We study exponentiated soft exchange in $d+2$ dimensional gauge and gravitational theories using the celestial CFT formalism. These models exhibit spontaneously broken asymptotic symmetries generated by gauge transformations with non-compact support,
and the effective dynamics of the associated Goldstone edge mode is expected to be $d$-dimensional. The introduction of an infrared regulator also explicitly breaks these symmetries so the edge mode in the regulated theory is really a $d$-dimensional pseudo-Goldstone boson. Symmetry considerations determine the leading terms in the effective action, whose coefficients are controlled by the infrared cutoff. Computations in this model reproduce the abelian infrared divergences in $d=2$, and capture the re-summed (infrared finite) soft exchange in higher dimensions. The model also reproduces the leading soft theorems in gauge and gravitational theories in all dimensions. Interestingly, we find that it is the shadow transform of the Goldstone mode that has local $d$-dimensional dynamics: the effective action expressed in terms of the Goldstone mode is non-local for $d>2$. We also introduce and discuss new magnetic soft theorems. Our analysis demonstrates that symmetry principles suffice to calculate soft exchange in gauge theory and gravity.
The holomorphic Coulomb gas formalism is a set of rules for computing minimal model observables using free field techniques. We attempt to derive and clarify these rules using standard techniques of QFT. We begin with a careful examination of the tim
elike linear dilaton. Although the background charge $Q$ breaks the scalar fields continuous shift symmetry, the exponential of the action is invariant under a discrete shift because $Q$ is imaginary. Gauging this symmetry makes the dilaton compact and introduces winding modes into the spectrum. One of these winding operators corresponds to the BRST current first introduced by Felder. The cohomology of this BRST charge isolates the irreducible representations of the Virasoro algebra within the linear dilaton Fock space, and the supertrace in the BRST complex reproduces the minimal model partition function. The model at the radius $R=sqrt{pp}$ has two marginal operators corresponding to the Dotsenko-Fateev screening charges. Deforming by them, we obtain a model that might be called a BRST quotiented compact timelike Liouville theory. The Hamiltonian of the zero-mode quantum mechanics is not Hermitian, but it is $PT$-symmetric and exactly solvable. Its eigenfunctions have support on an infinite number of plane waves, suggesting an infinite reduction in the number of independent states in the full QFT. Applying conformal perturbation theory to the exponential interactions reproduces the Coulomb gas calculations of minimal model correlators. In contrast to spacelike Liouville, these resonance correlators are finite because the zero mode is compact. We comment on subtleties regarding the reflection operator identification, as well as naive violations of truncation in correlators with multiple reflection operators inserted. This work is part of an attempt to understand the relationship between JT gravity and the $(2,p)$ minimal string.
The Hilbert space of a quantum system with internal global symmetry $G$ decomposes into sectors labelled by irreducible representations of $G$. If the system is chaotic, the energies in each sector should separately resemble ordinary random matrix th
eory. We show that such sector-wise random matrix ensembles arise as the boundary dual of two-dimensional gravity with a $G$ gauge field in the bulk. Within each sector, the eigenvalue density is enhanced by a nontrivial factor of the dimension of the representation, and the ground state energy is determined by the quadratic Casimir. We study the consequences of t Hooft anomalies in the matrix ensembles, which are incorporated by adding specific topological terms to the gauge theory action. The effect is to introduce projective representations into the decomposition of the Hilbert space. Finally, we consider ensembles with $G$ symmetry and time reversal symmetry, and analyze a simple case of a mixed anomaly between time reversal and an internal $mathbb{Z}_2$ symmetry.
General relativity predicts that the Kerr black hole develops qualitatively new and surprising features in the limit of maximal spin. Most strikingly, the region of spacetime near the event horizon stretches into an infinitely long throat and display
s an emergent conformal symmetry. Understanding dynamics in this NHEK (Near-Horizon Extreme Kerr) geometry is necessary for connecting theory to upcoming astronomical observations of high-spin black holes. We review essential properties of NHEK and its relationship to the rapidly rotating Kerr black hole. We then completely solve the geodesic equation in the NHEK region and describe how the resulting trajectories transform under the action of its enhanced symmetries. In the process, we derive explicit expressions for the angular integrals appearing in the Kerr geodesic equation and obtain a useful formula, valid at arbitrary spin, for a particles polar angle in terms of its radial motion. These results will aid in the analytic computation of astrophysical observables relevant to ongoing and future experiments.
The Event Horizon Telescope (EHT) is expected to soon produce polarimetric images of the supermassive black hole at the center of the neighboring galaxy M87. There are indications that this black hole is rapidly spinning. General relativity predicts
that such a high-spin black hole has an emergent conformal symmetry near its event horizon. In this paper, we use this symmetry to analytically predict the polarized near-horizon emissions to be seen at the EHT and find a distinctive pattern of whorls aligned with the spin.
We consider the tree-level scattering of massless particles in $(d+2)$-dimensional asymptotically flat spacetimes. The $mathcal{S}$-matrix elements are recast as correlation functions of local operators living on a space-like cut $mathcal{M}_d$ of th
e null momentum cone. The Lorentz group $SO(d+1,1)$ is nonlinearly realized as the Euclidean conformal group on $mathcal{M}_d$. Operators of non-trivial spin arise from massless particles transforming in non-trivial representations of the little group $SO(d)$, and distinguished operators arise from the soft-insertions of gauge bosons and gravitons. The leading soft-photon operator is the shadow transform of a conserved spin-one primary operator $J_a$, and the subleading soft-graviton operator is the shadow transform of a conserved spin-two symmetric traceless primary operator $T_{ab}$. The universal form of the soft-limits ensures that $J_a$ and $T_{ab}$ obey the Ward identities expected of a conserved current and energy momentum tensor in a Euclidean CFT$_d$, respectively.
Recently it has been shown that the vacuum state in QED is infinitely degenerate. Moreover a transition among the degenerate vacua is induced in any nontrivial scattering process and determined from the associated soft factor. Conventional computatio
ns of scattering amplitudes in QED do not account for this vacuum degeneracy and therefore always give zero. This vanishing of all conventional QED amplitudes is usually attributed to infrared divergences. Here we show that if these vacuum transitions are properly accounted for, the resulting amplitudes are nonzero and infrared finite. Our construction of finite amplitudes is mathematically equivalent to, and amounts to a physical reinterpretation of, the 1970 construction of Faddeev and Kulish.
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 use the subleading soft-graviton theorem to construct an operator $T_{zz}$ whose insertion in the four-dimensional tree-level quantum gravity $mathcal{S}$-matrix obeys the Virasoro-Ward identities of the energy momentum tensor of a two-dimensional
conformal field theory (CFT$_2$). The celestial sphere at Minkowskian null infinity plays the role of the Euclidean sphere of the CFT$_2$, with the Lorentz group acting as the unbroken $SL(2,mathbb{C})$ subgroup.
The area of a cross-sectional cut $Sigma$ of future null infinity ($mathcal{I}^+$) is infinite. We define a finite, renormalized area by subtracting the area of the same cut in any one of the infinite number of BMS-degenerate classical vacua. The ren
ormalized area acquires an anomalous dependence on the choice of vacuum. We relate it to the modular energy, including a soft graviton contribution, of the region of $mathcal{I}^+$ to the future of $Sigma$. Under supertranslations, the renormalized area shifts by the supertranslation charge of $Sigma$. In quantum gravity, we conjecture a bound relating the renormalized area to the entanglement entropy across $Sigma$ of the outgoing quantum state on $mathcal{I}^+$.
