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arXiv · 2312.12576

Level Repulsion in $\mathcal{N} = 4$ super-Yang-Mills via Integrability, Holography, and the Bootstrap

Shai M. Chester·Ross Dempsey·Silviu S. Pufu
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Abstract

We combine supersymmetric localization with the numerical conformal bootstrap to bound the scaling dimension and OPE coefficient of the lowest-dimension operator in $\mathcal{N} = 4$ $\text{SU}(N)$ super-Yang-Mills theory for a wide range of $N$ and Yang-Mills couplings $g_\text{YM}$. We find that our bounds are approximately saturated by weak coupling results at small $g_\text{YM}$. Furthermore, at large $N$ our bounds interpolate between integrability results for the Konishi operator at small $g_\text{YM}$ and strong-coupling results, including the first few stringy corrections, for the lowest-dimension double-trace operator at large $g_\text{YM}$. In particular, our scaling dimension bounds describe the level splitting between the single- and double-trace operators at intermediate coupling.

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Shai M. Chester, Ross Dempsey, Silviu S. Pufu. 2023-12-19. Level Repulsion in $\mathcal{N} = 4$ super-Yang-Mills via Integrability, Holography, and the Bootstrap. https://arxiv.org/abs/2312.12576

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