$\mathcal{N}=2$ SYK models with dynamical bosons and fermions
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| Format: | Preprint |
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2024
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| author | Benini, Francesco Reis, Tomas Soltani, Saman Zhang, Ziruo |
| author_facet | Benini, Francesco Reis, Tomas Soltani, Saman Zhang, Ziruo |
| contents | We study a class of SYK models with $\mathcal{N}=2$ supersymmetry, described by $N$ fermions in chiral Fermi multiplets, as well as $αN$ first-order bosons in chiral multiplets. The interactions are characterized by two integers $(p,q)$. We focus on the large $N$ and low energy limit of these models. Despite the presence of dynamical bosons, we find conformal behavior akin to the standard SYK model. We use $\mathcal{I}$-extremization of a Witten index to study the supersymmetric solutions. In particular, we find an exact expression for the entropy, which matches the numerical solutions to the Schwinger-Dyson equations. We further solve the model both in the large $p$ and large $p,q$ limits. Numerically, we verify our analytical results and obtain estimates for the Schwarzian coupling in the near zero-temperature limit. We also study the low-lying spectrum of operators to determine the parameter ranges where the Schwarzian mode dominates the IR dynamics. Lastly, we study out-of-time-ordered correlators to show that the model is maximally chaotic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08414 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\mathcal{N}=2$ SYK models with dynamical bosons and fermions Benini, Francesco Reis, Tomas Soltani, Saman Zhang, Ziruo High Energy Physics - Theory Strongly Correlated Electrons We study a class of SYK models with $\mathcal{N}=2$ supersymmetry, described by $N$ fermions in chiral Fermi multiplets, as well as $αN$ first-order bosons in chiral multiplets. The interactions are characterized by two integers $(p,q)$. We focus on the large $N$ and low energy limit of these models. Despite the presence of dynamical bosons, we find conformal behavior akin to the standard SYK model. We use $\mathcal{I}$-extremization of a Witten index to study the supersymmetric solutions. In particular, we find an exact expression for the entropy, which matches the numerical solutions to the Schwinger-Dyson equations. We further solve the model both in the large $p$ and large $p,q$ limits. Numerically, we verify our analytical results and obtain estimates for the Schwarzian coupling in the near zero-temperature limit. We also study the low-lying spectrum of operators to determine the parameter ranges where the Schwarzian mode dominates the IR dynamics. Lastly, we study out-of-time-ordered correlators to show that the model is maximally chaotic. |
| title | $\mathcal{N}=2$ SYK models with dynamical bosons and fermions |
| topic | High Energy Physics - Theory Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2402.08414 |