arXiv subjects

Noah Miller

Publications and source records attributed to Noah Miller.

11 recordsLinked to original sources

arXiv2026

The facts on quantum self-dual Einstein gravity and self-dual Yang-Mills theory

Self-dual Einstein gravity is a one-loop exact, UV and IR finite, diffeomorphism invariant, non-unitary theory of quantum gravity in four dimensions. The only non-trivial amplitudes are the one-loop-all-plus amplitudes, and they are equal to those of pure Einstein gravity. In these notes we review SDG and SDYM pedagogically. We walk the reader through key calculations, fill in some gaps in the literature, and point out directions for future research. Topics include: derivation of the self-dual actions from the full Einstein gravity/YM actions in lightcone gauge, decoupling of ghosts, Berends-Giele currents, vanishing of tree-level-one-minus amplitudes, celestial $Lw_{1+\infty}$ symmetry, perturbiners, double-off-shell current calculation of one-loop-all-plus SDYM and SDG amplitudes, dimension shifting, unitarity cuts, the BDPR gravity formula, one-loop color ordering, and the covariant formulations of the self-dual theories as well as their their gauge fixing. We also review some selected results from the celestial holography program, and briefly comment on an all-n expression for the one-loop-one-minus gravity amplitudes.

hep-th↗

arXiv2025

Generating Hodges' Graviton MHV Formula with an $Lw_{1+\infty}$ Ward Identity

Hodges' formula expresses the tree-level all-multiplicity Einstein gravity MHV amplitude as a matrix determinant. In this work, we prove that Hodges' determinant is generated by an $Lw_{1+\infty}$ Ward identity on the celestial sphere. The Ward identity takes the form of a recursion relation that has not previously appeared in the literature and is unrelated to BCFW. The proof makes use of the matrix-tree theorem.

hep-th↗

arXiv2025

Spacetime $Lw_{1+\infty}$ Symmetry and Self-Dual Gravity in Plebanski Gauge

The space of self-dual Einstein spacetimes in 4 dimensions is acted on by an infinite dimensional Lie algebra called the $Lw_{1+\infty}$ algebra. In this work we explain how one can ``build up'' self-dual metrics by acting on the flat metric with an arbitrary number of infinitesimal $Lw_{1+\infty}$ transformations, using a convenient choice of gauge called Plebanski gauge. We accomplish this through the use of something called a ``perturbiner expansion,'' which will perturbatively generate for us a self-dual metric starting from an initial set of quasinormal modes called integer modes. Each integer mode corresponds to a particular $Lw_{1+\infty}$ transformation, and this perturbiner expansion of integer modes will be written as a sum over ``marked tree graphs,'' instead of momentum space Feynman diagrams. We find that a subset of the $Lw_{1+\infty}$ transformations act as spacetime diffeomorphisms, and the algebra of these diffeomorphisms is $w_{\infty} \ltimes f$. We also show all analogous results hold for the $Ls$ algebra in self-dual Yang Mills.

hep-th↗

arXiv2025

Path integral games with de Sitter {\alpha}-vacua

The $\alpha$-vacua are a 1-parameter family of quantum field vacua in de Sitter space which are invariant under the isometry group $SO(1,d)$. In this work give a path integral construction of the de Sitter $\alpha$-vacua. We explain that these states can be prepared by acting on the Bunch-Davies vacuum with a certain non-local charge operator. While most conserved charges live on a single codimension-1 manifold, we show that this particular charge lives on a pair of two codimension-1 manifolds which are antipodal mirrors of each other. The rules for the manipulation of this charge as an insertion in the path integral are explained. We further explain how this charge can be used to solve for the wavefunctionals of the $\alpha$-vacua at $\mathcal{I}^+$ (in the regime that $\alpha$ is small) by deforming the equator of de Sitter space to $\mathcal{I}^+$ / $\mathcal{I}^-$. We also discuss the special $\alpha$-vacua known as the ``in'' and ``out'' vacua, for both heavy and light scalars. It is well known that the ``in'' and ``out'' vacua are equal in odd dimensions, but we also show that they are equal in even dimensions when $\sqrt{(d-1)^2/4 - m^2}$ is a half-integer. Finally, we investigate the question of whether the $\alpha$-vacua can be constructed in interacting quantum field theories. Using the fact that the antipodal charge operator is only conserved in a free theory, we give a symmetry based argument that in general they cannot be, explaining why interactions and $SO(1,d)$ invariance of the vacua are in tension.

hep-th↗

arXiv2024

Proof of the graviton MHV formula using Pleba\'nski's second heavenly equation

Self-dual spacetimes can be thought of as spacetimes containing only positive helicity gravitons. In this work we give a perturbiner expansion for self-dual spacetimes based on Pleba\'nski's second heavenly equation. The expansion is naturally organized as a sum over ``marked tree graphs'' where each node corresponds to a positive helicity graviton and can have an arbitrary number of edges. Negative helicity gravitons must be added in by hand. We then use this perturbiner expansion to give a first principles derivation of the NSVW tree formula for the MHV amplitude in Einstein gravity. A unique feature of this proof is that it does not use BCFW recursion or twistor theory. It works by plugging the spacetime with arbitrarily many $+$ gravitons and two $-$ gravitons into the on-shell gravitational action and evaluating it. The action we use is the self-dual Pleba\'nski action plus an additional boundary term, and the amplitude itself comes entirely from the boundary term. Along the way, we also find an interesting new generalization of the NSVW formula which has not previously appeared in the literature. In the appendix we give another way to express the perturbiner expansion using binary tree graphs instead of marked tree graphs, and prove the equivalence of these two expansions diagrammatically. We also provide an introduction to self-dual gravity aimed at non-experts, as well as a proof of the Parke-Taylor formula in Yang Mills theory analogous to our proof of the NSVW formula in gravity.

