Simplifying 2-Bundle Descriptions of Invariants and Local Dynamics
Abstract
A string couples to a two-form gauge potential whose local descriptions need not fit together as a single global form. Principal 2-bundles provide a geometric description of this gluing. However, we recover surface amplitudes and quantum partition functions, as well as local classical field dynamics, without the 2-bundle formalism. For global phases, topological and index invariants, and twisted-sheaf moduli, established equivalences give alternative descriptions through cocycles, bundles, operators, or modules, with the required global compatibility data. For three-dimensional finite gauge theories with cohomological actions, Fourier transformation expresses the partition function as a sum of partition functions of ordinary finite-group gauge theories. An invertible local substitution reduces invariant classical actions for a class of 2-bundle connections represented by finite-dimensional crossed modules to ordinary gauge and tensor dynamics. These finite and local reductions explicitly eliminate field variables. A four-dimensional quadratic example instead admits a direct cochain evaluation even when an ordinary gauge-theory reduction fails. These results therefore do not require the additional 2-bundle presentation.
Related
- Moduli descriptions of v-sheaf local models
- Support-Sensitive Bohnenblust-Hille Inequalities and Local Invariants on Hamming Schemes
- Local Connectivity of the Filled Julia Set Bundle over the Mandelbrot Set
- χ-Independence for BPS Invariants of Warped Local Curves
- On logarithmic Donaldson-Thomas invariants for local Calabi-Yau $4$-folds
BibTeX
@misc{bastien2026simplifying,
title = {{Simplifying 2-Bundle Descriptions of Invariants and Local Dynamics}},
author = {Ferreira Bastien},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35669},
eprint = {2610.35669},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35669},
}
RIS
TY - UNPB
TI - Simplifying 2-Bundle Descriptions of Invariants and Local Dynamics
AU - Ferreira Bastien
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35669
UR - https://arxiv.org/abs/2610.35669
AB - A string couples to a two-form gauge potential whose local descriptions need not fit together as a single global form. Principal 2-bundles provide a geometric description of this gluing. However, we recover surface amplitudes and quantum partition functions, as well as local classical field dynamics, without the 2-bundle formalism. For global phases, topological and index invariants, and twisted-sheaf moduli, established equivalences give alternative descriptions through cocycles, bundles, operators, or modules, with the required global compatibility data. For three-dimensional finite gauge theories with cohomological actions, Fourier transformation expresses the partition function as a sum of partition functions of ordinary finite-group gauge theories. An invertible local substitution reduces invariant classical actions for a class of 2-bundle connections represented by finite-dimensional crossed modules to ordinary gauge and tensor dynamics. These finite and local reductions explicitly eliminate field variables. A four-dimensional quadratic example instead admits a direct cochain evaluation even when an ordinary gauge-theory reduction fails. These results therefore do not require the additional 2-bundle presentation.
ER -