Recently a one-parameter family of deformed ℒ w_1+∞ soft symmetry algebras, denoted ℒ_Λw_1+∞, acting on tree-level gravitational theories in AdS_4 has been discovered. Here we show that all CFT_3s, including those dual to quantum gravity on AdS_4, admit an ℒ_Λw_1+∞ action generated by the ANEC operator, its conformal descendants and their commutators. This extends the previous tree-level results on these soft symmetries to the strongly-coupled quantum regime.

Abstract We consider a free complex massive scalar on the quotient spacetime AdS3 /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 CFT2. The Fock space norm is positive below the BF bound. In celestial holography, AdS3 /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 CFT2’ associated to the timelike and spacelike wedges of Klein space. Translation invariance is not present in the wedge CFT2 itself but emerges as a property of this maximally entangled state.

Single-minus tree-level $n$-gluon scattering amplitudes are reconsidered. Often presumed to vanish, they are shown here to be nonvanishing for certain "half-collinear" configurations existing in Klein space or for complexified momenta. We derive a piecewise-constant closed-form expression for the decay of a single minus-helicity gluon into $n-1$ plus-helicity gluons as a function of their momenta. This formula nontrivially satisfies multiple consistency conditions including Weinberg's soft theorem.

The n-point single-minus graviton amplitudes are nonzero in a special kinematic region that preserves some supersymmetry when embedded in supergravity. We compute these amplitudes within the BFSS matrix theory by relating them to an index problem considered by A. Sen. More precisely, the single-minus amplitudes are obtained from an index that counts BPS states in the Coulomb branch of four-dimensional N=4 super Yang-Mills. We explicitly check this relation in a specific kinematic region by computing the index using BPS wall-crossing formulae and matching it to the gravity result. We further employ BPS wall-crossing to show that the index satisfies a tower of w_1+∞ soft theorems in any kinematic regime, again matching gravity. Finally, we show that for certain kinematics, the single-minus amplitudes can be realized by scattering a graviton off a plane wave.

Quantum Yang-Mills theory in Euclidean AdS_4 with Neumann boundary conditions is studied as a function of the complex couplings 1/g_±^2≡1/g^2∓i θ/8 π^2. We define a "self-dual limit" by g_- → 0 with g_+ fixed. We argue that the limiting theory is well-defined perturbatively and equivalent to the BF formulation of self-dual Yang-Mills theory with a particular boundary condition relating B and F at the boundary ∂AdS_4. g_+ is the loop-counting parameter of the self-dual theory. This is in stark contrast to flat space, where θ has no effect on perturbative dynamics. In the self-dual limit, it is shown that all tree-level zero-plus and single-plus boundary correlators vanish. A closed form expression is given for any number of gluons for the double-plus tree correlators. Finally, we show that in the flat space limit of AdS_4, the total energy poles in the tree boundary correlators correctly reduce to the single-minus gluon amplitudes.

Abstract It is shown that time-ordered correlation functions of a unitary CFT2 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.

Scattering amplitudes of n particles in nonabelian gauge theories admit factorizations of the general form 𝒜_n = 𝒜^ soft_n ×𝒜^ hard_n, where 𝒜^ soft_n is IR divergent, while 𝒜^ hard_n is IR finite and encodes the higher loop corrections to scattering. We specify a particular all-orders definition of this factorization for planar N=4 super Yang-Mills (SYM) and argue that the resulting 𝒜_n^ hard obeys an uncorrected tree-level soft theorem. Moreover it furnishes a representation of the undeformed tree-level S-algebra generated by a tower of soft gluons. The results follow from several commonly invoked assumptions for N=4 SYM, including BDS one-loop exponentiation of the splitting function and amplitude/Wilson-loop duality.

