The celestial $Lw_{1+\infty}$ symmetries in asymptotically flat spacetimes have a natural geometric interpretation on twistor space in terms of Poisson diffeomorphisms. Using this framework, we provide a first-principle derivation of the canonical generators associated with these symmetries starting from the Poisson BF twistor action for self-dual gravity. We express these charges as surface integrals over the celestial sphere in terms of spacetime data at null infinity. The connection between twistor space and spacetime expressions at $\mathscr{I}$ is achieved via an integral formula for the asymptotic Bianchi identities due to Bramson and Tod. Finally, we clarify how $Lw_{1+\infty}$ transformations are symmetries of gravity from a phase space perspective by showing the invariance of the asymptotic Bianchi identities.
We explain how twistor theory represents the self-dual sector of four dimensional gravity in terms of the loop group of Poisson diffeomorphisms of the plane via Penrose's non-linear graviton construction. The symmetries of the self-dual sector are generated by the corresponding loop algebra $Lw_{1+\infty}$ of the algebra $w_{1+\infty}$ of these Poisson diffeomorphisms. We show that these coincide with the infinite tower of soft graviton symmetries in tree-level perturbative gravity recently discovered in the context of celestial amplitudes. We use a twistor sigma model for the self-dual sector…
There has been recent interest in the question of whether QCD collinear singularities can be viewed as the OPE of a two-dimensional CFT. We analyze a version of this question for the self-dual limit of pure gauge theory (incorporating states of both helicities). We show that the known one-loop collinear singulaties do not form an associative chiral algebra. The failure of associativity can be traced to a novel gauge anomaly on twistor space. We find that associativity can be restored for certain gauge groups if we introduce an unusual axion, which cancels the twistor space anomaly by a Green-S…
We consider the Moyal deformation of self-dual gravity. In the conformal primary basis, holomorphic collinear limits of the amplitudes of this theory show that it enjoys a perturbatively exact symmetry algebra $LW_\wedge$ that generalises $Lw_\wedge$, the loop algebra of the wedge algebra of $w_{1+\infty}$, which appears in self-dual gravity.
Celestial operator product expansions (OPEs) arise from the collinear limit of scattering amplitudes and play a vital role in celestial holography. In this paper, we derive the celestial OPEs of massless fields in string theory from the worldsheet. By studying the worldsheet OPEs of vertex operators in worldsheet CFT and further examining their behaviors in the collinear limit, we find that new vertex operators for the massless fields in string theory are generated and become dominant in the collinear limit. Mellin transforming to the conformal basis yields exactly the celestial OPEs in celest…
In this note we determine the graviton-graviton OPE and the null states in any $w_{1+\infty}$ symmetric theory on the celestial sphere. Our analysis shows that there exists a discrete \textit{infinite} family of such theories. The MHV-sector and the quantum self dual gravity are two members of this infinite family. Although the Bulk Lagrangian description of this family of theories is not currently known to us, the graviton scattering amplitudes in these theories are heavily constrained due to the existence of null states. Presumably they are exactly solvable in the same way as the minimal mod…
The operator product expansion of massless celestial primary operators of arbitrary spin is investigated. Poincaré symmetry is found to imply a set of recursion relations on the operator product expansion coefficients of the leading singular terms at tree-level in a holomorphic limit. The symmetry constraints are solved by an Euler beta function with arguments that depend simply on the right-moving conformal weights of the operators in the product. These symmetry-derived coefficients are shown not only to match precisely those arising from momentum-space tree-level collinear limits, but also t…
By using the $K$-free complex bosons and the $K$-free complex fermions, we construct the ${\cal N}=2$ supersymmetric $W_{\infty}^{K,K}$ algebra which is the matrix generalization of previous ${\cal N}=2$ supersymmetric $W_{\infty}$ algebra. By twisting this ${\cal N}=2$ supersymmetric $W_{\infty}^{K,K}$ algebra, we obtain the ${\cal N}=1$ supersymmetric $W_{\infty}^{K}$ algebra which is the matrix generalization of known ${\cal N}=1$ supersymmetric topological $W_{\infty}$ algebra. From this two-dimensional symmetry algebra, we propose the operator product expansion (OPE) between the soft grav…
