arXiv subjects

Paul Luis Roehl

Publications and source records attributed to Paul Luis Roehl.

3 recordsLinked to original sources

arXiv2026

Factorizations of 3d Interval Partition Functions

We show that interval partition functions (transition amplitudes) of three- dimensional $\mathcal{N} = 2$ theories admit factorizations into sums of products of hemisphere partition functions with Wilson loop insertions glued by suitable factors. We prove the factorization explicitly for supersymmetric quantum electrodynamics and Chern-Simons- Yang-Mills theories. In the former case, we show that the gluing factors can be naturally interpreted in terms of $S^2 \times S^1$ partition functions. In the latter case, we prove that hemisphere partition functions are affine characters and determine the gluing factors explicitly in special cases.

hep-th↗

arXiv2025

Giant Gravitons, Fermionic Forms and Vertex Algebras

We investigate the mathematical and physical content of the giant graviton expansion of three-dimensional $\mathcal{N}=4$ superconformal field theories in a simplifying limit. We uncover an interesting relation between the coefficients in this expansion, the Hilbert series of certain quiver varieties and the representation theory of vertex algebras. In particular, for the worldvolume theory of $N$ M2-branes at the tip of a toric hyper-Kähler four-fold cone: $X_{4}=\mathbb{C}^2 /{\mathbb{Z}_L} \times \mathbb{C}^2/{\mathbb{Z}_K}$, we derive an explicit expression for the coefficients in terms of affine fermionic forms and show that they coincide with characters of a direct sum of parafermionic W-algebras.

hep-th↗

arXiv2025

Sinh Deformed Nakajima Operators

We prove a novel action of the (three-dimensional) Heisenberg algebra on the equivariant K-theory of the Hilbert scheme of points on C2. These operators are defined via pushforwards and pullbacks via the Nakajima correspondences while tensoring the square roots of the canonical line bundles of the correspondences. We show, using supersymmetric localisation in 6d (1, 1) Super Yang-Mills compactified on a circle, that these operators correspond to instanton line operators wrapping the extra circle.

hep-th↗