Conformally soft theorem in gauge theory
TL;DR: In this paper, the soft limit of tree-level Minkowskian scattering amplitudes in a conformal group on the celestial two-sphere at null infinity is considered.
Abstract: Four-dimensional Minkowskian scattering amplitudes can also be presented in a basis of a different group ($S\phantom{\rule{0}{0ex}}L(2,C)$), which acts as the conformal group on the celestial two-sphere at null infinity. This type of representation is useful for understanding the flat-space holography. The authors propose a procedure for taking the (conformally) soft limit of tree-level scattering amplitudes in this basis.
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TL;DR: In this paper, 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 ∆ is provided.
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.
147 citations
18 Feb 2021
TL;DR: In this paper, it was shown that all information about massless excitations can be obtained from an infinitesimal neighbourhood of the past boundary of future null infinity and does not require observations over all of futurenull infinity.
Abstract: We argue that, in a theory of quantum gravity in a four dimensional asymptotically flat spacetime, all information about massless excitations can be obtained from an infinitesimal neighbourhood of the past boundary of future null infinity and does not require observations over all of future null infinity. Moreover, all information about the state that can be obtained through observations near a cut of future null infinity can also be obtained from observations near any earlier cut although the converse is not true. We provide independent arguments for these two assertions. Similar statements hold for past null infinity. These statements have immediate implications for the information paradox since they suggest that the fine-grained von Neumann entropy of the state defined on a segment $(-\infty,u)$ of future null infinity is independent of u. This is very different from the oft-discussed Page curve that this entropy is sometimes expected to obey. We contrast our results with recent discussions of the Page curve in the context of black hole evaporation, and also discuss the relation of our results to other proposals for holography in flat space.
145 citations
TL;DR: In this article, the authors construct two towers of 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights, which generate the symmetries associated to an infinite tower of conformally soft theorems.
Abstract: All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D currents acting on the celestial sphere. A complete classification of these symmetries and their algebras is an open problem. Here we construct two towers of such 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights. These generate the symmetries associated to an infinite tower of conformally soft theorems. The current algebra commutators are explicitly derived from the poles in the OPE coefficients, and found to comprise a rich closed subalgebra of the complete symmetry algebra.
144 citations
TL;DR: In this paper, various properties of massless four-point scalar and gluon celestial amplitudes such as conformal partial wave decomposition, crossing relations and optical theorem were studied.
Abstract: Massless scattering amplitudes in four-dimensional Minkowski spacetime can be Mellin-transformed to correlation functions on the celestial sphere at null infinity called celestial amplitudes. We study various properties of massless four-point scalar and gluon celestial amplitudes such as conformal partial wave decomposition, crossing relations and optical theorem. As a byproduct, we derive the analog of the single and double soft limits for all gluon celestial amplitudes.
128 citations
TL;DR: In this article, the authors use soft and collinear theorems of Einstein-Yang-Mills theory to derive the OPEs of BMS field operators generating superrotations and supertranslations.
Abstract: We elaborate on the proposal of flat holography in which four-dimensional physics is encoded in two-dimensional celestial conformal field theory (CCFT). The symmetry underlying CCFT is the extended BMS symmetry of (asymptotically) flat space time. We use soft and collinear theorems of Einstein-Yang-Mills theory to derive the OPEs of BMS field operators generating superrotations and supertranslations. The energy momentum tensor, given by a shadow transform of a soft graviton operator, implements superrotations in the Virasoro subalgebra of 𝔟𝔪𝔰4. Supertranslations can be obtained from a single translation generator along the light-cone direction by commuting it with the energy-momentum tensor. This operator also originates from a soft graviton and generates a flow of conformal dimensions. All supertranslations can be assembled into a single primary conformal field operator on celestial sphere.
117 citations
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TL;DR: In this paper, the results of Christodoulou and Klainerman were applied within a suitable finite neighborhood of the Minkowski vacuum to identify diagonal elements BMS0 of BMS+ × BMS−.
Abstract: BMS+ transformations act nontrivially on outgoing gravitational scattering data while preserving intrinsic structure at future null infinity (
$$ \mathrm{\mathcal{I}} $$
+). BMS− transformations similarly act on ingoing data at past null infinity (
$$ \mathrm{\mathcal{I}} $$
−). In this paper we apply — within a suitable finite neighborhood of the Minkowski vacuum — results of Christodoulou and Klainerman to link $$ \mathrm{\mathcal{I}} $$
+ to $$ \mathrm{\mathcal{I}} $$
− and thereby identify “diagonal” elements BMS0 of BMS+ × BMS−. We argue that BMS0 is a nontrivial infinite-dimensional symmetry of both classical gravitational scattering and the quantum gravity $$ \mathcal{S} $$
-matrix. It implies the conservation of net accumulated energy flux at every angle on the conformal S
2 at $$ \mathrm{\mathcal{I}} $$
. The associated Ward identity is shown to relate S-matrix elements with and without soft gravitons. Finally, BMS0 is recast as a U(1) Kac-Moody symmetry and an expression for the Kac-Moody current is given in terms of a certain soft graviton operator on the boundary of $$ \mathrm{\mathcal{I}} $$
.
841 citations
TL;DR: In this paper, the theory of interacting heterotic strings is presented and vertex operators are derived in both the bosonic and fermionic formulations of the theory and are shown to be consistent with gauge invariance, Lorentz invariance and supersymmetry.
786 citations
TL;DR: In this paper, the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions is taken to be the semi-direct sum of supertranslations with infinitesimal local conformal transformations.
Abstract: After a review of symmetries and classical solutions involved in the AdS3/CFT2 correspondence, we apply a similar analysis to asymptotically flat spacetimes at null infinity in 3 and 4 dimensions. In the spirit of two dimensional conformal field theory, the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions is taken to be the semi-direct sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra. As a first application, we derive how the symmetry algebra is realized on solution space. In particular, we work out the behavior of Bondi’s news tensor, mass and angular momentum aspects under local conformal transformations.
685 citations
Posted Content•
TL;DR: A transcript of a course given by Strominger at Harvard in spring semester 2016 as discussed by the authors contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic symmetries in four-dimensional QED, nonabelian gauge theory and gravity with applications to black holes.
Abstract: This is a redacted transcript of a course given by the author at Harvard in spring semester 2016. It contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic symmetries in four-dimensional QED, nonabelian gauge theory and gravity with applications to black holes. The lectures may be viewed online at this https URL. Please send typos or corrections to strominger@physics.this http URL.
599 citations