Abstract:Recently it was conjectured that a certain infinite-dimensional "diagonal" subgroup of BMS supertranslations acting on past and future null infinity (I − and I + ) is an exact symmetry of the quantum gravity S-matrix, and an associated Ward identity was derived. In this paper we show that this supertranslation Ward identity is precisely equivalent to Weinberg's soft graviton theorem. Along the way we construct the canonical generators of supertranslations at I ± , including the relevant soft graviton contributions. Boundary conditions at the past and future of I ± and a correspondingly modified Dirac bracket are required. The soft gravitons enter as boundary modes and are manifestly the Goldstone bosons of spontaneously broken supertranslation invariance.

An infinite number of physically nontrivial symmetries are found for abelian gauge theories with massless charged particles. They are generated by large U (1) gauge transformations that asymptotically approach an arbitrary function ε(z,z) on the conformal sphere at future null infinity (I + ) but are independent of the retarded time. The value of ε at past null infinity (I − ) is determined from that on I + by the condition that it take the same value at either end of any light ray crossing Minkowski space. The ε = constant symmetries are spontaneously broken in the usual vacuum. The associated Goldstone modes are zero-momentum photons and comprise a U (1) boson living on the conformal sphere. The Ward identity associated with this asymptotic symmetry is shown to be the abelian soft photon theorem.Recently a general equivalence relation has emerged between soft theorems and asymptotic symmetries [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Soft theorems are relations between n and n + 1 particle scattering amplitudes, where the extra particle is soft. Any linear relation between scattering amplitudes can be recast as an infinitesimal symmetry of the S-matrix. It is gratifying that in some cases the resulting symmetries have turned out to be known space-time or gauge symmetries. For example Weinberg's soft graviton theorem [20,21] is equivalent to a symmetry of the S-matrix generated by a certain diagonal subgroup [2] of the product of BMS [22] supertranslations acting on past and future null infinity, I + and I − .This equivalence relation is of interest for several reasons. It "explains" why soft theorems exist and are so universal: they arise from a symmetry principle. Moreover, it imparts observational meaning to Minkowskian asymptotic symmetries, which have at times eluded physical interpretation.The framework has proven useful for establishing new symmetries [14] and new soft theorems [4][5][6]. In the quantum gravity case, the symmetries provide the starting point for any attempt at a holographic formulation, see e.g. [23]. In the gauge theory case, they are potentially useful for improving the accuracy of collider predictions, see e.g. [24].The purpose of the present paper is to argue that the soft photon theorem in massless QED [25] [20] [26] can be understood as a new asymptotic symmetry. The symmetry is generated by "large" U(1) gauge transformations which approach an arbitrary function ε(z,z) on the conformal sphere at I but are constant along the null generators, even as they antipodally cross from I − to I + through spatial infinity. Except for the constant transformation, these symmetries are spontaneously broken

Scattering amplitudes of any four-dimensional theory with nonabelian gauge group G may be recast as two-dimensional correlation functions on the asymptotic twosphere at null infinity. The soft gluon theorem is shown, for massless theories at the semiclassical level, to be the Ward identity of a holomorphic two-dimensional G-Kac-Moody symmetry acting on these correlation functions. Holomorphic Kac-Moody current insertions are positive helicity soft gluon insertions. The Kac-Moody transformations are a CP T invariant subgroup of gauge transformations which act nontrivially at null infinity and comprise the four-dimensional asymptotic symmetry group.

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Abstract:Recently a boundary energy-momentum tensor T zz has been constructed from the soft graviton operator for any 4D quantum theory of gravity in asymptotically flat space. Up to an "anomaly" which is one-loop exact, T zz generates a Virasoro action on the 2D celestial sphere at null infinity. Here we show by explicit construction that the effects of the IR divergent part of the anomaly can be eliminated by a one-loop renormalization that shifts T zz .

We discuss the physics of momentum diffusion in a charged plasma. Following the holographic strategy outlined in [1] we construct an open effective field theory for the low-lying modes of the conserved currents. The charged plasma is modeled holographically in terms of a Reissner-Nordström-AdSd+1 black hole. We analyze graviton and photon fluctuations about this background, decoupling in the process the long-lived momentum diffusion mode from the short-lived charged transport mode. Furthermore, as in the aforementioned reference, we argue that the dynamics of these modes are captured by a set of designer scalars in the background geometry. These scalars have their gravitational coupling modulated by an auxiliary dilaton with long-lived modes being weakly coupled near the spacetime asymptopia. Aided by these observations, we obtain the quadratic effective action that governs the fluctuating hydrodynamics of the charge current and stress tensor, reproducing in the process transport data computed previously. We also point out an interesting length scale lying between the inner and outer horizon radii of the charged black hole associated with Ohmic conductivity.

We perform a careful study of the infrared sector of massless non-abelian gauge theories in four-dimensional Minkowski spacetime using the covariant phase space formalism, taking into account the boundary contributions arising from the gauge sector of the theory. Upon quantization, we show that the boundary contributions lead to an infinite degeneracy of the vacua. The Hilbert space of the vacuum sector is not only shown to be remarkably simple, but also universal. We derive a Ward identity that relates the n-point amplitude between two generic in- and out-vacuum states to the one computed in standard QFT. In addition, we demonstrate that the familiar single soft gluon theorem and multiple consecutive soft gluon theorem are consequences of the Ward identity.

We show that Weinberg's leading soft photon theorem in massless abelian gauge theories implies the existence of an infinite-dimensional large gauge symmetry which acts non-trivially on the null boundaries I ± of (d + 2)-dimensional Minkowski spacetime. These symmetries are parameterized by an arbitrary function ε(x) of the d-dimensional celestial sphere living at I ± . This extends the previously established equivalence between Weinberg's leading soft theorem and asymptotic symmetries from four and higher even dimensions to all higher dimensions.The remaining ones are then determined by Lorentz invariance. Similarly, the fall-offs for the Coulombic part are determined by Gauss's law, which also determines the fall-offs for the matter current(2.10)We would now like to determine the precise large r expansion for both the radiative and the Coulombic fields.4 As we shall see in (2.23), in odd dimensions, the radiative field has an expansion in both integer and half-integer powers of |r|, as indicated in the first column of (2.9). In even dimensions, we obtain later in (2.27) that the radiative field has an expansion in integer powers of |r|, though non-analytic terms of the form log r are also present (not shown in (2.9)).