Non-Commutative Gauge Theory at the Beach
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915981698269184 |
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| author | Bittleston, Roland Heuveline, Simon Raghavendran, Surya Skinner, David |
| author_facet | Bittleston, Roland Heuveline, Simon Raghavendran, Surya Skinner, David |
| contents | The KP equation is perhaps the most famous example of a three-dimensional integrable system. Here we show that a non-commutative five-dimensional Chern-Simons theory living on the projective spinor bundle of three-dimensional space-time compactifies to a Lagrangian formulation of the KP equation. Essential to the definition of the theory is a 2-form pulled back from minitwistor space. The dispersionless limit of the KP equation is similarly described by Poisson-Chern-Simons theory. We further show that, consistent with integrability, all tree level amplitudes vanish. The universal vertex algebra living on a two-dimensional surface defect in $5d$ is $W_{1+\infty}$, and its operator products coincide with collinear splitting functions on space-time. Taking the dispersionless limit contracts the vertex algebra to $w_{1+\infty}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20643 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Commutative Gauge Theory at the Beach Bittleston, Roland Heuveline, Simon Raghavendran, Surya Skinner, David High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems The KP equation is perhaps the most famous example of a three-dimensional integrable system. Here we show that a non-commutative five-dimensional Chern-Simons theory living on the projective spinor bundle of three-dimensional space-time compactifies to a Lagrangian formulation of the KP equation. Essential to the definition of the theory is a 2-form pulled back from minitwistor space. The dispersionless limit of the KP equation is similarly described by Poisson-Chern-Simons theory. We further show that, consistent with integrability, all tree level amplitudes vanish. The universal vertex algebra living on a two-dimensional surface defect in $5d$ is $W_{1+\infty}$, and its operator products coincide with collinear splitting functions on space-time. Taking the dispersionless limit contracts the vertex algebra to $w_{1+\infty}$. |
| title | Non-Commutative Gauge Theory at the Beach |
| topic | High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2509.20643 |