Related papers: All $S$ invariant gluon OPEs on the celestial sphe…
In this paper we continue our study of the tree level MHV graviton scattering amplitudes from the point of view of celestial holography. In arXiv:2008.04330 we showed that the celestial OPE of two gravitons in the MHV sector can be written…
We investigate Lie symmetry algebra of the Benney-Roskes/Zakharov-Rubenchik systems. The invariance algebra turns out to be infinite-dimensional. We also find several exact solutions of periodic, line-soliton and stationary types.
We overview some attempts to find S-duality analogues of non-supersymmetric Yang-Mills theory, in the context of gravity theories. The case of MacDowell-Mansouri gauge theory of gravity is discussed. Three-dimensional dimensional reductions…
The maximally supersymmetric Yang-Mills theory in four-dimensional Minkowski space is an exceptional model of mathematical physics. Even more so in the planar limit, where the theory is believed to be integrable. In particular, the…
In an earlier paper [arXiv:2511.03669] we extracted the OPE of celestial CFT operator duals of positive helicity graviton and scalar particles from the Mellin transformed relevant MHV amplitudes of conformal gravity, realised as the bosonic…
Yang-Mills gauge theory on Minkowski space supports a Batalin-Vilkovisky-infinity algebra structure, all whose operations are local. To make this work, the axioms for a BV-infinity algebra are deformed by a quadratic element, here the…
We consider the S-duality transformation of gauge invariant operators and states in $\mathcal{N}$ $=4$ SYM theory. The transformation is realized through an operator $ S $ which is the $ SL(2,Z) $ canonical transformation in loop space with…
We give an explicit gauge invariant, off-shell and local double copy construction of gravity from Yang-Mills theory to quartic order. To this end we use the framework of homotopy algebras, and we identify a rich new algebraic structure…
We study orbifolds of ${\cal N} = 4$ U(n) super-Yang-Mills theory given by discrete subgroups of SU(2) and SU(3). We have reached many interesting observations that have graph-theoretic interpretations. For the subgroups of SU(2), we have…
We classify strongly homotopy Lie algebras - also called L-infinity algebras - of one even and two odd dimensions, which are related to $2|1$-dimensional $Z_2$-graded Lie algebras. What makes this case interesting is that there are many…
We consider a N=2 supersymmetric Yang-Mills-Chern-Simons model, coupled to matter, in the Wess-Zumino gauge. The theory is characterized by a superalgebra which displays two kinds of obstructions to the closure on the translations: field…
The extension of the noncommutative u*(N) Lie algebra to noncommutative orthogonal and symplectic Lie algebras is studied. Using an anti-automorphism of the star-matrix algebra, we show that the u*(N) can consistently be restricted to o*(N)…
$\mathcal{N}=4$ supersymmetric Yang-Mills theories with algebra $\mathfrak{so}(4N)$ and appropriate choices of global structure can have non-invertible symmetries. We identify the branes holographically dual to the non-invertible…
We study $n$-ary commutative superalgebras and $L_{\infty}$-algebras that possess a skew-symmetric invariant form, using the derived bracket formalism. This class of superalgebras includes for instance Lie algebras and their $n$-ary…
We study theories of the "General Relativity + Yang-Mills" type in 4d spacetime with cosmological constant, focusing on formulations where the basic variables are connections and curvatures (but no metric). We present a new Lagrangian for…
In this paper, we explore the $\mathbb{Z}_2^n$-graded Lie (super)algebras as novel possible generators of symmetries of $S$-matrix. As the results, we demonstrate that a $\mathbb{Z}_2^n$-graded extension of the supersymmetric algebra can be…
We derive the nonlinear sigma model as a peculiar dimensional reduction of Yang-Mills theory. In this framework, pions are reformulated as higher-dimensional gluons arranged in a kinematic configuration that only probes cubic interactions.…
We consider quantum mechanical Yang-Mills theories with eight supercharges and a $Spin(5) \times SU(2)_R$ flavor symmetry. We show that all normalizable ground states in these gauge theories are invariant under this flavor symmetry. This…
Recently N. Seiberg has shown that certain N=1 supersymmetric Yang -- Mills theories have the property that their infrared physics can be equivalently described by {\it two different} gauge theories, with the strong coupling region of one…
In SU($N$) gauge-Higgs theories, with a single Higgs field in the fundamental representation, there exists in addition to the local gauge symmetry a global SU(2) symmetry, at $N=2$, and a global U(1) symmetry, for $N \ne 2$. We construct a…