Andrew Strominger

A bstract: It is shown that time-ordered correlation functions of a unitary CFT ₂ in 2D Minkowski space admit a single-valued, conformally-invariant extension to the Lorentzian signature torus provided that the S ¹ × S ¹ spatial and temporal radii are equal. The result extends to Lorentzian CFT _D on equal-radii S ^{D −1} × S ¹ under the assumption that branch cuts occur only when a pair of operator insertions are null separated.

A bstract: We consider a free complex massive scalar on the quotient spacetime AdS ₃ / ℤ, which has the isometry group SO(2, 2) rather than its universal cover. This problem is of interest as a special example of QFT on a spacetime with closed timelike curves (CTCs), as a new context in which to study generalizations of AdS/CFT and for its role in celestial holography. A basis of time-periodic solutions to the Klein-Gordon wave equation is found in terms of hypergeometric functions. They fall into a PT even and a PT odd principal series representation, rather than the more familiar highest-weight representations of the cover of SO(2, 2). For masses below the Breitenlohner-Freedman (BF) bound, the modes fall on the unitary principal series. The presence of CTCs precludes the usual canonical quantization, but geometric quantization, which begins with a symplectic form on the phase space of classical solutions, is applicable. Operators, commutators, an SO(2, 2) invariant vacuum and a Fock space are constructed and transform like those of a CFT ₂ . The Fock space norm is positive below the BF bound. In celestial holography, AdS ₃ / ℤ arises as leaves of a hyperbolic foliation of Klein space. Our analysis determines new entries in the symmetry-constrained celestial bulk-to-boundary dictionary. In particular the Klein space 𝒮-matrix is dual to a maximally entangled state in the tensor product of two copies of the ‘wedge CFT ₂ ’ associated to the timelike and spacelike wedges of Klein space. Translation invariance is not present in the wedge CFT ₂ itself but emerges as a property of this maximally entangled state.

Families of Lorentz, but not Poincare, invariant vacua are constructed for a massless scalar field in 4D Minkowski space. These are generalizations of the Rindler vacuum with a larger symmetry group. Explicit expressions are given as squeezed excitations of the Poincare vacuum. The effective reduced vacua on the 3D hyperbolic de Sitter slices are the well-known de Sitter α-vacua with antipodal singularities in the Wightman function. Several special interesting cases are discussed.

Celestial amplitudes may be decomposed as weighted integrals of AdS₃-Witten diagrams associated to each leaf of a hyperbolic foliation of spacetime. We show, for the Kleinian three-point MHV amplitude, that each leaf subamplitude is smooth except for the expected light-cone singularities. Moreover, we find that the full translationally-invariant celestial amplitude is simply the residue of the pole in the leaf amplitude at the point where the total conformal weights of the gluons equals three. This full celestial amplitude vanishes up to light-cone contact terms, as required by spacetime translation invariance, and reduces to the expression previously derived by Mellin transformation of the Parke-Taylor formula.

Celestial MHV amplitudes are comprised of non-distributional leaf amplitudes associated to an AdS₃ leaf of a foliation of flat spacetime. It is shown here that the leaf amplitudes are governed by the same infinite-dimensional soft ‘S-algebra’ as their celestial counterparts. Moreover, taking the soft limit of the smooth three-point MHV leaf amplitude yields a nondegenerate minus-minus two-point leaf amplitude. The two- and three-point MHV leaf amplitudes are used to compute the plus-minus-minus leaf operator product coefficients.

BFSS proposed that asymptotically flat M-theory is dual to a large N limit of the matrix quantum mechanics describing N nonrelativistic D0-branes. Recent insights on the soft symmetries of any quantum theory of gravity in asymptotically flat space are applied to the BFSS matrix model. It is shown that soft gravitons are realized by submatrices whose rank is held fixed in the large N M-theory limit, rather than the usual linear scaling with N for hard gravitons. The soft expansion is identified with the large N expansion and the soft theorem becomes a universal formula for the quantum mechanical scattering of such submatrix excitations. This formula is shown to be the Ward identity of large type IIA U(1)_RR asymptotic gauge symmetry in the matrix model, whose asymptotic boundaries are at future and past timelike infinity.

We present a discrete basis of solutions of the massless Klein-Gordon equation in 3 + 1 Minkowski space which transform as 𝔰𝔩(2, ℂ) Lorentz/conformal primaries and descendants, and whose elements all have integer conformal dimension. We show that the basis is complete in the sense that the Wightman function can be expressed as a quadratic sum over the basis elements.

The black hole photon ring is a prime target for upcoming space-based VLBI missions seeking to image the fine structure of astrophysical black holes. The classical Lyapunov exponents of the corresponding nearly bound null geodesics control the quasinormal ringing of a perturbed black hole as it settles back down to equilibrium, and they admit a holographic interpretation in terms of quantum Ruelle resonances of the microstate dual to the Kerr black hole. Recent work has identified a number of emergent symmetries related to the intricate self-similar structure of the photon ring. Here, we explore this web of interrelated phenomena in an exactly soluble example that arises as an approximation to the near-extremal Kerr black hole. The self-dual warped AdS₃ geometry has a photon ring as well as S L ( 2 , R ) isometries and an exactly calculable quasinormal mode (QNM) spectrum. We show explicitly that the geometric optics approximation reproduces the eikonal limit of the exact scalar QNM spectrum, as well as the approximate ‘near-ring’ wavefunctions. The S L ( 2 , R ) isometries are directly related to the emergent conformal symmetry of the photon ring in black hole images but are distinct from a recently discussed conformal symmetry of the eikonal QNM spectrum. The equivalence of the classical QNM spectrum—and thus the photon ring—to the quantum Ruelle resonances in the context of a spacetime with a putative holographic dual suggests that the photon ring of a warped black hole is indeed part of the black hole hologram.