Recently, a double-copy formalism was used to calculate gravitational radiation from classical Yang-Mills radiation solutions. This work shows that the Yang-Mills theory coupled to a biadjoint scalar field admits a radiative double copy that agrees with solutions in the Einstein-Yang-Mills theory at the lowest finite order. Within this context, the trace-reversed metric ${\overline{h}}^{\mu \nu }$ is a natural double copy of the gauge boson $A^{\mu a}$. This work provides additional evidence that solutions in gauge and gravity theories are related, even though their respective Lagrangians and nonlinear equations of motion appear to be different.

Six-dimensional spinors with $Spin(3,3)$ symmetry are utilized to efficiently encode three generations of matter. $E_{8(-24)}$ is shown to contain physically relevant subgroups with representations for GUT groups, spacetime symmetries, three generations of the standard model fermions, and Higgs bosons. Pati–Salam, $SU\left(5\right)$, and $Spin\left(10\right)$ grand unified theories are found when a single generation is isolated. For spacetime symmetries, $Spin(4,2)$ may be used for conformal symmetry, $Ad{S}_5\to d{S}_4$, or simply broken to $Spin(3,1)$ of a Minkowski space. Another class of representations finds $Spin(2,2)$ and can give $Ad{S}_3$ with various GUTs. An action for three generations of fermions in the Majorana–Weyl spinor $\mathbf{128}$ of $Spin(4,12)$ is found with $Spin\left(3\right)$ flavor symmetry inside $E_{8(-24)}$. The 128 of $Spin(12,4)$ can be regarded as the tangent space to a particular pseudo-Riemannian form of the octo-octonionic Rosenfeld projective plane $E_{8(-24)}/Spin(12,4)=\left(\mathbb{O}sx\mathbb{O}\right){\mathbb{P}}^2$.

We present a set of one-loop integral coefficient relations in QCD. The unitarity method is useful for exposing one-loop amplitudes in terms of tree amplitudes. The coefficient relations are induced by tree-level Bern-Carrasco-Johansson amplitude relations. We provide examples for box, triangle, and bubble coefficients. These relations reduce the total number of independent coefficients needed to calculate one-loop QCD amplitudes.

Some time ago, Bars found $D=11+3$ supersymmetry and Sezgin proposed super Yang-Mills theory (SYM) in $D=11+3$. Using the “magic star” projection of ${\mathfrak{e}}_{8(-24)}$, we show that the geometric structure of SYM’s in $12+4$ and $11+3$ space-time dimensions descends to the affine symmetry of the space ${\mathrm{AdS}}_4\otimes S^8$. By reducing to transverse transformations along maximal embeddings, the near-horizon geometries of the M2 brane (${\mathrm{AdS}}_4\otimes S^7$) and M5 brane (${\mathrm{AdS}}_7\otimes S^4$) of M-theory are recovered. Utilizing the recently introduced “exceptional periodicity” (EP) and exploiting the embedding of semisimple rank-3 Jordan algebras into rank-3 T-algebras of special type yields the spaces ${\mathrm{AdS}}_4\otimes S^{8n}$ and ${\mathrm{AdS}}_{8n-1}\otimes S^5$ with reduced subspaces ${\mathrm{AdS}}_4\otimes S^{8n-1}$ and ${\mathrm{AdS}}_{8n-1}\otimes S^4$, respectively. As such, EP describes the near-horizon geometries of an infinite class of novel exceptional SYM’s in $(8n+3)+3$ dimensions that generalize M-theory for $n=1$. Remarkably, the $n=3$ level hints at M2 and M21 branes as solutions of bosonic M-theory and gives support for Witten’s monstrous AdS/CFT construction.

We modify the simulation hypothesis to a self-simulation hypothesis, where the physical universe, as a strange loop, is a mental self-simulation that might exist as one of a broad class of possible code theoretic quantum gravity models of reality obeying the principle of efficient language axiom. This leads to ontological interpretations about quantum mechanics. We also discuss some implications of the self-simulation hypothesis such as an informational arrow of time.

We investigate operator algebraic origins of the classical Koopman–von Neumann wave function $$\psi _{KvN}$$ψ KvN as well as the quantum-mechanical one $$\psi _{QM}$$ψ QM . We introduce a formalism of Operator Mechanics (OM) based on a noncommutative Poisson, symplectic, and noncommutative differential structures. OM serves as a pre-quantum algebra from which algebraic structures relevant to real-world classical and quantum mechanics follow. In particular, $$\psi _{KvN}$$ψ KvN and $$\psi _{QM}$$ψ QM are both consequences of this pre-quantum formalism. No a priori Hilbert space is needed. OM admits an algebraic notion of operator expectation values without invoking states. A phase space bundle $${{\mathcal {E}}}$$E follows from this. $$\psi _{KvN}$$ψ KvN and $$\psi _{QM}$$ψ QM are shown to be sections in $${{\mathcal {E}}}$$E . The difference between $$\psi _{KvN}$$ψ KvN and $$\psi _{QM}$$ψ QM originates from a quantization map interpreted as “twisting” of sections over $${{\mathcal {E}}}$$E . We also show that the Schrödinger equation is obtained from the Koopman–von Neumann equation. What this suggests is that neither the Schrödinger equation nor the quantum wave function are fundamental structures. Rather, they both originate from a pre-quantum operator algebra. Finally, we comment on how entanglement between these operators suggests emergence of space; and possible extensions of this formalism to field theories.