Flat Space Limit Research Articles

Kerr black holes with synchronised scalar hair and boson stars in the Einstein-Friedberg-Lee-Sirlin model

We consider the Friedberg-Lee-Sirlin model minimally coupled to Einstein gravity in four spacetime dimensions. The renormalizable Friedberg-Lee-Sirlin model consists of two interacting scalar fields, where the mass of the complex scalar field results from the interaction with the real scalar field which has a finite vacuum expectation value. We here study a new family of self-gravitating axially-symmetric, rotating boson stars in this model. In the flat space limit these boson stars tend to the corresponding Q-balls. Subject to the usual synchronization condition, the model admits spinning hairy black hole solutions with two different types of scalar hair. We here investigate parity-even and parity-odd boson stars and their associated hairy black holes. We explore the domain of existence of the solutions and address some of their physical properties. The solutions exhibit close similarity to the corresponding boson stars and Kerr black holes with synchronised scalar hair in the O(3)-sigma model coupled to Einstein gravity and to the corresponding solutions in the Einstein-Klein-Gordon theory with a complex scalar field, where the latter are recovered in a limit.

Genus-one string amplitudes from conformal field theory

We explore and exploit the relation between non-planar correlators in mathcal{N} = 4 super-Yang-Mills, and higher-genus closed string amplitudes in type IIB string theory. By conformal field theory techniques we construct the genus-one, four-point string amplitude in AdS5 × S5 in the low-energy expansion, dual to an mathcal{N} = 4 super-Yang-Mills correlator in the ’t Hooft limit at order 1/c2 in a strong coupling expansion. In the flat space limit, this maps onto the genus-one, four-point scattering amplitude for type II closed strings in ten dimensions. Using this approach we reproduce several results obtained via string perturbation theory. We also demonstrate a novel mechanism to fix subleading terms in the flat space limit of AdS amplitudes by using string/M-theory.

Double copy structure of CFT correlators

We consider the momentum-space 3-point correlators of currents, stress tensors and marginal scalar operators in general odd-dimensional conformal field theories. We show that the flat space limit of these correlators is spanned by gauge and gravitational scattering amplitudes in one higher dimension which are related by a double copy. Moreover, we recast three-dimensional CFT correlators in terms of tree-level Feynman diagrams without energy conservation, suggesting double copy structure beyond the flat space limit.

Fundamental Solutions and Gegenbauer Expansions of Helmholtz Operators in Riemannian Spaces of Constant Curvature.

We perform global and local analysis of oscillatory and damped spherically symmetric fundamental solutions for Helmholtz operators (-Δ±β 2) in d-dimensional, R-radius hyperbolic and hyperspherical geometry, which represent Riemannian manifolds with positive constant and negative constant sectional curvature respectively. In particular, we compute closed-form expressions for fundamental solutions of (-Δ±β 2) on , (-Δ±β 2) on , and present two candidate fundamental solutions for (-Δ - β 2) on . Flat-space limits, with their corresponding asymptotic representations, are used to restrict proportionality constants for these fundamental solutions. In order to accomplish this, we summarize and derive new large degree asymptotics for associated Legendre and Ferrers functions of the first and second kind. Furthermore, we prove that our fundamental solutions on the hyperboloid are unique due to their decay at infinity. To derive Gegenbauer polynomial expansions of our fundamental solutions for Helmholtz operators on hyperspheres and hyperboloids, we derive a collection of infinite series addition theorems for Ferrers and associated Legendre functions which are generalizations and extensions of the addition theorem for Gegenbauer polynomials. Using these addition theorems, in geodesic polar coordinates for dimensions greater than or equal to three, we compute Gegenbauer polynomial expansions for these fundamental solutions, and azimuthal Fourier expansions in two-dimensions.

Supersymmetry breaking phase in three dimensional large N gauge theories

Three dimensional supersymmetric gauge theories are often in a gapped phase, in which SUSY is spontaneously broken, if all the matter fields are massive and decoupled in the low energy. We study this phase in the large N limit using the localization technique for the theory on the ellipsoid, which interpolates the round three sphere and the flat space compactified on S1. We find a large N saddle point solution for the gauge theory with some massive matter fields. This solution gives a vanishing (generalized) Polyakov loop in the flat space limit, thus, it corresponds to the confining phase at the leading order in the 1/N expansion.

