Search

Abstract We consider massless scattering from the point of view of the position, momentum, and celestial bases. In these three languages different properties of physical processes become manifest or obscured. Within the soft sector, they highlight distinct aspects of the infrared triangle: quantum field theory soft theorems arise in the limit of vanishing energy ω, memory effects are described via shifts of fields at the boundary along the null time coordinate u, and celestial symmetry algebras are realized via currents that appear at special values of the conformal dimension ∆. We focus on the subleading soft theorems at ∆ = 1 − s for gauge theory (s = 1) and gravity (s = 2) and explore how to translate the infrared triangle to the celestial basis. We resolve an existing tension between proposed overleading gauge transformations as examined in the position basis and the ‘Goldstone-like’ modes where we expect celestial symmetry generators to appear. In the process we elucidate various order-of-limits issues implicit in the celestial formalism. We then generalize our construction to the tower of w 1+∞ generators in celestial CFT, which probe further subleading-in-ω soft behavior and are related to subleading-in-r vacuum transitions that measure higher multipole moments of scatterers. In the end we see that the celestial basis is ‘just right’ for identifying the symmetry structure.

Abstract Celestial diamonds encode the global conformal multiplets of the conformally soft sector, elucidating the role of soft theorems, symmetry generators and Goldstone modes. Upon adding supersymmetry they stack into a pyramid. Here we treat the soft charges associated to the fermionic layers that tie this structure together. This extends the analysis of conformally soft currents for photons and gravitons which have been shown to generate asymptotic symmetries in gauge theory and gravity to infinite-dimensional fermionic symmetries. We construct fermionic charge operators in 2D celestial CFT from a suitable inner product between 4D bulk field operators and spin s = 1 2 $$ \frac{1}{2} $$ and 3 2 $$ \frac{3}{2} $$ conformal primary wavefunctions with definite SL(2, ℂ) conformal dimension ∆ and spin J where |J| ≤ s. The generator for large supersymmetry transformations is identified as the conformally soft gravitino primary operator with ∆ = 1 2 $$ \frac{1}{2} $$ and its shadow with ∆ = 3 2 $$ \frac{3}{2} $$ which form the left and right corners of the celestial gravitino diamond. We continue this analysis to the subleading soft gravitino and soft photino which are captured by degenerate celestial diamonds. Despite the absence of a gauge symmetry in these cases, they give rise to conformally soft factorization theorems in celestial amplitudes and complete the celestial pyramid.

Supersymmetric microstate geometries with five non-compact dimensions haverecently been shown by Eperon, Reall, and Santos (ERS) to exhibit a non-linearinstability featuring the growth of excitations at an "evanescent ergosurface"of infinite redshift. We argue that this growth may be treated as adiabaticevolution along a family of exactly supersymmetric solutions in the limit wherethe excitations are Aichelburg-Sexl-like shockwaves. In the 2-charge systemsuch solutions may be constructed explicitly, incorporating full backreaction,and are in fact special cases of known microstate geometries. In a near-horizonlimit, they reduce to Aichelburg-Sexl shockwaves in $AdS_3 \times S^3$propagating along one of the angular directions of the sphere. Noting that theERS analysis is valid in the limit of large microstate angular momentum $j$, weuse the above identification to interpret their instability as a transitionfrom rare smooth microstates with large angular momentum to more typicalmicrostates with smaller angular momentum. This entropic driving terminateswhen the angular momentum decreases to $j \sim \sqrt{n_1n_5}$ where the densityof microstates is maximal. We argue that, at this point, the large stringycorrections to such microstates will render them non-linearly stable. Weidentify a possible mechanism for this stabilization and detail an illustrativetoy model.

Abstract We provide a unified treatment of conformally soft Goldstone modes which arise when spin-one or spin-two conformal primary wavefunctions become pure gauge for certain integer values of the conformal dimension ∆. This effort lands us at the crossroads of two ongoing debates about what the appropriate conformal basis for celestial CFT is and what the asymptotic symmetry group of Einstein gravity at null infinity should be. Finite energy wavefunctions are captured by the principal continuous series ∆ ∈ 1 + iℝ and form a complete basis. We show that conformal primaries with analytically continued conformal dimension can be understood as certain contour integrals on the principal series. This clarifies how conformally soft Goldstone modes fit in but do not augment this basis. Conformally soft gravitons of dimension two and zero which are related by a shadow transform are shown to generate superrotations and non-meromorphic diffeomorphisms of the celestial sphere which we refer to as shadow superrotations. This dovetails the Virasoro and Diff(S2) asymptotic symmetry proposals and puts on equal footing the discussion of their associated soft charges, which correspond to the stress tensor and its shadow in the two-dimensional celestial CFT.

