SciPost Submission Page
2d dualities from 4d
by Jiaqun Jiang, Satoshi Nawata, Jiahao Zheng
Submission summary
| Authors (as registered SciPost users): | Jiang Jiaqun · Satoshi Nawata · Jiahao Zheng |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2407.17350v2 (pdf) |
| Date submitted: | 2025-02-17 05:56 |
| Submitted by: | Nawata, Satoshi |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We find new $\mathcal{N}=(2,2)$ and $\mathcal{N}=(0,2)$ dualities through the twisted compactifications of 4d supersymmetric theories on $S^2$. Our findings include dualities for both $\mathcal{N}=(2,2)$ and $\mathcal{N}=(0,2)$ non-Abelian gauge theories, as well as $\mathcal{N}=(0,2)$ Gauge/Landau-Ginzburg duality.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
As noted above, the entire structure of the paper has been reorganized.
Section 2 has undergone a minor revision:
- In Section 2.3, we clarify that the term discussed is the scalar potential, not the superpotential. In an \(\mathcal{N}=(2,2)\) theory, the scalar potential is present even when there is no superpotential.
- Below equation (2.6) for the elliptic genus, we mention that the coordinate ring of the target space \((\mathrak{t} \times \mathrak{t}) / S_N\) is generated by \(\text{Tr}(\phi^i \sigma^j)\). However, we are unclear about the precise relation between these generators, and thus do not fully understand the cancellation mechanism that leads to such a simple expression for the elliptic genus.
Section 3 has undergone a major revision with the addition of new dualities:
- Section 3.1 provides a more detailed discussion of the duality of SU gauge theories originally found by Gadde-Razamat-Willet [arXiv:1506.08795], addressing various subtleties.
- Section 3.2 generalizes the (0,2) Seiberg-like duality for the Sp gauge group into a new triality. In a similar vein, we propose a new triality involving SO gauge theory, SU+1Sym gauge theory, and a Landau-Ginzburg model. Based on these results, we uncover new (0,2) dualities in the following subsections:
- Section 3.3 proposes a new duality between Sp gauge theory and SU quiver gauge theory.
- Section 3.4 presents a duality between two SU+1AS gauge theories.
- Section 3.5 introduces a duality between two SU+1Sym gauge theories.
- Section 3.6 investigates SO and Sp gauge theories with adjoint chiral matter, exploring their dualities with free chiral theories.
- Section 3.7 explores theories that contain both symmetric and anti-symmetric chiral multiplets, presenting a duality to a Landau-Ginzburg model.
We have added Appendix C to provide additional technical details on the (0,2) dualities that are too specialized for the main text:
- Appendix C.1 explains the twisted compactification of the 4d \(\mathcal{N}=1\) Intriligator-Seiberg duality on \(S^2\), which leads to a duality between (0,2) SO gauge theory and a Landau-Ginzburg model.
- Appendix C.2 proposes a triality similar to the one discussed in Section 3.2.
- Appendices C.3 and C.4 cover dualities not included in Section 3.5.