arXiv 2510.033922025-10-03hep-th

4维 Maxwell 理论及其基于码的系综的全息描述

Holographic description of 4d Maxwell theories and their code-based ensembles

Ahmed Barbar, Anatoly Dymarsky, Alfred Shapere

AI总结：

本文建立 4 维 U(1)^g Maxwell 理论系综与 5 维 Abelian BF 理论间的精确全息对偶，并用自对偶稳定子码刻画边界条件与拓扑，推广至关联函数及大 N Eisenstein 级数描述。

摘要：

我们构建了一个精确的全息对偶：一侧是生活在自旋四流形 M_4 上的 4 维 U(1)^g Maxwell 理论的系综，另一侧是 level N 的 Abelian BF 型 2-形式规范理论，并对所有以 M_4 为边界的五流形求和。边界系综的元素是由 Z_N 上自对偶辛码所指定的 Abelian 规范理论，这些码参数化了 5 维 TQFT 中的拓扑边界条件。类似地，由该 5 维理论区分的拓扑等价类由正交自对偶码参数化。因此，该全息对偶可以用量子稳定子码的语言重新表述。这一对偶与 2 维 Narain 共形场论系综和 3 维 level-N Abelian Chern-Simons 理论之间的全息关系密切相关。在两种情形中，对偶都可推广到关联函数。在大 N 极限下，我们发现边界系综平均收敛为对规范耦合模空间的积分，并且在有限时等于正交群的 Eisenstein 级数，即出现在 2d/3d 情形中的 Siegel–Weil 公式的一个版本。作为附带结果，我们阐明了 4 维 N=4 超 Yang–Mills 理论的规范群与体中单态部分边界条件之间的全息关系。

英文摘要：

We formulate a precise holographic duality between an ensemble of 4d $U(1)^g$ Maxwell theories living on a spin four-manifold $M_4$ and an Abelian BF-type 2-form gauge theory of level $N$, summed over all five-manifolds with boundary $M_4$. The elements of the boundary ensemble are Abelian gauge theories specified by self-dual symplectic codes over $Z_N$, that parameterize topological boundary conditions in the 5d TQFT. Similarly, the equivalence classes of topologies distinguished by the 5d theory are parameterized by orthogonal self-dual codes. Hence the holographic duality can be reformulated in the language of quantum stabilizer codes. This duality is closely related to the holographic relationship between ensembles of Narain conformal field theories in 2d and level-$N$ Abelian Chern-Simons theories in 3d. In both contexts, the duality extends to correlation functions. In the large-$N$ limit, we find that the boundary ensemble average converges to an integral over the moduli space of the gauge couplings and, when finite, is equal to an Eisenstein series of the orthogonal group, a version of the Siegel-Weil formula that appears in the 2d/3d context. As a spinoff, we clarify the holographic relationship between the gauge group of the 4d N=4 super Yang-Mills theory and the boundary conditions of the singleton sector in the bulk.

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