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arXiv · 2308.08725

Improving Modular Bootstrap Bounds with Integrality

A. Liam Fitzpatrick·Wei Li
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Abstract

We implement methods that efficiently impose integrality -- i.e., the condition that the coefficients of characters in the partition function must be integers -- into numerical modular bootstrap. We demonstrate the method with a number of examples where it can be used to strengthen modular bootstrap results. First, we show that, with a mild extra assumption, imposing integrality improves the bound on the maximal allowed gap in dimensions of operators in theories with a $U(1)^c$ symmetry at $c=3$, and reduces it to the value saturated by the $SU(4)_1$ WZW model point of $c=3$ Narain lattices moduli space. Second, we show that our method can be used to eliminate all but a discrete set of points saturating the bound from previous Virasoro modular bootstrap results. Finally, when central charge is close to $1$, we can slightly improve the upper bound on the scaling dimension gap.

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A. Liam Fitzpatrick, Wei Li. 2023-08-17. Improving Modular Bootstrap Bounds with Integrality. https://arxiv.org/abs/2308.08725

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