Flat Space Limit Research Articles

A Chiral Λ-[formula omitted] Symmetry of AdS4 Gravity

Generalising the chiral boundary conditions of R1,3 gravity for AdS4 gravity, we derive chiral locally AdS4 solutions in the Newman-Unti gauge consistent with a variational principle whose asymptotic symmetry algebra we show, to be an infinite-dimensional chiral extension of so(2,3). This symmetry algebra coincides with the chiral bms4 algebra in the flat space limit with the corresponding solutions mapping to the space of gravitational vacua in R1,3 gravity. We posit this symmetry algebra as the chiral version of recently discovered Λ-bms4 algebra. We propose line integral charges from the bulk AdS4 gravity associated with this asymptotic symmetry algebra and show that they obey the semi-classical limit of a W-algebra. We derive this W-algebra for finite central charge c and level κ using associativity constraints of 2d CFT and find it to be isomorphic to one of quasi-superconformal algebra that existed in the literature.

Towards bootstrapping F-theory

We consider type IIB string theory with N D3 branes and various configurations of sevenbranes, such that the string coupling gs is fixed to a constant finite value. These are the simplest realizations of F-theory, and are holographically dual to rank N Argyres-Douglas conformal field theories (CFTs) with SU(2) and SU(3) flavor groups, and Minahan-Nemeschansky CFTs with E6, E7 and E8 flavor groups. We use the Seiberg-Witten curves of these theories to compute the mass deformed sphere free energy F (m) at large N in terms of novel matrix models with non-polynomial potentials. We show how F (m) can be used along with the analytic bootstrap to fix the large N expansion of flavor multiplet correlators in these CFTs, which are dual to scattering of gluons on AdS5 × S3, and in the flat space limit determine the effective theory of sevenbranes in F-theory. As a first step in this program, we use the matrix models to compute the log N term in F (m) and thereby fix the logarithmic threshold in the AdS5 × S3 holographic correlator, which matches the flat space prediction.

Supergluon scattering in AdS: constructibility, spinning amplitudes, and new structures

We elaborate on a new recursive method proposed in [1] for computing tree-level n-point supergluon amplitudes as well as those with one gluon, i.e. spinning amplitudes, in AdS5 × S3. We present an improved proof for the so-called “constructibility” of supergluon and spinning amplitudes based on their factorizations and flat-space limit, which allows us to determine these amplitudes in Mellin space to all n. We present explicit and remarkably simple expressions for up to n = 7 supergluon amplitudes and n = 6 spinning amplitudes, which can be viewed as AdS generalizations of the scalar-scaffolded gluon amplitudes proposed recently. We then reveal a series of hidden structures of these AdS amplitudes including (1). an understanding of general pole structures especially the precise truncation on descendent poles (2). a derivation of simple “Feynman rules” for the all-n amplitudes with the simplest R-symmetry structures, and (3). certain universal behavior analogous to the soft/collinear limit of flat-space amplitudes.

Flat-space limit of holographic pseudoentropy in (A)dS spacetimes

The real part of pseudoentropy in conformal field theories is holographically calculated by the area of some extremal spacelike surfaces in the dual de Sitter (dS) and anti–de Sitter (AdS) spacetimes. We show that the flat-space limit of these curves in three-dimensional (A)dS spacetimes is well defined. We find that, if the length of the curves is calculated from the radial coordinate where the retarded time is extremum, then after taking the flat-space limit, the entanglement entropy of the dual theory of three-dimensional flat spacetime is obtained. For dS spacetime, the radial coordinate corresponding to the extremum of retarded time is located inside the cosmological horizon. Our results suggest that, on the field theory side, the entanglement entropy in the dual theory of flat spacetimes should be obtained from the ultrarelativistic limit of pseudoentropy in the dual conformal field theory to (A)dS spacetimes. Published by the American Physical Society 2024