Complexity growth in flat spacetimes

We use the complexity equals action proposal to calculate the rate of complexity growth for field theories that are the holographic duals of asymptotically flat spacetimes. To this aim, we evaluate the on-shell action of asymptotically flat spacetime on the Wheeler-DeWitt patch. This results in the same expression as can be found by taking the flat-space limit from the corresponding formula related to the asymptotically AdS spacetimes. For the bulk dimensions that are greater than three, the rate of complexity growth at late times approaches from above to Lloyd's bound. However, for the three-dimensional bulks, this rate is a constant and differs from Lloyd's bound by a logarithmic term.

M-theory reconstruction from (2,0) CFT and the chiral algebra conjecture

We study various aspects of the M-theory uplift of the AN −1 series of (2, 0) CFTs in 6d, which describe the worldvolume theory of N M5 branes in flat space. We show how knowledge of OPE coefficients and scaling dimensions for this CFT can be directly translated into features of the momentum expansion of M-theory. In particular, we develop the expansion of the four-graviton S-matrix in M-theory via the flat space limit of four-point Mellin amplitudes. This includes correctly reproducing the known contribution of the R4 term from 6d CFT data. Central to the calculation are the OPE coefficients for half-BPS operators not in the stress tensor multiplet, which we obtain for finite N via the previously conjectured relation [1] between the quantum {mathcal{W}}_N algebra and the AN −1 (2, 0) CFT. We further explain how the 1/N expansion of {mathcal{W}}_N structure constants exhibits the structure of protected vertices in the M-theory action. Conversely, our results provide strong evidence for the chiral algebra conjecture.

Holographic calculation of two-point correlation functions of CFT stress tensor in the BMS gauge and flat-space holography

In this paper, we use the holographic renormalization method to calculate the two-point correlation functions of the CFT stress tensor. In the gravity side, we write the asymptotically AdS spacetimes in the BMS gauge and apply the standard holographic renormalization method for these space-times. The significance of using multi-point functions in this gauge is that its flat-space limit is well-defined. We discuss this point in the last section of the paper.

Enhanced asymptotic BMS3 algebra of the flat spacetime solutions of generalized minimal massive gravity

We apply the new fall of conditions presented in the paper [1] on asymptotically flat spacetime solutions of Chern–Simons-like theories of gravity. We show that the considered fall of conditions asymptotically solve equations of motion of generalized minimal massive gravity. We demonstrate that there exist two type of solutions, one of those is trivial and the others are non-trivial. By looking at non-trivial solutions, for asymptotically flat spacetimes in the generalized minimal massive gravity, in contrast to Einstein gravity, cosmological parameter can be non-zero. We obtain the conserved charges of the asymptotically flat spacetimes in generalized minimal massive gravity, and by introducing Fourier modes we show that the asymptotic symmetry algebra is a semidirect product of a BMS3 algebra and two U(1) current algebras. Also we verify that the BMS3 algebra can be obtained by a contraction of the AdS3 asymptotic symmetry algebra when the AdS3 radius tends to infinity in the flat-space limit. Finally we find energy, angular momentum and entropy for a particular case and deduce that these quantities satisfy the first law of flat space cosmologies.

Asymptotic fragility, near AdS2 holography and Toverline{T}

We present the exact solution for the scattering problem in the flat space Jackiw-Teitelboim (JT) gravity coupled to an arbitrary quantum field theory. JT gravity results in a gravitational dressing of field theoretical scattering amplitudes. The exact expression for the dressed S-matrix was previously known as a solvable example of a novel UV asymptotic behavior, dubbed asymptotic fragility. This dressing is equivalent to the Toverline{T} deformation of the initial quantum field theory. JT gravity coupled to a single mass-less boson provides a promising action formulation for an integrable approximation to the worldsheet theory of confining strings in 3D gluodynamics. We also derive the dressed S-matrix as a flat space limit of the near AdS2 holography. We show that in order to preserve the flat space unitarity the conventional Schwarzian dressing of boundary correlators needs to be slightly extended. Finally, we propose a new simple expression for flat space amplitudes of massive particles in terms of correlators of holographic CFT’s.

