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Superrotations are local extensions of the Lorentz group at null infinity that have been argued to be symmetries of gravitational scattering. In their smooth version, they can be identified with the group of diffeomorphisms on the celestial sphere. Their canonical realization requires treating the celestial metric as a variable in the gravitational phase space, along with the news and shear tensors. In this paper, we derive the resulting Poisson brackets (PB). The standard PB algebra of the news and shear tensors is augmented by distributional terms at the boundaries of null infinity, including novel PB relations between the celestial metric and the radiative variables., Comment: 72 pages

We consider soft electrons in massless QED at tree-level. The emission amplitude at leading order in the soft electron energy factorizes in a way similar to the soft photon case. We recast the soft electron factorization formula as a Ward identity of an asymptotic charge. This leads to the first example of an asymptotic fermionic symmetry in a theory with no conventional supersymmetry, suggesting that tree-level massless QED may posses an asymptotic supersymmetry algebra. Although our approach does not yet allow us to completely characterize the algebra, it suggests that subleading soft photons should feature in the anticommutator of two fermionic symmetry generators., Comment: 29 pages

Asymptotic symmetries of gauge theories are known to encode infrared properties of radiative fields. In the context of tree-level Yang-Mills theory, the leading soft behavior of gluons is captured by large gauge symmetries with parameters that are $O(1)$ in the large $r$ expansion towards null infinity. This relation can be extended to subleading order provided one allows for large gauge symmetries with $O(r)$ gauge parameters. The latter, however, violate standard asymptotic field fall-offs and thus their interpretation has remained incomplete. We improve on this situation by presenting a relaxation of the standard asymptotic field behavior that is compatible with $O(r)$ gauge symmetries at linearized level. We show the extended space admits a symplectic structure on which $O(1)$ and $O(r)$ charges are well defined and such that their Poisson brackets reproduce the corresponding symmetry algebra., Comment: 28 pages

The Lie algebra generated by supertranslation and superrotation vector fields at null infinity, known as the extended BMS (eBMS) algebra is expected to be a symmetry algebra of the quantum gravity S matrix. However, the algebra of commutators of the quantized eBMS charges has been a thorny issue in the literature. On the one hand, recent developments in celestial holography point towards a symmetry algebra which is a closed Lie algebra with no central extension or anomaly, and on the other hand, work of Distler, Flauger and Horn has shown that when these charges are quantized at null infinity, the commutator of a supertranslation and a superrotation charge does not close into a supertranslation but gets deformed by a 2 cocycle term, which is consistent with the original proposal of Barnich and Troessaert. In this paper, we revisit this issue in light of recent developments in the classical understanding of superrotation charges. We show that, for extended BMS symmetries, a phase space at null infinity is an extension of hitherto considered phase spaces which also includes a mode associated to the spin memory and its conjugate partner. We also show that for holomorphic vector fields on the celestial plane, quantization of the eBMS charges in the new phase space leads to an algebra which closes without a 2 cocycle. The degenerate vacua are labelled by the soft news and a Schwarzian mode which corresponds to deformations of the celestial metric by superrotations. The closed eBMS quantum algebra may also lead to a convergence between two manifestations of asymptotic symmetries, one via asymptotic quantization at null infinity and the other through celestial holography., Comment: 35 pages, No Figures

We give a double copy construction for the symmetries of the self-dual sectors of Yang-Mills (YM) and gravity, in the light-cone formulation. We find an infinite set of double copy constructible symmetries. We focus on two families which correspond to the residual diffeomorphisms on the gravitational side. For the first one, we find novel non-perturbative double copy rules in the bulk. The second family has a more striking structure, as a non-perturbative gravitational symmetry is obtained from a perturbatively defined symmetry on the YM side. At null infinity, we find the YM origin of the subset of extended Bondi-Metzner-Sachs (BMS) symmetries that preserve the self-duality condition. In particular, holomorphic large gauge YM symmetries are double copied to holomorphic supertranslations. We also identify the single copy of superrotations with certain non-gauge YM transformations that to our knowledge have not been previously presented in the literature., Comment: 45 pages, 1 figure, replaced to match published version

