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arXiv 1202.6364hep-thgr-qc
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微分自耦合理论的经典对偶

Classical Duals of Derivatively Self-Coupled Theories

Gregory Gabadadze, Kurt Hinterbichler, David Pirtskhalava

备注：
20 pages. v2 refs added
发表信息：
Phys.Rev. D85 (2012) 125007
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摘要：

具有导数自耦合的标量理论的解通常具有非线性很重要的区域。给定一个经典源，通常有一个以范施泰因半径为界的区域，在该区域内经典非线性占主导地位，而量子效应仍然可以忽略不计。如果用微扰理论来寻找这样的解，当从外部接近万施泰因半径时，膨胀一般会破裂。在这里，我们表明，它是可能的，通过在某些辅助领域的整合，重新制定这些理论，以这样一种方式，非线性变得小的Vainshtein半径内，和它的大。这提供了一个互补的，或经典的双重，描述相同的理论-一个非微扰区域成为可访问的微扰。我们考虑几个例子的经典解决方案与各种对称性，并发现，在所有的情况下，对偶制定使得它相当简单的研究制度，在原来的微扰理论无法工作。作为一个例子，我们再现微扰计算的一些已知的非微扰的结果，一个点状源，宇宙弦，和域壁，并得出一个新的。对偶公式可能是有用的发展PPN形式主义的修正引力理论，产生这样的标量理论。

英文摘要：

Solutions to scalar theories with derivative self-couplings often have regions where non-linearities are important. Given a classical source, there is usually a region, demarcated by the Vainshtein radius, inside of which the classical non-linearities are dominant, while quantum effects are still negligible. If perturbation theory is used to find such solutions, the expansion generally breaks down as the Vainshtein radius is approached from the outside. Here we show that it is possible, by integrating in certain auxiliary fields, to reformulate these theories in such a way that non-linearities become small inside the Vainshtein radius, and large outside it. This provides a complementary, or classically dual, description of the same theory -- one in which non-perturbative regions become accessible perturbatively. We consider a few examples of classical solutions with various symmetries, and find that in all the cases the dual formulation makes it rather simple to study regimes in which the original perturbation theory fails to work. As an illustration, we reproduce by perturbative calculations some of the already known non-perturbative results, for a point-like source, cosmic string, and domain wall, and derive a new one. The dual formulation may be useful for developing the PPN formalism in the theories of modified gravity that give rise to such scalar theories.

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