Exploring superconformal Yang-Mills theories through matrix Bessel kernels
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| Format: | Preprint |
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2024
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| _version_ | 1866911043560669184 |
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| author | Bajnok, Zoltan Boldis, Bercel Korchemsky, Gregory P. |
| author_facet | Bajnok, Zoltan Boldis, Bercel Korchemsky, Gregory P. |
| contents | A broad class of observables in four-dimensional $\mathcal{N}=2$ and $\mathcal{N}=4$ superconformal Yang-Mills theories can be exactly computed for arbitrary 't Hooft coupling as Fredholm determinants of integrable Bessel operators. These observables admit a unifying description through a one-parameter generating function, which possesses a determinant representation involving a matrix generalization of the Bessel operator. We analyze this generating function over a wide range of parameter values and finite 't Hooft coupling. We demonstrate that it has a well-behaved weak-coupling expansion with a finite radius of convergence. In contrast, the strong-coupling expansion exhibits factorially growing coefficients, necessitating the inclusion of non-perturbative corrections that are exponentially suppressed at strong coupling. We compute these non-perturbative corrections and observe a striking resemblance between the resulting trans-series expansion of the generating function and the partition function of a strongly coupled theory expanded in powers of a mass gap. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_08732 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exploring superconformal Yang-Mills theories through matrix Bessel kernels Bajnok, Zoltan Boldis, Bercel Korchemsky, Gregory P. High Energy Physics - Theory Mathematical Physics A broad class of observables in four-dimensional $\mathcal{N}=2$ and $\mathcal{N}=4$ superconformal Yang-Mills theories can be exactly computed for arbitrary 't Hooft coupling as Fredholm determinants of integrable Bessel operators. These observables admit a unifying description through a one-parameter generating function, which possesses a determinant representation involving a matrix generalization of the Bessel operator. We analyze this generating function over a wide range of parameter values and finite 't Hooft coupling. We demonstrate that it has a well-behaved weak-coupling expansion with a finite radius of convergence. In contrast, the strong-coupling expansion exhibits factorially growing coefficients, necessitating the inclusion of non-perturbative corrections that are exponentially suppressed at strong coupling. We compute these non-perturbative corrections and observe a striking resemblance between the resulting trans-series expansion of the generating function and the partition function of a strongly coupled theory expanded in powers of a mass gap. |
| title | Exploring superconformal Yang-Mills theories through matrix Bessel kernels |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2412.08732 |