Abstract The four-dimensional S-matrix is reconsidered as a correlator on the celestial sphere at null infinity. Asymptotic particle states can be characterized by the point at which they enter or exit the celestial sphere as well as their SL(2, ℂ) Lorentz quantum numbers: namely their conformal scaling dimension and spin h ± h ¯ $$ h\pm \overline{h} $$ instead of the energy and momentum. This characterization precludes the notion of a soft particle whose energy is taken to zero. We propose it should be replaced by the notion of a conformally soft particle with h = 0 or h ¯ $$ \overline{h} $$ = 0. For photons we explicitly construct conformally soft SL(2, ℂ) currents with dimensions (1, 0) and identify them with the generator of a U(1) Kac-Moody symmetry on the celestial sphere. For gravity the generator of celestial conformal symmetry is constructed from a (2, 0) SL(2, ℂ) primary wavefunction. Interestingly, BMS supertranslations are generated by a spin-one weight ( 3 2 $$ \frac{3}{2} $$ , 1 2 $$ \frac{1}{2} $$ ) operator, which nevertheless shares holomorphic characteristics of a conformally soft operator. This is because the right hand side of its OPE with a weight (h, h ¯ $$ \overline{h} $$ ) operator O h , h ¯ $$ {\mathcal{O}}_{h,\overline{h}} $$ involves the shifted operator O h + 1 2 , h ¯ + 1 2 $$ {\mathcal{O}}_{h+\frac{1}{2},\overline{h}+\frac{1}{2}} $$ . This OPE relation looks quite unusual from the celestial CFT2 perspective but is equivalent to the leading soft graviton theorem and may usefully constrain celestial correlators in quantum gravity.

Abstract Inspired by the recent work of Bao and Ooguri (BO), we study the distinguishability of the black hole microstates from the thermal state as captured by the average of their relative entropies: the Holevo information. Under the assumption that the vacuum conformal block dominates the entropy calculation, BO find that the average relative entropy vanishes on spatial regions smaller than half the size of the CFT. However, vacuum block dominance fails for some microstates of the M = 0 BTZ black hole. We show that this renders the average relative entropy nonzero even on infinitesimal intervals at O(c 0).

Abstract Supersymmetric microstate geometries with five non-compact dimensions have recently been shown by Eperon, Reall, and Santos (ERS) to exhibit a non-linear instability featuring the growth of excitations at an “evanescent ergosurface” of infinite redshift. We argue that this growth may be treated as adiabatic evolution along a family of exactly supersymmetric solutions in the limit where the excitations are Aichelburg-Sexl-like shockwaves. In the 2-charge system such solutions may be constructed explicitly, incorpo-rating full backreaction, and are in fact special cases of known microstate geometries. In a near-horizon limit, they reduce to Aichelburg-Sexl shockwaves in AdS 3 × S 3 propagating along one of the angular directions of the sphere. Noting that the ERS analysis is valid in the limit of large microstate angular momentum j, we use the above identification to interpret their instability as a transition from rare smooth microstates with large angular momentum to more typical microstates with smaller angular momentum. This entropic driving terminates when the angular momentum decreases to j ∼ n 1 n 5 $$ j\sim \sqrt{n_1{n}_5} $$ where the density of microstates is maximal. We argue that, at this point, the large stringy corrections to such microstates will render them non-linearly stable. We identify a possible mechanism for this stabilization and detail an illustrative toy model.

We investigate the recent black hole firewall argument. For a black hole in a typical state we argue that unitarity requires every quantum of radiation leaving the black hole to carry information about the initial state. An information-free horizon is thus inconsistent with unitary at every step of the evaporation process. The required horizon-scale structure is manifest in the fuzzball proposal which provides a mechanism for holding up the structure. In this context we want to address the experience of an infalling observer and discuss the recent fuzzball complementarity proposal. Unlike black hole complementarity and observer complementarity which postulate asymptotic observers experience a hot membrane while infalling ones pass freely through the horizon, fuzzball complementarity postulates that fine-grained operators experience the details of the fuzzball microstate and coarse-grained operators experience the black hole. In particular, this implies that an in-falling detector tuned to energy E ~ TH, where TH is the asymptotic Hawking temperature, does not experience free infall while one tuned to E ≫ TH does. [ABSTRACT FROM AUTHOR]