Abstract Flat Minkowski space (M 4 ) and AdS 4 can both be conformally mapped to the Einstein cylinder. The maps may be judiciously chosen so that some null generators of the I + boundary of M 4 coincide with antipodally-terminating null geodesic segments on the boundary of AdS 4 . Conformally invariant nonabelian gauge theories in M 4 have an asymptotic S -algebra generated by a tower of soft gluons given by weighted null line integrals on I + . We show that, under the conformal map to AdS 4 , the leading soft gluons are dual to light transforms of the conserved global symmetry currents in the boundary CFT 3 . The tower of light ray operators obtained from the S O ( 3 , 2 ) descendants of this light transform realize a full set of generators of the S -algebra in the boundary CFT 3 . This provides a direct connection between holographic symmetry algebras in M 4 and AdS 4 .

Single-minus tree-level $n$-graviton scattering amplitudes are revisited. Often presumed to vanish, they are shown here to be nonvanishing for certain "half-collinear" configurations existing in Klein space or for complexified momenta. A Berends-Giele recursion relation for these amplitudes is derived and solved in a form involving a sum over trees. In a restricted kinematic decay region, this solution simplifies significantly to an $(n{-}2)$-fold product of soft factors. It is further shown in this region that, combined with suitable analyticity assumptions, the $n$-graviton amplitude is generated by a recursive $\mathcal{L}w_{1+\infty}$ Ward identity with the three-graviton amplitude as a seed.

Some time ago, Seiberg and Witten solved for moduli spaces of vacua parameterized by scalar vacuum expectation values in N = 2 gauge theories. More recently, new vacua associated to soft theorems and asymptotic symmetries have been found. This paper takes some first steps towards a complete picture of the infrared geometry of N = 2 gauge theory incorporating both of these infrared structures.

Some time ago, Seiberg and Witten solved for moduli spaces of vacua parameterized by scalar vacuum expectation values in gauge theories. More recently, new vacua associated to soft theorems and asymptotic symmetries have been found. This paper takes some first steps towards a complete picture of the infrared geometry of gauge theory incorporating both of these infrared structures.

Flat Minkowski space (M^4) and AdS_4 can both be conformally mapped to the Einstein cylinder. The maps may be judiciously chosen so that some null generators of the ℐ^+ boundary of M^4 coincide with antipodally-terminating null geodesic segments on the boundary of AdS_4. Conformally invariant nonabelian gauge theories in M^4 have an asymptotic S-algebra generated by a tower of soft gluons given by weighted null line integrals on ℐ^+. We show that, under the conformal map to AdS_4, the leading soft gluons are dual to light transforms of the conserved global symmetry currents in the boundary CFT_3. The tower of light ray operators obtained from the SO(3,2) descendants of this light transform realize a full set of generators of the S-algebra in the boundary CFT_3. This provides a direct connection between holographic symmetry algebras in M^4 and AdS_4.

Analytic continuation from (3, 1) signature Minkowski to (2, 2) signature Klein space has emerged as a useful tool for the understanding of scattering amplitudes and flat space holography. Under this continuation, past and future null infinity merge into a single boundary ( J) which is the product of a null line with a (1, 1) signature torus. The Minkowskian S-matrix continues to a Kleinian S-vector which in turn may be represented by a Poincar & eacute;-invariant vacuum state |C > in the Hilbert space built on J. |C > contains all information about S in a novel, repackaged form. We give an explicit construction of |C > in a Lorentz/conformal basis for a free massless scalar. J separates into two halves J +/- which are the asymptotic null boundaries of the regions timelike and spacelike separated from the origin. |C > is shown to be a maximally entangled state in the product of the J +/- Hilbert spaces.

Celestial MHV amplitudes are comprised of non-distributional leaf amplitudes associated to an AdS$_3$ 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.