It has been argued that the symmetries of gravity at null infinity should include a Diff$(S^2)$ factor associated to diffeomorphisms on the celestial sphere. However, the standard phase space of gravity does not support the action of such transformations. Building on earlier work by Laddha and one of the authors, we present an extension of the phase space of gravity at null infinity on which Diff$(S^2)$ acts canonically. The Poisson brackets of supertranslation and Diff$(S^2)$ charges reproduce the generalized BMS algebra introduced in arXiv:1408.2228 ., Comment: 30 pages. Corrected paragraph after Eq. (1.9) and second to last paragraph in discussion section. Submitted to PRD

Recently Sahoo and Sen obtained a series of remarkable results concerning sub-leading soft photon and graviton theorems in four dimensions. Even though the S- matrix is infrared divergent, they have shown that the sub-leading soft theorems are well defined and exact statements in QED and perturbative Quantum Gravity. However unlike the well studied Cachazo-Strominger soft theorems in tree-level amplitudes, the new sub-leading soft expansion is at the order ln {\omega} (where {\omega} is the soft frequency) and the corresponding soft factors structurally show completely different properties then their tree-level counterparts. Whence it is natural to ask if these theorems are associated to asymptotic symmetries of the S-matrix. We consider this question in the context of sub-leading soft photon theorem in scalar QED and show that there are indeed an infinity of conservation laws whose Ward identities are equivalent to the loop-corrected soft photon theorem. This shows that in the case of four dimensional QED, the leading and sub-leading soft photon theorems are equivalent to Ward identities of (asymptotic) charges., Comment: 33 pages, no figures

Hamada and Shiu have recently shown that tree level amplitudes in QED satisfy an infinite hierarchy of soft photon theorems, the first two of which are Weinberg and Low's theorems respectively. In this paper we propose that in tree level massless QED, this entire hierarchy is equivalent to a hierarchy of (asymptotic) conservation laws. We prove the equivalence explicitly for the case of sub-subleading soft photon theorem and give substantial evidence that the equivalence continues to hold for the entire hierarchy. Our work also brings out the (complimentary) relationship between the asymptotic charges associated to soft theorems and the well known Newman-Penrose charges., Comment: 37 pages

In recent years soft factorization theorems in scattering amplitudes have been reinterpreted as conservation laws of asymptotic charges. In gauge, gravity, and higher spin theories the asymptotic charges can be understood as canonical generators of large gauge symmetries. Such a symmetry interpretation has been so far missing for scalar soft theorems. We remedy this situation by treating the massless scalar field in terms of a dual two-form gauge field. We show that the asymptotic charges associated to the scalar soft theorem can be understood as generators of large gauge transformations of the dual two-form field. The dual picture introduces two new puzzles: the charges have very unexpected Poisson brackets with the fields, and the monopole term does not always have a dual gauge transformation interpretation. We find analogs of these two properties in the Kramers-Wannier duality on a finite lattice, indicating that the free scalar theory has new edge modes at infinity that canonically commute with all the bulk degrees of freedom., Comment: 16 pages, 2 figures

There has been a recent resurgence of interest in the structure of the gravitational field at null infinity, sparked by new results on soft charges and infrared issues related to the S matrix theory in perturbative quantum gravity. We summarize these developments and put them in the broader context of research in the relativity community that dates back to several decades. In keeping with intent of this series, this overview is addressed to gravitational scientists who are not experts in this specific area., Comment: 19 pages, no figures. Prepared for the "Introduction to Current Research Series." Clarifications added following correspondence with expert, typos corrected, version to appear in the journal

We study asymptotic charges associated to a spin-zero analogue of Weinberg's soft photon and graviton theorems in even dimensions. Simple spacetime expressions for the charges are given, but unlike gravity or electrodynamics, the symmetry interpretation for the charges remains elusive. This work is a higher dimensional extension of the four dimensional case studied in arXiv:1703.07885 ., Comment: 15 pages

We study Hawking radiation on the quantum space-time of a collapsing null shell. We use the geometric optics approximation as in Hawking's original papers to treat the radiation. The quantum space-time is constructed by superposing the classical geometries associated with collapsing shells with uncertainty in their position and mass. We show that there are departures from thermality in the radiation even though we are not considering back reaction. One recovers the usual profile for the Hawking radiation as a function of frequency in the limit where the space-time is classical. However, when quantum corrections are taken into account, the profile of the Hawking radiation as a function of time contains information about the initial state of the collapsing shell. More work will be needed to determine if all the information can be recovered. The calculations show that non-trivial quantum effects can occur in regions of low curvature when horizons are involved, as for instance advocated in the firewall scenario., Comment: 25 pages, 3 figures, removed extra figure in previous version and made small changes