Flat space spinning massive amplitudes from momentum space CFT

We discuss the flat space limit of AdS using the momentum space representation of CFT correlators. The flat space limit involves sending the AdS radius and the dimensions of operators dual to massive fields to infinity while also scaling appropriately the sources of the dual operators. In this limit, d-dimensional CFT correlators become (d + 1)-dimensional scattering amplitudes. We exemplify our discussion with the computation of the flat-space limit of the CFT 3-point function of a conserved current, a non-conserved charged vector operator and its conjugate. The flat-space limit should yield the scattering amplitude of an Abelian gauge field with two massive vector fields. This scattering amplitude computes the electromagnetic form factors of the electromagnetic current in a spin-1 state, and these form factors encode the electromagnetic properties of the massive vector field (charge, magnetic moment and quadruple moment). In terms of the CFT, the flat-space limit amounts to zooming in the infrared region of the triple-K integrals that determine the 3-point function, while also scaling to infinity the order of (some of) the Bessel functions that feature in the triple-K integrals. In this limit the triple-K integral becomes proportional to the energy-preserving delta function, and the flat space limit correctly yields the corresponding flat space scattering amplitude in complete detail.

Photon propagator for inflation in the general covariant gauge

Photon propagator for power-law inflation is considered in the general covariant gauges within the canonical quantization formalism. Photon mode functions in covariant gauges are considerably more complicated than their scalar counterparts, except for the special choice of the gauge-fixing parameter we call the simple covariant gauge. We explicitly construct the position space photon propagator in the simple covariant gauge, and find the result considerably more complicated than its scalar counterpart. This is because of the need for explicitly inverting the Laplace operator acting on the scalar propagator, which results in Appell’s fourth function. Our propagator correctly reproduces the de Sitter and flat space limits. We use this propagator to compute two simple observables: the off-coincident field strength-field strength correlator and the energy-momentum tensor, both of which yield consistent results. As a spinoff of our computation we also give the exact expression for the Coulomb gauge propagator in power-law inflation in arbitrary dimensions.

Constructibility of AdS Supergluon Amplitudes.

We prove that all tree-level n-point supergluon (scalar) amplitudes in AdS_{5} can be recursively constructed, using factorization and flat-space limit. Our method is greatly facilitated by a natural R-symmetry basis for planar color-ordered amplitudes, which reduces the latter to "partial amplitudes" with simpler pole structures and factorization properties. Given the n-point scalar amplitude, we first extract spinning amplitudes with n-2 scalars and one gluon by imposing "gauge invariance," and then use a special "no-gluon kinematics" to determine the (n+1)-point scalar amplitude completely (which in turn contains the n-point single-gluon amplitude). Explicit results of up to 8-point scalar amplitudes and up to 6-point single-gluon amplitudes are included as Supplemental Material.

Soft theorems for boostless amplitudes

We consider effective field theories (EFTs) of scalar fields with broken Lorentz boosts, which arise by taking the decoupling and flat-space limits of the EFT of inflation, and derive constraints that must be satisfied by the corresponding scattering amplitudes if there is an underlying non-linearly realised symmetry. We primarily concentrate on extended shift symmetries which depend on the space-time coordinates, and find that combinations of scattering amplitudes obey enhanced Adler zeros. That is, such combinations vanish as one external momentum is taken soft, with the rate at which they vanish dictated by the corresponding symmetry. In our soft theorem derivation, we pay particular care to the energy and momentum-conserving delta functions that arise due to space-time translations, and show that when acted upon by derivatives with respect to spatial momenta, they yield a tower of soft theorems which are ultimately required for closure of the underlying symmetry algebra. All of our soft theorems correspond to constraints that must be satisfied by on-shell amplitudes and, even for symmetries that depend on the time coordinate, our soft theorems only require derivatives to be taken with respect to spatial momenta. We perform a soft bootstrap procedure to find solutions to our soft theorems, and compare these solutions to what we find from an off-shell analysis using the coset construction.

Quantum entanglement on black hole horizons in string theory and holography

We compute the exact one-loop partition function of ℤN orbifolds of Euclidean BTZ black hole with the aim to compute the entanglement entropy of the black hole horizon in string theory as a function of the mass and spin of the black hole and the AdS3 radius. We analyze the tachyonic contribution to the modular integrand for the partition function known for odd integers N > 1 and show that it admits an analytic continuation resulting in a finite answer for the modular integral in the physical region 0 < N ≤ 1. We discuss the flat space limit and the relevance of this computation for quantum gravity near black hole horizons and holography in relation to the thermal entropy.