hep-th↗

arXiv2023

An Integer Basis for Celestial Amplitudes

We present a discrete basis of solutions of the massless Klein-Gordon equation in 3+1 Minkowski space which transform as sl(2,C) Lorentz/conformal primaries and descendants, and whose elements all have integer conformal dimension. We show that the basis is complete in the sense that the Wightman function can be expressed as a quadratic sum over the basis elements.

hep-th↗

arXiv2022

Soft Gravitons in the BFSS Matrix Model

BFSS proposed that asymptotically flat M-theory is dual to a large $N$ limit of the matrix quantum mechanics describing $N$ nonrelativistic D0-branes. Recent insights on the soft symmetries of any quantum theory of gravity in asymptotically flat space are applied to the BFSS matrix model. It is shown that soft gravitons are realized by submatrices whose rank is held fixed in the large $N$ M-theory limit, rather than the usual linear scaling with $N$ for hard gravitons. The soft expansion is identified with the large $N$ expansion and the soft theorem becomes a universal formula for the quantum mechanical scattering of such submatrix excitations. This formula is shown to be the Ward identity of large type IIA $U(1)_{RR}$ asymptotic gauge symmetry in the matrix model, whose asymptotic boundaries are at future and past timelike infinity.

hep-th↗

arXiv2021

From Noether's Theorem to Bremsstrahlung: a pedagogical introduction to large gauge transformations and classical soft theorems

Electromagnetism contains an infinite dimensional symmetry group of large gauge transformations. This gives rise to an infinite number of conserved quantities called "soft charges" via Noether's theorem. When charged particles scatter, the conservation of soft charge constrains the overall amount of radiation emitted per angle. Here we describe the physical consequences of soft charge conservation and give fresh accounts of the roles of spacelike and timelike infinity in these conservation laws. We conclude by exploring the possibility of creating a dual boundary theory of electromagnetism.

hep-th↗

arXiv2021

Black Holes in Klein Space

The analytic continuation of the general signature $(1,3)$ Lorentzian Kerr-Taub-NUT black holes to signature $(2,2)$ Kleinian black holes is studied. Their global structure is characterized by a toric Penrose diagram resembling their Lorentzian counterparts. Kleinian black holes are found to be self-dual when their mass and NUT charge are equal for any value of the Kerr rotation parameter $a$. Remarkably, it is shown that the rotation $a$ can be eliminated by a large diffeomorphism; this result also holds in Euclidean signature. The continuation from Lorentzian to Kleinian signature is naturally induced by the analytic continuation of the S-matrix. Indeed, we show that the geometry of linearized black holes, including Kerr-Taub-NUT, is captured by $(2,2)$ three-point scattering amplitudes of a graviton and a massive spinning particle. This stands in sharp contrast to their Lorentzian counterparts for which the latter vanishes kinematically, and enables a direct link to the S-matrix.

hep-th↗

arXiv2021

Accelerating Black Hole Thermodynamics with Boost Time

We derive a thermodynamic first law for the electrically charged C-metric with vanishing cosmological constant. This spacetime describes a pair of identical accelerating black holes each pulled by a cosmic string. Treating the "boost time" of this spacetime as the canonical time, we find a thermodynamic first law in which every term has an unambiguous physical meaning. We then show how this first law can be derived using Noetherian methods in the covariant phase space formalism. We argue that the area of the acceleration horizon contributes to the entropy and that the appropriate notion of energy of this spacetime is a "boost mass", which vanishes identically. The recovery of the Reissner-Nordstrom first law in the limit of small string tension is also demonstrated. Finally, we compute the action of the Euclidean section of the C-metric and show it agrees with the thermodynamic grand potential, providing an independent confirmation of the validity of our first law. We also briefly speculate on the significance of firewalls in this spacetime.

hep-th↗

arXiv2021

State-Operator Correspondence in Celestial Conformal Field Theory

The bulk-to-boundary dictionary for 4D celestial holography is given a new entry defining 2D boundary states living on oriented circles on the celestial sphere. The states are constructed using the 2D CFT state-operator correspondence from operator insertions corresponding to either incoming or outgoing particles which cross the celestial sphere inside the circle. The BPZ construction is applied to give an inner product on such states whose associated bulk adjoints are shown to involve a shadow transform. Scattering amplitudes are then given by BPZ inner products between states living on the same circle but with opposite orientations. 2D boundary states are found to encode the same information as their 4D bulk counterparts, but organized in a radically different manner.

hep-th↗