Large gauge symmetries in Minkowski spacetime are often studied in two distinct regimes: either at asymptotic (past or future) times or at spatial infinity. By working in harmonic gauge, we provide a unified description of large gauge symmetries (and their associated charges) that applies to both regimes. At spatial infinity the charges are conserved and interpolate between those defined at the asymptotic past and future. This explains the equality of asymptotic past and future charges, as recently proposed in connection with Weinberg's soft photon theorem., Comment: 23 pages

Recently it has been understood that certain soft factorization theorems for scattering amplitudes can be written as Ward identities of new asymptotic symmetries. This relationship has been established for soft particles with spins $s > 0$, most notably for soft gravitons and photons. Here we study the remaining case of soft scalars. We show that a class of Yukawa-type theories, where a massless scalar couples to massive particles, have an infinite number of conserved charges. This raises the question as to whether one can associate asymptotic symmetries to scalars., Comment: 31 pages. Version accepted in PRD

We argue that a conformally invariant extension of general relativity coupled to the Standard Model is the fundamental theory that needs to be quantized. We show that it can be treated by loop quantum gravity techniques. Through a gauge fixing and a modified Higgs mechanism particles acquire mass and one recovers general relativity coupled to the Standard Model. The theory suggests new views with respect to the definition of the Hamiltonian constraint in loop quantum gravity, the semi-classical limit and the issue of finite renormalization in quantum field theory in quantum space-time. It also gives hints about the elimination of ambiguities that arise in quantum field theory in quantum space-time in the calculation of back-reaction., Comment: 5 pages

We present strong evidence that the sub-subleading soft theorem in semi-classical (tree level) gravity discovered by Cachazo and Strominger is equivalent to the conservation of asymptotic charges associated to a new class of vector fields not contained within the previous extensions of BMS algebra. Our analysis crucially relies on analyzing the hitherto established equivalences between soft theorems and Ward identities from a new perspective. In this process we naturally (re)discover a class of `magnetic' charges at null infinity that are associated to the dual of the Weyl tensor., Comment: 41 pages

Lysov, Pasterski and Strominger have shown how Low's subleading soft photon theorem can be understood as Ward identities of new symmetries of massless QED. In this paper we offer a different perspective and show that there exists a class of large $U(1)$ gauge transformations such that (i) the associated (electric and magnetic) charges can be computed from first principles (ii) their Ward identities are equivalent to Low's theorem. Our framework paves the way to analyze the sub-subleading theorem in gravity in terms of Ward identities associated to large diffeomorphisms., Comment: 17 pages

Due to seminal works of Weinberg, Cachazo and Strominger we know that tree level quantum gravity amplitudes satisfy three factorization constraints. Building on previous works which relate two of these constraints to symmetries of quantum gravity at null infinity, we present rather strong evidence that the third constraint is also equivalent to a new set of symmetries of (perturbative) quantum gravity. Our analysis implies that the symmetry group of quantum gravity may be even richer than the BMS group (or infinite dimensional extension thereof) previously considered., Comment: 5 pages

The problem of how space-time responds to gravitating quantum matter in full quantum gravity has been one of the main questions that any program of quantization of gravity should address. Here we analyze this issue by considering the quantization of a collapsing null shell coupled to spherically symmetric loop quantum gravity. We show that the constraint algebra of canonical gravity is Abelian both classically and when quantized using loop quantum gravity techniques. The Hamiltonian constraint is well defined and suitable Dirac observables characterizing the problem were identified at the quantum level. We can write the metric as a parameterized Dirac observable at the quantum level and study the physics of the collapsing shell and black hole formation. We show how the singularity inside the black hole is eliminated by loop quantum gravity and how the shell can traverse it. The construction is compatible with a scenario in which the shell tunnels into a baby universe inside the black hole or one in which it could emerge through a white hole., Comment: 4 pages, RevTex

