STU模型的精确结果
Exact results for an STU-model
摘要：
Sen和Vafa的STU模型的对偶对称性是非常严格的。这是用来确定全纯函数，编码其二阶导数威尔逊有效作用量和耦合到Weyl张量的平方到五阶微扰论。在第五阶，仍存在一些模糊性，这些模糊性在进行到下一阶时预期会自行解决。随后，相应的拓扑弦配分函数的$S$，$T$和$U$的独立不变量的扩展进行了研究，系数函数依赖于一个有效的对偶不变耦合常数$u$，这是定义在黎曼曲面$\mathbb{C}$。独立于$S$、$T$和$U$的不变量的系数函数通过重算确定到所有阶。其他函数也可以用代数方法或通过求解微分方程来求解，微分方程的解与积分常数有关。拓扑弦配分函数的这种确定，虽然本身很有趣，但揭示了威尔逊作用量结果中的新的定性特征，否则很难理解。它演示了如何最终消除各种歧义的有效行动和拓扑字符串的结果进行比较。虽然我们只证明了这一点的主导条款，我们推测，这将保持在一般的这个模型。
英文摘要：
The duality symmetries of the STU-model of Sen and Vafa are very restrictive. This is utilized to determine the holomorphic function that encodes its two-derivative Wilsonian effective action and its couplings to the square of the Weyl tensor to fifth order in perturbation theory. At fifth order some ambiguities remain which are expected to resolve themselves when proceeding to the next order. Subsequently, a corresponding topological string partition function is studied in an expansion in terms of independent invariants of $S$, $T$ and $U$, with coefficient functions that depend on an effective duality invariant coupling constant $u$, which is defined on a Riemann surface $\mathbb{C}$. The coefficient function of the invariant that is independent of $S$, $T$ and $U$ is determined to all orders by resummation. The other functions can be solved as well, either algebraically or by solving differential equations whose solutions have ambiguities associated with integration constants. This determination of the topological string partition function, while interesting in its own right, reveals new qualitative features in the result for the Wilsonian action, which would be difficult to appreciate otherwise. It is demonstrated how eventually the various ambiguities are eliminated by comparing the results for the effective action and the topological string. While we only demonstrate this for the leading terms, we conjecture that this will hold in general for this model.
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