Abstract
AbstractWe present a general construction of integrable degenerate $$\mathcal {E}$$
E
-models on a 2d manifold $$\Sigma $$
Σ
using the formalism of Costello and Yamazaki based on 4d Chern–Simons theory on $$\Sigma \times {\mathbb {C}}{P}^1$$
Σ
×
C
P
1
. We begin with a physically motivated review of the mathematical results of Benini et al. (Commun Math Phys 389(3):1417–1443, 2022. https://doi.org/10.1007/s00220-021-04304-7) where a unifying 2d action was obtained from 4d Chern–Simons theory which depends on a pair of 2d fields h and $${\mathcal {L}}$$
L
on $$\Sigma $$
Σ
subject to a constraint and with $${\mathcal {L}}$$
L
depending rationally on the complex coordinate on $${\mathbb {C}}{P}^1$$
C
P
1
. When the meromorphic 1-form $$\omega $$
ω
entering the action of 4d Chern–Simons theory is required to have a double pole at infinity, the constraint between h and $${\mathcal {L}}$$
L
was solved in Lacroix and Vicedo (SIGMA 17:058, 2021. https://doi.org/10.3842/SIGMA.2021.058) to obtain integrable non-degenerate $$\mathcal {E}$$
E
-models. We extend the latter approach to the most general setting of an arbitrary 1-form $$\omega $$
ω
and obtain integrable degenerate $$\mathcal {E}$$
E
-models. To illustrate the procedure, we reproduce two well-known examples of integrable degenerate $$\mathcal {E}$$
E
-models: the pseudo-dual of the principal chiral model and the bi-Yang-Baxter $$\sigma $$
σ
-model.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Nuclear and High Energy Physics,Statistical and Nonlinear Physics
Reference61 articles.
1. Benini, M., Schenkel, A., Vicedo, B.: Homotopical analysis of 4d ChernSimons theory and integrable field theories. Commun. Math. Phys. 389(3), 1417–1443 (2022). https://doi.org/10.1007/s00220-021-04304-7. arXiv:2008.01829 [hep-th]
2. Lacroix, S., Vicedo, B.: Integrable E-models, 4d Chern-Simons theory and affine Gaudin models. I. Lagrangian aspects. SIGMA 17, 058 (2021). https://doi.org/10.3842/SIGMA.2021.058. arXiv:2011.13809 [hep-th]
3. Costello, K., Yamazaki, M.: Gauge theory and integrability, III. (2019). arXiv:1908.02289 [hep-th]
4. Costello, K.: Integrable lattice models from four-dimensional field theories, In: Donagi, R., Douglas, M.R., Kamenova, L., Rocek, M. (eds). Proceedings of Symposia in Pure Mathematics, vol. 88, pp. 3–24. (2014). https://doi.org/10.1090/pspum/088/01483. arXiv:1308.0370 [hep-th]
5. Costello, K.: Supersymmetric gauge theory and the Yangian. (2013). arXiv:1303.2632 [hep-th]
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