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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.02394 |
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| _version_ | 1866915091931201536 |
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| author | Muteeb, M. Nouman Zayas, Leopoldo A. Pando |
| author_facet | Muteeb, M. Nouman Zayas, Leopoldo A. Pando |
| contents | The two-dimensional gauged linear sigma model has provided a physical model for the quantum cohomology of a Kähler manifold, $X$. A three-dimensional version of such construction has recently been shown to shed light on models of quantum K-theory of $X$. We consider an $\mathcal{N}=1$ four-dimensional version consisting of a $U(1)$ vector multiplet and chiral multiplets, generalizing the two-dimensional $\mathcal{N}=(2,2)$ setup. We compute the four-dimensional partition function on $D^2\times \mathbb{T}^2$ and demonstrates that it satisfies a difference equation which reduces to the deformed quantum K-theoretic one in the appropriate limit. We also demonstrate, though indirectly, that 4d invariants reduce to 3d quantum K-theory invariants in the same limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02394 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Four-dimensional Gauge Theory Perspective on Quantum K-theory Muteeb, M. Nouman Zayas, Leopoldo A. Pando High Energy Physics - Theory The two-dimensional gauged linear sigma model has provided a physical model for the quantum cohomology of a Kähler manifold, $X$. A three-dimensional version of such construction has recently been shown to shed light on models of quantum K-theory of $X$. We consider an $\mathcal{N}=1$ four-dimensional version consisting of a $U(1)$ vector multiplet and chiral multiplets, generalizing the two-dimensional $\mathcal{N}=(2,2)$ setup. We compute the four-dimensional partition function on $D^2\times \mathbb{T}^2$ and demonstrates that it satisfies a difference equation which reduces to the deformed quantum K-theoretic one in the appropriate limit. We also demonstrate, though indirectly, that 4d invariants reduce to 3d quantum K-theory invariants in the same limit. |
| title | A Four-dimensional Gauge Theory Perspective on Quantum K-theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2501.02394 |