We elaborate on the Green's functions that appeared in [1,2] when generalizing, from massless to massive particles, various equivalences between soft theorems and Ward identities of large gauge symmetries. We analyze these Green's functions in considerable detail and show that they form a hierarchy of functions which describe `boundary to bulk' propagators for large $U(1)$ gauge parameters, supertranslations and sphere vector fields respectively. As a consistency check we verify that the Green's functions associated to the large diffeomorphisms map the Poincare group at null infinity to the Poincare group at time-like infinity., Comment: 16 pages

The existing equivalence between (generalized) BMS Ward identities with leading and subleading soft graviton theorems is extended to the case where the scattering particles are massive scalars. By extending the action of generalized BMS group off null infinity at late times, we show that there is a natural action of such group not only on the radiative data at null infinity but also on the scattering data of the massive scalar field. This leads to a formulation of Ward identities associated to the generalized BMS group when the scattering states are massive scalars or massless gravitons and we show that these Ward identities are equivalent to the leading and subleading soft graviton theorems., Comment: 30 pages

Various equivalences between so-called soft theorems which constrain scattering amplitudes and Ward identities related to asymptotic symmetries have recently been established in gauge theories and gravity. So far these equivalences have been restricted to the case of massless matter fields, the reason being that the asymptotic symmetries are defined at null infinity. The restriction is however unnatural from the perspective of soft theorems which are insensitive to the masses of the external particles. In this work we remove the aforementioned restriction in the context of scalar QED. Inspired by the radiative phase space description of massless fields at null infinity, we introduce a manifold description of time-like infinity on which the asymptotic phase space for massive fields can be defined. The "angle dependent" large gauge transformations are shown to have a well defined action on this phase space, and the resulting Ward identities are found to be equivalent to Weinberg's soft photon theorem., Comment: 19 pages, no figures

In [15] we proposed a generalization of the BMS group G which is a semidirect product of supertranslations and smooth diffeomorphisms of the conformal sphere. Although an extension of BMS, G is a symmetry group of asymptotically flat space times. By taking G as a candidate symmetry group of the quantum gravity S-matrix, we argued that the Ward identities associated to the generators of Diff(S^2) were equivalent to the Cachazo-Strominger subleading soft graviton theorem. Our argument however was based on a proposed definition of the Diff(S^2) charges which we could not derive from first principles as G does not have a well defined action on the radiative phase space of gravity. Here we fill this gap and provide a first principles derivation of the Diff(S^2) charges. The result of this paper, in conjunction with the results of [4, 15] prove that the leading and subleading soft theorems are equivalent to the Ward identities associated to G., Comment: 19 pages

We construct a quantum kinematics for asymptotically flat spacetimes based on the Koslowski-Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying Loop Quantum Gravity (LQG) which supports, in addition to the usual LQG operators, the action of `background exponential operators' which are connection dependent operators labelled by `background' $su(2)$ electric fields. KS states have, in addition to the LQG state label corresponding to 1 dimensional excitations of the triad, a label corresponding to a `background' electric field which describes 3 dimensional excitations of the triad. Asymptotic behaviour in quantum theory is controlled through asymptotic conditions on the background electric fields which label the {\em states} and the background electric fields which label the {\em operators}. Asymptotic conditions on the triad are imposed as conditions on the background electric field state label while confining the LQG spin net graph labels to compact sets. We show that KS states can be realised as wave functions on a quantum configuration space of generalized connections and that the asymptotic behaviour of each such generalized connection is determined by that of the background electric fields which label the background exponential operators. Similar to the spatially compact case, the Gauss Law and diffeomorphism constraints are then imposed through Group Averaging techniques to obtain a large sector of gauge invariant states. It is shown that this sector supports a unitary action of the group of asymptotic rotations and translations and that, as anticipated by Friedman and Sorkin, for appropriate spatial topology, this sector contains states which display fermionic behaviour under $2\pi$ rotations., Comment: 64 pages

We describe the canonical phase space of asymptotically flat gravity in Ashtekar-Barbero variables. We show that the Gauss constraint multiplier must fall off slower than previously considered in order to recover ADM phase space. The generators of the asymptotic Poincare group are derived within the Ashtekar-Barbero phase space without reference to the ADM generators. The resulting expressions are shown to agree, modulo Gauss constraint terms, with those obtained from the ADM generators. A payoff of this procedure is a new expression for the generator of asymptotic rotations which is polynomial in the triad and hence better suited for quantum theory. Our treatment complements earlier description by Thiemann in the context of self-dual variables., Comment: 18 pages

