Emergent Supersymmetry at Large $N$
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arXiv
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| Format: | Preprint |
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2023
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| author | Prakash, Shiroman Sinha, Shubham Kumar |
| author_facet | Prakash, Shiroman Sinha, Shubham Kumar |
| contents | We search for infrared fixed points of Gross-Neveu Yukawa models with matrix degrees of freedom in $d=4-\varepsilon$. We consider three models -- a model with $SU(N)$ symmetry in which the scalar and fermionic fields both transform in the adjoint representation, a model with $SO(N)$ symmetry in which the scalar and fermion fields both transform as real symmetric-traceless matrices, and a model with $SO(N)$ symmetry in which the scalar field transforms as a real symmetric-traceless matrix, while the fermion transforms in the adjoint representation. These models differ at finite $N$, but their large-$N$ limits are perturbatively equivalent. The first two models contain a supersymmetric fixed point for all $N$, which is attractive to all classically-marginal deformations for $N$ sufficiently large. The third model possesses a stable fixed point that, although non-supersymmetric, gives rise to many correlation functions that are identical to those of a supersymmetric fixed point when $N$ is sufficiently large. We also find several non-supersymmetric fixed points at finite and large-$N$. Planar diagrams dominate the large-$N$ limit of these fixed points, which suggests the possibility of a stringy holographic dual description. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_06841 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Emergent Supersymmetry at Large $N$ Prakash, Shiroman Sinha, Shubham Kumar High Energy Physics - Theory Strongly Correlated Electrons We search for infrared fixed points of Gross-Neveu Yukawa models with matrix degrees of freedom in $d=4-\varepsilon$. We consider three models -- a model with $SU(N)$ symmetry in which the scalar and fermionic fields both transform in the adjoint representation, a model with $SO(N)$ symmetry in which the scalar and fermion fields both transform as real symmetric-traceless matrices, and a model with $SO(N)$ symmetry in which the scalar field transforms as a real symmetric-traceless matrix, while the fermion transforms in the adjoint representation. These models differ at finite $N$, but their large-$N$ limits are perturbatively equivalent. The first two models contain a supersymmetric fixed point for all $N$, which is attractive to all classically-marginal deformations for $N$ sufficiently large. The third model possesses a stable fixed point that, although non-supersymmetric, gives rise to many correlation functions that are identical to those of a supersymmetric fixed point when $N$ is sufficiently large. We also find several non-supersymmetric fixed points at finite and large-$N$. Planar diagrams dominate the large-$N$ limit of these fixed points, which suggests the possibility of a stringy holographic dual description. |
| title | Emergent Supersymmetry at Large $N$ |
| topic | High Energy Physics - Theory Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2307.06841 |