The planar limit of $\mathcal{N}=2$ superconformal field theories
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| Format: | Preprint |
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2020
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| _version_ | 1866916319113248768 |
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| author | Fiol, Bartomeu Martínez-Montoya, Jairo Fukelman, Alan Rios |
| author_facet | Fiol, Bartomeu Martínez-Montoya, Jairo Fukelman, Alan Rios |
| contents | We obtain the perturbative expansion of the free energy on $S^4$ for four dimensional Lagrangian ${\cal N}=2$ superconformal field theories, to all orders in the 't Hooft coupling, in the planar limit. We do so by using supersymmetric localization, after rewriting the 1-loop factor as an effective action involving an infinite number of single and double trace terms. The answer we obtain is purely combinatorial, and involves a sum over tree graphs. We also apply these methods to the perturbative expansion of the free energy at finite $N$, and to the computation of the vacuum expectation value of the 1/2 BPS circular Wilson loop, which in the planar limit involves a sum over rooted tree graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2003_02879 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The planar limit of $\mathcal{N}=2$ superconformal field theories Fiol, Bartomeu Martínez-Montoya, Jairo Fukelman, Alan Rios High Energy Physics - Theory We obtain the perturbative expansion of the free energy on $S^4$ for four dimensional Lagrangian ${\cal N}=2$ superconformal field theories, to all orders in the 't Hooft coupling, in the planar limit. We do so by using supersymmetric localization, after rewriting the 1-loop factor as an effective action involving an infinite number of single and double trace terms. The answer we obtain is purely combinatorial, and involves a sum over tree graphs. We also apply these methods to the perturbative expansion of the free energy at finite $N$, and to the computation of the vacuum expectation value of the 1/2 BPS circular Wilson loop, which in the planar limit involves a sum over rooted tree graphs. |
| title | The planar limit of $\mathcal{N}=2$ superconformal field theories |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2003.02879 |