The classical double copy in curved spacetimes: perturbative Yang-Mills from the bi-adjoint scalar

We formulate a version of the double copy for classical fields in curved spacetimes. We provide a correspondence between perturbative solutions to the bi-adjoint scalar equations and those of the Yang-Mills equations in position space. At the linear level, we show that there exists a map between these solutions for maximally symmetric spacetime backgrounds, that provides every Yang-Mills solution by the action of an appropriate differential operator on a bi-adjoint scalar solution. Given the existence of a linearized map, we show that it is possible to cast the solutions of the Yang-Mills equations at arbitrary perturbation order in terms of the corresponding bi-adjoint scalar solutions. This all-order map is reminiscent of the flat space BCJ double copy, and works for any curved spacetime where the perturbative expansion holds. We show that these results have the right flat space limit, and that the correspondence is agnostic to the choice of gauge.

Six-point AdS gluon amplitudes from flat space and factorization

We present a powerful new approach to compute tree-level higher-point holographic correlators. Our method only exploits the flat-space limit, where we point out an important simplification, and factorization of amplitudes in AdS. In particular, it makes minimal use of supersymmetry, crucial in all previous bootstrap methods. We demonstrate our method by computing the six-point super gluon amplitude of super Yang-Mills in AdS5. Published by the American Physical Society 2024

Gluon scattering in AdS at finite string coupling from localization

We consider gluons scattering in Type IIB string theory on AdS5 × S5/ℤ2 in the presence of D7 branes, which is dual to the flavor multiplet correlator in a certain 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 USp(2N) gauge theory with SO(8) flavor symmetry and complexified coupling τ. We compute this holographic correlator in the large N and finite τ expansion using constraints from derivatives of the mass deformed sphere free energy, which we compute to all orders in 1/N and finite τ using supersymmetric localization. In particular, we fix the F4 higher derivative correction to gluon scattering on AdS at finite string coupling τs = τ in terms of Jacobi theta functions, which feature the expected relations between the SL(2, ℤ) duality and the SO(8) triality of the CFT, and match it to the known flat space term. We also use the flat space limit to compute D2F4 corrections of the correlator at finite τ in terms of a non-holomorphic Eisenstein series. At weak string coupling, we find that the AdS correlator takes a form which is remarkably similar to that of the flat space Veneziano amplitude.

Skyrmions and pion stars in the gauged U(1) Einstein-Skyrme model

We consider topological and nontopological regular soliton solutions in the Einstein-Maxwell-Skyrme theory. We analyze the properties of these solutions and determine their domains of existence. The dependence of the solutions on the gauge coupling and on the strength of the effective gravitational coupling are examined. Topologically trivial localized field configurations, , are shown to exist, as nonlinear gravitational bound states of the Skyrme field. Both spherically symmetric and axially symmetric pion stars are considered. We find that these solutions share many features with the usual (mini)boson stars. In particular they also exhibit a spiraling behavior and do not possess a flat space limit. Published by the American Physical Society 2024

Soft graviton exchange and the information paradox

We show that there is a remarkable phase in quantum gravity where gravitational scattering amplitudes mediated by virtual gravitons can be calculated explicitly in effective field theory, when the impact parameter b satisfies LPl≪b≲RS, with RS being the Schwarzschild radius. This phase captures collisions with energies satisfying s≫γMPl (with γ∼MPl/MBH) near the horizon. We call this the black hole eikonal phase, in contrast to its flat space analog where collisions are trans-Planckian. Hawking’s geometric optics approximation neglects gravitational interactions near the horizon, and results in thermal occupation numbers in the Bogoliubov coefficients. We show that these interactions are mediated by graviton exchange in 2→2 scattering near the horizon, and explicitly calculate the S-matrix nonperturbatively in MPl/MBH. This involves a resummation of infinitely many ladder diagrams near the horizon, all mediated by virtual soft gravitons. The S-matrix turns out to be a pure phase upon this resummation and is agnostic of Planckian physics and any specific ultraviolet completion. In contrast to the flat-space eikonal limit, the black hole eikonal phase captures collisions of extremely low energy near the horizon. Published by the American Physical Society 2024

