arXiv subjects

Charles Alastair Stephen Young

Publications and source records attributed to Charles Alastair Stephen Young.

3 recordsLinked to original sources

arXiv2026

Integrability from Homotopy Algebras

Homotopy algebraic methods have become increasingly influential in studying field theories. We consider semi-holomorphic Chern-Simons theory and its relation with the principal chiral model. In particular, we establish an explicit quasi-isomorphism between the cyclic $L_\infty$-algebras governing both theories which directly gives the Lax connection. This provides a concrete example for studying integrability of a two-dimensional system through the homotopy algebraic lens.

hep-th↗

arXiv2024

Full S-matrices and Witten diagrams with (relative) L-infinity algebras

The $L_\infty$-algebra approach to scattering amplitudes elegantly describes the nontrivial part of the $S$-matrix but fails to take into account the trivial part. We argue that the trivial contribution to the $S$-matrix should be accounted for by another, complementary $L_\infty$-algebra, such that a perturbative field theory is described by a cyclic relative $L_\infty$-algebra. We further demonstrate that this construction reproduces Witten diagrams that arise in AdS/CFT including, in particular, the trivial Witten diagrams corresponding to CFT two-point functions. We also discuss Chern-Simons theory and Yang-Mills theory on manifolds with boundaries using this approach.

hep-th↗

arXiv2024

Homotopy representations of extended holomorphic symmetry in holomorphic twists

We argue that holomorphic twists of supersymmetric field theories naturally come with a symmetry $L_\infty$-algebra that nontrivially extends holomorphic symmetry. This symmetry acts on spacetime fields only up to homotopy, and the extension is only visible at the level of higher components of the action. We explicitly compute this for the holomorphic twist of ten-dimensional supersymmetric Yang-Mills theory, which produces a nontrivial action of a higher $L_\infty$-algebra on (a graded version) of five-dimensional affine space.

hep-th↗