arXiv subjects

Jesse Woods

Publications and source records attributed to Jesse Woods.

4 recordsLinked to original sources

arXiv2026

Alakazam: Symbolic Tensor Algebra for Field Theory in Julia

We present "Alakazam", a Julia package for performing symbolic manipulations of tensor expressions arising in the study of field theories and quantum mechanics. This will serve as a powerful tool for studying spacetime and supersymmetric structures, including support for calculations in superspace. The package implements many key features such as raising and lowering indices, simplification of terms with dummy indices, replacement patterns, differential and variational calculus, bosonic and fermionic grading, gamma matrix identities, and Lie brackets and commutators. We present notable speed improvements over established systems. Some possible applications include the study of descendants and invariants.

hep-th↗

arXiv2026

Decomposing Grassmann Monomials for Superfield Expansions

Superspace extends spacetime by anticommuting Grassmann coordinates, whose indices may transform under spin and flavour groups. Decomposing Grassmann monomials into independent invariant structures is a central step in constructing superfield expansions, but becomes increasingly difficult in extended superspace. We present a general representation-theoretic procedure for decomposing the space $\Lambda^n(\mathbb{C}^{d_S}\otimes \mathbb{C}^{d_F})$, where $d_S$ and $d_F$ are the dimensions of the spin and flavour representations. The branching multiplicities for $\mathrm{GL}(m)\downarrow{\mathrm{Sp}(m)}$ and $\mathrm{GL}(m)\downarrow{\mathrm{SO}(m)}$ are computed by exact Weyl-character comparison at deterministic rational sample points, avoiding Littlewood-Richardson modification rules. We establish completeness of the character ansatz and analyse the computational complexity, showing that it is polynomial in the number of partitions of $n$ and in the group rank, without dependence on Littlewood-Richardson combinatorics. We validate the resulting decompositions via dimension checks. We provide an accompanying standalone Julia script which implements this algorithm for groups of arbitrary rank, and produces the explicit contractions with invariant tensors.

hep-th↗

arXiv2026

Semiclassics at the cusp

We study cusped Wilson line operators in the Abelian Higgs model in $ d = 4 - ε$ at large external charges. Using a double-scaling limit $ Q \to \infty $, $ ε\to 0 $ with $ Qε$ fixed, we develop a semiclassical framework that provides analytic control beyond fixed-order perturbation theory. We compute the cusp anomalous dimension for arbitrary charges up to next-to-next-to-leading order in the gauge coupling, while resumming scalar self-interactions to all orders. Our results interpolate between perturbative and large-charge regimes, accessing domains that are invisible in fixed-order perturbation theory. As an application, we provide new predictions for various defect CFT observables, including the Mandelstam-Schwinger-dressed two-point function characterizing the superconducting phase transition.

hep-th↗

arXiv2023

Hyper-Dilaton Weyl Multiplets of 5D and 6D Minimal Conformal Supergravity

By extending the recent analysis of arXiv:2203.12203 for ${\mathcal{N}}=2$ conformal supergravity in four dimensions, we define new hyper-dilaton Weyl multiplets for five-dimensional ${\mathcal{N}}=1$, and six-dimensional ${\mathcal{N}}=(1,0)$ conformal supergravities. These are constructed by coupling the five- and six-dimensional standard Weyl multiplets to on-shell hypermultiplets and reinterpreting the systems as new multiplets of conformal supergravity. In the five-dimensional case, we also construct a new hyper-dilaton Poincaré supergravity by coupling to an off-shell vector multiplet compensator. As in four dimensions, a $BF$-coupling induces a non-trivial scalar potential for the five-dimensional dilaton that admits AdS$_5$ vacua.

hep-th↗