Recent work has shown that loop corrections from massless particles generate $\frac{3}{2}\log T_{\text{Hawking}}$ corrections to black hole entropy which dominate the thermodynamics of cold near-extreme charged black holes. Here we adapt this analysis to near-extreme Kerr black holes. Like AdS$_2\times S^2$, the Near-Horizon Extreme Kerr (NHEK) metric has a family of normalizable zero modes corresponding to reparametrizations of boundary time. The path integral over these zero modes leads to an infrared divergence in the one-loop approximation to the Euclidean NHEK partition function. We regulate this divergence by retaining the leading finite temperature correction in the NHEK scaling limit. This "not-NHEK" geometry lifts the eigenvalues of the zero modes, rendering the path integral infrared finite. The quantum-corrected near-extremal entropy exhibits $\frac{3}{2}\log T_{\text{Hawking}}$ behavior characteristic of the Schwarzian model and predicts a lifting of the ground state degeneracy for the extremal Kerr black hole.

It is shown that a 2D CFT consisting of a central charge $c$ Liouville theory, a chiral level one, rank $N$ Kac-Moody algebra and a weight $-3/2$ free fermion holographically generate 4D MHV tree-level scattering amplitudes. The correlators of this 2D CFT give directly the 4D leaf amplitudes associated to a single hyperbolic slice of flat space. The 4D celestial amplitudes arise in a large-$N$ and semiclassical large-$c$ limit, according to the holographic dictionary, as a translationally-invariant combination of leaf amplitudes. A step in the demonstration is showing that the semiclassical limit of Liouville correlators are given by contact AdS$_3$ Witten diagrams.

It is shown that a 2D conformal field theory consisting of a central charge c Liouville theory, a chiral level one, rank N Kac-Moody algebra, and a weight -3/2 free fermion holographically generate 4D maximal helicity violating tree-level scattering amplitudes. The correlators of this 2D conformal field theory give directly the 4D leaf amplitudes associated to a single hyperbolic slice of flat space. The 4D celestial amplitudes arise in a large-N and semiclassical large-c limit, according to the holographic dictionary, as a translationally invariant combination of leaf amplitudes. A step in the demonstration is showing that the semiclassical limit of Liouville correlators are given by contact 3D anti-de Sitter Witten diagrams.

We present the Black Hole Explorer (BHEX), a mission that will produce the sharpest images in the history of astronomy by extending submillimeter Very-Long-Baseline Interferometry (VLBI) to space. BHEX will discover and measure the bright and narrow "photon ring" that is predicted to exist in images of black holes, produced from light that has orbited the black hole before escaping. This discovery will expose universal features of a black hole's spacetime that are distinct from the complex astrophysics of the emitting plasma, allowing the first direct measurements of a supermassive black hole's spin. In addition to studying the properties of the nearby supermassive black holes M87* and Sgr A*, BHEX will measure the properties of dozens of additional supermassive black holes, providing crucial insights into the processes that drive their creation and growth. BHEX will also connect these supermassive black holes to their relativistic jets, elucidating the power source for the brightest and most efficient engines in the universe. BHEX will address fundamental open questions in the physics and astrophysics of black holes that cannot be answered without submillimeter space VLBI. The mission is enabled by recent technological breakthroughs, including the development of ultra-high-speed downlink using laser communications, and it leverages billions of dollars of existing ground infrastructure. We present the motivation for BHEX, its science goals and associated requirements, and the pathway to launch within the next decade.

The general form of a 2D conformal field theory (CFT) correlator on a Euclidean Riemann surface, Lorentzian plane or Lorentzian cylinder is well-known. This paper describes the general form of 2- and 3-point CFT correlators on the Lorentzian torus $\mathcal{LT}^2$ which arises as the conformal boundary of the group manifold $\mathrm{SL}(2,\mathbb{R})$ $\simeq \text{AdS}_3/\mathbb{Z}$. We consider only generic points, thereby omitting an analysis of contact terms, which already exhibits a surprisingly rich structure. The results are relevant to celestial holography, for which the $\mathcal{LT}^2$ at the boundary of Klein space is the home of the putative celestial CFT.