One-loop tests of supersymmetric gauge theories on spheres

We show that a recently conjectured form for perturbative supersymmetric partition functions on spheres of general dimension d is consistent with the flat space limit of 6-dimensional mathcal{N} = 1 super Yang-Mills. We also show that the partition functions for mathcal{N} =18-and9-dimensionaltheoriesareconsistentwiththeirknownflatspacelimits.

Conformal higher spin scattering amplitudes from twistor space

We use the formulation of conformal higher spin (CHS) theories in twistor space to study their tree-level scattering amplitudes, finding expressions for all three-point overline{mathrm{MHV}} amplitudes and all MHV amplitudes involving positive helicity conformal gravity particles and two negative helicity higher spins. This provides the on-shell analogue for the covariant coupling of CHS fields to a conformal gravity background. We discuss the restriction of the theory to a ghost-free unitary subsector, analogous to restricting conformal gravity to general relativity with a cosmological constant. We study the flat-space limit and show that the restricted amplitudes vanish, supporting the conjecture that in the unitary sector the S-matrix of CHS theories is trivial. However, by appropriately rescaling the amplitudes we find non-vanishing results which we compare with chiral flat-space higher spin theories.

Salty popcorn in a homogeneous low-dimensional toy model of holographic QCD

Recently, a homogeneous ansatz has been used to study cold dense nuclear matter in the Sakai–Sugimoto model of holographic QCD. To justify this homogeneous approximation we here investigate a homogeneous ansatz within a low-dimensional toy version of Sakai–Sugimoto to study finite baryon density configurations and compare it to full numerical solutions. We find the ansatz corresponds to enforcing a dyon salt arrangement in which the soliton solutions are split into half-soliton layers. Within this ansatz we find analogues of the proposed baryonic popcorn transitions, in which solutions split into multiple layers in the holographic direction. The homogeneous results are found to qualitatively match the full numerical solutions, lending confidence to the homogeneous approximations of the full Sakai–Sugimoto model. In addition, we find exact compact solutions in the high density, flat space limit which demonstrate the existence of further popcorn transitions to three layers and beyond.

Super-BMS3 algebras from N = 2 $$ \mathcal{N}=2 $$ flat supergravities

We consider two possible flat space limits of three dimensional $\mathcal{N} = (1,1)$ AdS supergravity. They differ by how the supercharges are scaled with the AdS radius $\ell$: the first limit (democratic) leads to the usual super-Poincare theory, while a novel `twisted' theory of supergravity stems from the second (despotic) limit. We then propose boundary conditions such that the asymptotic symmetry algebras at null infinity correspond to supersymmetric extensions of the BMS algebras previously derived in connection to non- and ultra-relativistic limits of the $\mathcal{N}=(1,1)$ Virasoro algebra in two dimensions. Finally, we study the supersymmetric energy bounds and find the explicit form of the asymptotic and global Killing spinors of supersymmetric solutions in both flat space supergravity theories.

Flat-space holography and stress tensor of Kerr black hole

We propose a stress tensor for the Kerr black hole written in the Boyer-Lindquist coordinate. To achieve this, we use the dictionary of the Flat/CCFT correspondence and take the flat-space limit from the quasi-local stress tensor of the four-dimensional Kerr-AdS black hole. The proposed stress tensor yields the correct values for the mass and angular momentum of the Kerr black hole at spatial infinity. We also calculate some components of the energy momentum tensor of the three dimensional CCFT and show that they are consistent with the holographic calculation of the Kerr black hole. The calculation we present in this paper is another confirmation for the Flat/CCFT proposal.

Matter-coupled de Sitter supergravity

De Sitter supergravity describes interaction of supergravity with general chiral and vector multiplets as well as one nilpotent chiral multiplet. The extra universal positive term in the potential due to the nilpotent multiplet, corresponding to the anti-D3 brane in string theory, supports de Sitter vacua in these supergravity models. In the flat space limit these supergravity models include the Volkov-Akulov model with a non-linearly realized supersymmetry. The rules for constructing pure de Sitter supergravity action are generalized here in presence of other matter multiplets. We present a strategy to derive the complete closed form general supergravity action with a given Kahler potential $K$, superpotential $W$ and vector matrix $f_{AB}$ interacting with a nilpotent chiral multiplet. It has the potential $V=e^K(|F^2 |+ |DW|^2 - 3 |W|^2)$, where $F$ is a necessarily non-vanishing value of the auxiliary field of the nilpotent multiplet. De Sitter vacua are present under simple condition that $|F^2|- 3|W|^2>0$. A complete explicit action in the unitary gauge is presented.