Motivated by the equivalence between soft graviton theorem and Ward identities for the supertranslation symmetries belonging to the BMS group, we propose a new extension (different from the so-called extended BMS) of the BMS group which is a semi-direct product of supertranslations and Diff(S^2). We propose a definition for the canonical generators associated to the smooth diffeomorphisms and show that the resulting Ward identities are equivalent to the subleading soft graviton theorem of Cachazo and Strominger., Comment: 25 pages, published version

The Koslowski-Sahlmann (KS) representation is a generalization of the representation underlying the discrete spatial geometry of Loop Quantum Gravity (LQG), to accommodate states labelled by smooth spatial geometries. As shown recently, the KS representation supports, in addition to the action of the holonomy and flux operators, the action of operators which are the quantum counterparts of certain connection dependent functions known as "background exponentials". Here we show that the KS representation displays the following properties which are the exact counterparts of LQG ones: (i) the abelian $*$ algebra of $SU(2)$ holonomies and `$U(1)$' background exponentials can be completed to a $C^*$ algebra (ii) the space of semianalytic $SU(2)$ connections is topologically dense in the spectrum of this algebra (iii) there exists a measure on this spectrum for which the KS Hilbert space is realised as the space of square integrable functions on the spectrum (iv) the spectrum admits a characterization as a projective limit of finite numbers of copies of $SU(2)$ and $U(1)$ (v) the algebra underlying the KS representation is constructed from cylindrical functions and their derivations in exactly the same way as the LQG (holonomy-flux) algebra except that the KS cylindrical functions depend on the holonomies and the background exponentials, this extra dependence being responsible for the differences between the KS and LQG algebras. While these results are obtained for compact spaces, they are expected to be of use for the construction of the KS representation in the asymptotically flat case.

The discrete spatial geometry underlying Loop Quantum Gravity (LQG) is degenerate almost everywhere. This is at apparent odds with the non- degeneracy of asymptotically flat metrics near spatial infinity. Koslowski generalised the LQG representation so as to describe states labelled by smooth non- degenerate triad fields. His representation was further studied by Sahlmann with a view to imposing gauge and spatial diffeomorphism invariance through group averaging methods. Motivated by the desire to model asymptotically flat quantum geometry by states with triad labels which are non- degenerate at infinity but not necessarily so in the interior, we initiate a generalisation of Sahlmann's considerations to triads of varying degeneracy. In doing so, we include delicate phase contributions to the averaging procedure which are crucial for the correct implementation of the gauge and diffeomorphism constraints, and whose existence can be traced to the background exponential functions recently constructed by one of us. Our treatment emphasizes the role of symmetries of quantum states in the averaging procedure. Semianalyticity, influential in the proofs of the beautiful uniqueness results for LQG, plays a key role in our considerations. As a by product, we re- derive the group averaging map for standard LQG, highlighting the role of state symmetries and explicitly exhibiting the essential uniqueness of its specification.

Since black holes can be formed through widely varying processes, the horizon structure is highly complicated in the dynamical phase. Nonetheless, as numerical simulations show, the final state appears to be universal, well described by the Kerr geometry. How are all these large and widely varying deviations from the Kerr horizon washed out? To investigate this issue, we introduce a well-suited notion of horizon multipole moments and equations governing their dynamics, thereby providing a coordinate and slicing independent framework to investigate the approach to equilibrium. In particular, our flux formulas for multipoles can be used as analytical checks on numerical simulations and, in turn, the simulations could be used to fathom possible universalities in the way black holes approach their final equilibrium., Comment: 27 pages, 1 figure. Thanks to the referee's suggestion, two remarks at the end of section III.B were added to clarify certain issues addressed to the numerical relativity community. They in turn led to several new references

The holonomy-flux algebra $\A$ of loop quantum gravity is known to admit a natural representation that is uniquely singled out by the requirement of covariance under spatial diffeomorphisms. In the cosmological context, the requirement of spatial homogeneity naturally reduces $\A$ to a much smaller algebra, $\A_{\rm Red}$, used in loop quantum cosmology. In Bianchi I models, it is shown that the requirement of covariance under \emph{residual} diffeomorphism symmetries again uniquely selects the representation of $\A_{\rm Red}$ that has been commonly used. We discuss the close parallel between the two uniqueness results and also point out a difference., Comment: 9 pages