In this paper we extract from a large-$r$ expansion of the vacuum Einstein's equations a dynamical system governing the time evolution of an infinity of higher-spin charges. Upon integration, we evaluate the canonical action of these charges on the gravity phase space. The truncation of this action to quadratic order and the associated charge conservation laws yield an infinite tower of soft theorems. We show that the canonical action of the higher spin charges on gravitons in a conformal primary basis, as well as conformally soft gravitons reproduces the higher spin celestial symmetries deriv…
The $w_{1+\infty}$ symmetry algebra appears in the Einstein--Yang--Mills theory, proposed recently by Strominger. In this paper, we derive the supersymmetric $w_{1+\infty}$ symmetry by using the known results on the operator product expansions (OPEs) between the graviton, gravitino, gluon, and gluino in the supersymmetric version of the above theory. We calculate the four additional commutator relations between the soft currents explicitly. In addition, we analyze the works of Odake et al. and Pope et al. and introduce the additional symmetry current that corresponds to the celestial gluino op…
We summarise some of our recent works on $L_\infty$-algebras and quasi-groups with regard to higher principal bundles and their applications in twistor theory and gauge theory. In particular, after a lightning review of $L_\infty$-algebras, we discuss their Maurer-Cartan theory and explain that any classical field theory admitting an action can be reformulated in this context with the help of the Batalin-Vilkovisky formalism. As examples, we explore higher Chern-Simons theory and Yang-Mills theory. We also explain how these ideas can be combined with those of twistor theory to formulate maxima…
Celestial $Lw_{1+\infty}$ Symmetries and Subleading Phase Space of Null Hypersurfaces
Harvard University（哈佛大学）；Perimeter Institute for Theoretical Physics（珀杜姆理论物理研究所）；Université Libre de Bruxelles and International Solvay Institutes（布鲁塞尔自由大学与国际索尔维研究所）；Collège de France（法兰西学院）
Using tools from color-kinematics duality we propose a holographic construction of gravitational amplitudes, based on a 2d Kac-Moody theory on the celestial sphere. In the $N\to \infty$ limit the gauge group corresponds to $w_{1+\infty}$, due to the $U(N)$ generators enjoying a simple quantum group structure, which is in turn inherited from a twistor fiber over the celestial sphere. We show how four-dimensional momentum-space is emergent in this picture, which connects directly to the so-called kinematic algebra of the tree-level S-Matrix. On the other hand, the framework can be embedded withi…
The infrared behavior of gravity in 4D asymptotically flat spacetime exhibits a rich set of symmetries. This has led to a proposed holographic duality between the gravitational $\mathcal{S}$-matrix and a dual field theory living on the celestial sphere. Most of our current understanding of the dictionary relies on knowledge of the 4D bulk. As such, identifying intrinsic 2D models that capture the correct symmetries and soft dynamics of 4D gravity is an active area of interest. Here we propose that a 2D generalization of SYK provides an instructive toy model for the soft limit of the gravitatio…
Higher-spin charges and the $L_Λ w_{1 + \infty}$ algebra in (A)dS$_4$
Università degli Studi di Udine（乌迪内大学）；Institute for Fundamental Physics of the Universe (IFPU)（宇宙基础物理研究所）；Istituto Nazionale di Fisica Nucleare, sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；King’s College London（伦敦国王学院）
Preliminary investigations of the topological phase of string theory along the lines of a (restricted) $\dot{w}_{\infty}$ non-linear sigma model are provided. Gauge fixing the w gravity gauge fields by preserving a geometric identity Lorenz covariantizes the w-particle and gauge covariantizes the YM. The notion of foliation ghosts is introduced. Connection between $\dot{w}_{\infty}$ and homotopy associative algebras is indicated. The second quantized twistor space of string theory is constructed and compared with the first quantised one. Speculations about the relevance of the massive string f…
We consider the covariant quantization of the D=11 massless superparticle (M0-brane) in the spinor moving frame or twistor-like Lorentz harmonics formulation. The action involves the set of 16 constrained 32 component Majorana spinors, the spinor Lorentz harmonics parametrizing (as homogeneous coordinates, modulo gauge symmetries) the celestial sphere S9. There presence allows us to separate covariantly the first and the second class constraints of the model. After taking into account the second class constraints by means of Dirac brackets and after further reducing the first class constraints…