Gravitational anomalies, entanglement entropy, and flat-space holography

We introduce a prescription to compute the entanglement entropy of Galilean conformal field theories by combining gravitational anomalies and an \.{I}n\"{o}n\"{u}-Wigner contraction. We find that our expression for the entanglement entropy in the thermal limit reproduces the Cardy formula for Galilean conformal field theories. Using this proposal, we calculate the entanglement entropy for a class of Galilean conformal field theories, which are believed to be dual to three-dimensional flat-space cosmological solutions. These geometries describe expanding (contracting) universes and can be viewed as the flat-space limit of rotating Ba\~nados-Teitelboim-Zanelli black holes. We show that our finding reduces, in the appropriate limits, to the results discussed in the literature and provide interpretations for the previously unexplored regimes, such as flat-space chiral gravity.

Gravity with a cosmological constant from rational curves

We give a new formula for all tree-level correlators of boundary field insertions in gauged N=8 supergravity in AdS_4; this is an analog of the tree-level S-matrix in anti-de Sitter space. The formula is written in terms of rational maps from the Riemann sphere to twistor space, with no reference to bulk perturbation theory. It is polynomial in the cosmological constant, and equal to the classical scattering amplitudes of supergravity in the flat space limit. The formula is manifestly supersymmetric, independent of gauge choices on twistor space, and equivalent to expressions computed via perturbation theory at 3-point MHV-bar and n-point MHV. We also show that the formula factorizes and obeys BCFW recursion in twistor space.

Gravitating sphalerons in the Skyrme model

We construct self-gravitating axially symmetric sphaleron solutions of the $3+1$-dimensional Skyrme model coupled to Einstein gravity. The solutions are static and asymptotically flat; they are characterized by two integers $n$ and $m$, where $\ifmmode\pm\else\textpm\fi{}n$ are the winding numbers of the constituents and the second integer $m$ defines the type of the solution. These configurations correspond to the chains of charge $n$ Skyrmions and charge $\ensuremath{-}n$ anti-Skyrmions placed along the axis of symmetry in alternating order. We investigate the dependency of the masses of the gravitating sphalerons on the gravitational coupling. We find new chains of self-gravitating $|n|=1$ Skyrmions-anti-Skyrmions that emerge at some critical nonzero value of the gravitational coupling and do not have flat space limit. In contrast, the branches of self-gravitating $|n|\ensuremath{\ge}2$ Skyrmion-anti-Skyrmion chains emerge from the corresponding flat space configurations. In both cases these branches merge at some maximal value of the effective gravitational coupling the branches of different type. The branch of the gravitating Skyrmion-anti-Skyrmion pair extends all the way back to the limit of vanishing coupling constant where solutions approach the corresponding generalized Bartnik-McKinnon solutions. The upper branch of gravitating Skyrmion-anti-Skyrmion-Skyrmion chain exists up to some critical value of the gravitational coupling at which the chain becomes broken. We further find that for small values of the coupling constant on the upper branches, the solutions correspond to composite systems, consisting of a scaled inner Einstein-Yang-Mills solution and outer Skyrmions that are separating from the inner configuration.

Factorization of Mellin amplitudes

We introduce Mellin amplitudes for correlation functions of k scalar operators and one operator with spin in conformal field theories (CFT) in general dimension. We show that Mellin amplitudes for scalar operators have simple poles with residues that factorize in terms of lower point Mellin amplitudes, similarly to what happens for scattering amplitudes in flat space. Finally, we study the flat space limit of Anti-de Sitter (AdS) space, in the context of the AdS/CFT correspondence, and generalize a formula relating CFT Mellin amplitudes to scattering amplitudes of the bulk theory, including particles with spin.