Bootstrapping bulk locality. Part I: Sum rules for AdS form factors

The problem of constructing local bulk observables from boundary CFT data is of paramount importance in holography. In this work, we begin addressing this question from a modern bootstrap perspective. Our main tool is the boundary operator expansion (BOE), which holds for any QFT in AdS. Following Kabat and Lifschytz, we argue that the BOE is strongly constrained by demanding locality of correlators involving bulk fields. Focusing on ‘AdS form factors’ of one bulk and two boundary insertions, we reformulate these locality constraints as a complete set of sum rules on the BOE data. We show that these sum rules lead to a manifestly local representation of form factors in terms of ‘local blocks’. The sum rules are valid non-perturbatively, but are especially well-adapted for perturbative computations in AdS where they allow us to bootstrap the BOE data in a systematic fashion. Finally, in the flat space limit, we show that the AdS form factor reduces to an ordinary QFT form factor. We provide a phase shift formula for it in terms of the BOE and CFT data. In two dimensions, this formula makes manifest Watson’s equations for integrable form factors under certain extremality assumptions on the CFT. We discuss the eventual modifications of our formalism to account for dressed operators in AdS.

The Källén-Lehmann representation in de Sitter spacetime

We study two-point functions of symmetric traceless local operators in the bulk of de Sitter spacetime. We derive the Källén-Lehmann spectral decomposition for any spin and show that unitarity implies its spectral densities are nonnegative. In addition, we recover the Källén-Lehmann decomposition in Minkowski space by taking the flat space limit. Using harmonic analysis and the Wick rotation to Euclidean Anti de Sitter, we derive an inversion formula to compute the spectral densities. Using the inversion formula, we relate the analytic structure of the spectral densities to the late-time boundary operator content. We apply our technical tools to study two-point functions of composite operators in free and weakly coupled theories. In the weakly coupled case, we show how the Källén-Lehmann decomposition is useful to find the anomalous dimensions of the late-time boundary operators. We also derive the Källén-Lehmann representation of two-point functions of spinning primary operators of a Conformal Field Theory on de Sitter.

Genus-one open string amplitudes on AdS5×S3 from CFT

We bootstrap one-loop string corrections to the four-point function of half-BPS operators in a 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SCFT with flavour group SO(8), dual to gluon scattering at genus one on AdS5×S3. We identify an 8-dimensional organising principle which governs the spectrum of double-trace anomalous dimensions, valid to all orders in the string length. This has precise implications for the structure of one-loop Mellin amplitudes, which we explicitly compute for the first three orders beyond the field-theory limit. We also consider the corresponding position space representation, which is entirely determined by the square of a certain differential operator acting on a simpler “pre-correlator”. Finally, we show that the flat-space limit of the Mellin amplitudes exactly matches the logarithmic terms of the genus-one amplitude in 8-dimensional flat space, which we compute via a partial-wave analysis.

Dominant spacetime in three dimensional de Sitter gravity

In three dimensions, Kerr-de Sitter spacetime as a solution of Einstein gravity with positive cosmological constant has a single cosmological horizon. The flat-space limit (zero cosmological constant limit) of this spacetime is well-defined and yields the flat-space cosmological solution which is a significant spacetime in the context of flat-space holography. In this paper, we calculate the free energy of this spacetime and compare it with the free energy of the three-dimensional de Sitter spacetime. We investigate which one of these two spacetimes will dominate in the semi-classical approximation for estimating the partition function. It is shown that for the same temperature of cosmological horizon of two spacetimes this is the de Sitter spacetime which is always dominant. Hence, contrary to asymptotically flat and asymptotically AdS spacetimes, there is no phase transition in three dimensional de Sitter gravity.

On the spectrum and structure constants of short operators in N=4 SYM at strong coupling

We study short operators in planar mathcal{N} = 4 SYM at strong coupling, for general spin and SO(6) symmetric traceless representations. At strong coupling their dimension grows like Delta sim 2sqrt{delta }{lambda}^{1/4} and their spectrum of degeneracies can be analysed by considering the massive spectrum of type II strings in flat space-time. We furthermore compute their structure constants with two arbitrary chiral primary operators. This is done by considering the four-point correlator of arbitrary chiral primary operators at strong coupling in planar mathcal{N} = 4 SYM, including the supergravity approximation plus the infinite tower of stringy corrections that contributes in the flat space limit. Our results are valid for generic rank n symmetric traceless representations of SO(6) and in particular for n ≫ 1, as long as n ≪ λ1/4.

Graviton trispectrum from gluons

The tree-level wavefunction coefficient for four gravitons in de Sitter space was recently bootstrapped using the Cosmological Optical Theorem, flat space limit, and Manifestly Local Test [1]. Inspired by the double copy for scattering amplitudes, we derive a compact new expression for this quantity starting from the wavefunction coefficient for gluons.