A {\cal R} "dual" transform is introduced which relates Quantum Field Theoryand String regimes, both in a curved background with D-non compact dimensions.This operation maps the characteristic length of one regime into the other(and, as a consequence, mass domains as well). The {\cal R}-transform is not anassumed or {\it a priori} imposed symmetry but is revealed by the QFT andString dynamics in curved backgrounds. The Hawking-Gibbons temperature and thestring maximal or critical temperature are {\cal R}-mapped one into the other.If back reaction of quantum matter is included, Quantum Field Theory and Stringphases appear, and {\cal R}-relations between them manifest as well. These{\cal R}-transformations are explicitly shown in two relevant examples: BlackHole and de Sitter space times.
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机译：引入了一个{\ cal R}“双重”变换，该变换将量子场论和弦体制联系在一起，两者都在具有D-非紧凑维的弯曲背景中进行。该操作将一个体制的特征长度映射到另一个体制（因此，结果） ，以及质量域）。 {\ cal R}变换不是假定的或{\先验的}对称的，但是可以通过弯曲背景中的QFT和String动力学来揭示。霍金长臂猿的温度和弦的最高或临界温度相互映射{\ cal R}。如果包括量子物质的反作用，则会出现量子场论和弦相，并且它们之间的{\ cal R}关系体现。这些{\ cal R}转换在两个相关示例中得到了明确显示：BlackHole和de Sitter时空。
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