific form of the warping w.r.t. the Riemann surface Σ2. Even though a direct computation of the holographic free energy of the would-be dual CFT1 yields a divergent behaviour, it reveals the typical N3 scaling of a 6d theory upon introducing a hard cut-off. We claim that such geometries may be interpreted as the gravity duals of M(atrix) models describing an IR phase of the (2, 0) theory of M5 branes, in presence of momentum and NUT charges. We discuss parallel AdS2 geometries describing longitudinal M2 branes in the UV, where the counting of the number of degrees of freedom correctly reproduces the expected N3/2 behaviour of the dual field theory. These geometries provide explicit examples where deconstructed extra dimensions yield well-defined UV descriptions in terms of higher-dimensional CFTs.

Holographic spontaneous anisotropy

We construct a family of holographic duals to anisotropic states in a strongly coupled gauge theory. On the field theory side the anisotropy is generated by giving a vacuum expectation value to a dimension three operator. We obtain our gravity duals by considering the geometry corresponding to the intersection of D3- and D5- branes along 2+1 dimensions. Our backgrounds are supersymmetric and solve the fully backreacted equations of motion of ten-dimensional supergravity with smeared D5-brane sources. In all cases the geometry flows to AdS5× \U0001d54a5 in the UV, signaling an isotropic UV fixed point of the dual field theory. In the IR, depending on the parameters of the solution, we find two possible behaviors: an isotropic fixed point or a geometry with anisotropic Lifshitz-like scaling symmetry. We study several properties of the solutions, including the entanglement entropy of strips. We show that any natural extension of existing c-functions will display non-monotonic behavior, conforming with the presence of new degrees of freedom only at intermediate regions between the boundary and the origin of the holographic dual.