Large charge meets semiclassics in $\mathcal{N}=4$ super Yang-Mills
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909579319705600 |
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| author | Brown, Augustus Galvagno, Francesco Grassi, Alba Iossa, Cristoforo Wen, Congkao |
| author_facet | Brown, Augustus Galvagno, Francesco Grassi, Alba Iossa, Cristoforo Wen, Congkao |
| contents | We study the large-charge sector of $\mathcal{N}=4$ super Yang-Mills theory (SYM) with $SU(N)$ gauge group by constructing a special class of half-BPS heavy operators, termed "canonical operators". Such operators exhibit remarkable simplicity in the large-charge 't Hooft limit, where the dimension of the operators $Δ\to \infty$ with $Δ\, g_{\text{YM}}^2$ held finite. Canonical operator insertions in this regime map $\mathcal{N}=4$ SYM onto the Coulomb branch, by assigning a classical profile to the scalar fields with non-vanishing values along the diagonals given by the roots of unity. We follow a semiclassical approach to study two-point, three-point and Heavy-Heavy-Light-Light (HHLL) correlators. In particular we show that HHLL correlators in the large-charge 't Hooft limit are computed as two-point functions in a background determined by the classical profiles. We provide consistent evidence of our findings by computing the same observables via supersymmetric localization. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_02028 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large charge meets semiclassics in $\mathcal{N}=4$ super Yang-Mills Brown, Augustus Galvagno, Francesco Grassi, Alba Iossa, Cristoforo Wen, Congkao High Energy Physics - Theory We study the large-charge sector of $\mathcal{N}=4$ super Yang-Mills theory (SYM) with $SU(N)$ gauge group by constructing a special class of half-BPS heavy operators, termed "canonical operators". Such operators exhibit remarkable simplicity in the large-charge 't Hooft limit, where the dimension of the operators $Δ\to \infty$ with $Δ\, g_{\text{YM}}^2$ held finite. Canonical operator insertions in this regime map $\mathcal{N}=4$ SYM onto the Coulomb branch, by assigning a classical profile to the scalar fields with non-vanishing values along the diagonals given by the roots of unity. We follow a semiclassical approach to study two-point, three-point and Heavy-Heavy-Light-Light (HHLL) correlators. In particular we show that HHLL correlators in the large-charge 't Hooft limit are computed as two-point functions in a background determined by the classical profiles. We provide consistent evidence of our findings by computing the same observables via supersymmetric localization. |
| title | Large charge meets semiclassics in $\mathcal{N}=4$ super Yang-Mills |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.02028 |