We study a $T\overline{T}$-deformed $O(N)$ vector model, which is classically equivalent to the Nambu-Goto action with static gauge. The thermal free energy density can be computed exactly by using the Burgers equation as a special property of $T\overline{T}$-deformation. The resulting expression is valid for an arbitrary value of N. One may consider a large N limit while preserving this expression. We try to derive this result in the field-theoretical approach directly by employing the large N limit. As a result, the leading contribution coincides with the exact one. That is, the $1/N$ corrections are canceled out through a non-trivial mechanism.

中文翻译：

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Burgers 方程与 TT¯ 变形的 O(N) 向量模型中的大 N 限制

我们研究一个 $吨\overline{吨}$-变形 $哦(N)$矢量模型，经典上等同于具有静态规范的 Nambu-Goto 动作。热自由能密度可以通过使用 Burgers 方程作为$吨\overline{吨}$-形变。结果表达式对N的任意值有效。在保留这个表达式的同时，可以考虑一个大的N限制。我们试图通过使用大N限制直接在场论方法中推导出这个结果。因此，领先的贡献与确切的贡献一致。那就是$1/N$ 更正通过一个非平凡的机制被取消。