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arXiv 1409.0867hep-th
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部分超重力破缺与相容截断的有效Action

Partial Supergravity Breaking and the Effective Action of Consistent Truncations

Thomas W. Grimm, Andreas Kapfer, Severin Lust

摘要:

我们研究了N = 4的五维半最大规范超引力真空,并确定了真空周围的有效理论的重要性质。主要的焦点是刚好有两个超对称性破缺的组态,因为它们经常出现在弦论和超引力的相容截断中。通过对陈-西蒙斯项的单圈修正进行评估,我们发现了必要的条件,以确保一个一致的截断也会引起一个更基本的理论的适当有效作用。为了得到具体的例子,我们确定了M理论在具有背景通量的六维SU(2)结构流形上的N=4作用量。欧拉数为零的Calabi-Yau三重流形是产生N=2 Minkowski真空的SU(2)-结构流形的例子。我们发现,一个循环校正的陈-西蒙斯条款平凡地消失,从而不施加约束,以确定有效的理论。这一结果可以追溯到这些几何上没有等距线。等距的例子来自于压扁的Sasaki-Einstein流形上的IIB型超引力。在这种情况下,单圈规范的Chern-Simons项由于非平凡的抵消而消失,而单圈引力的Chern-Simons项则不为零。

英文摘要:

We study vacua of N = 4 half-maximal gauged supergravity in five dimensions and determine crucial properties of the effective theory around the vacuum. The main focus is on configurations with exactly two broken supersymmetries, since they frequently appear in consistent truncations of string theory and supergravity. Evaluating one-loop corrections to the Chern-Simons terms we find necessary conditions to ensure that a consistent truncation also gives rise to a proper effective action of an underlying more fundamental theory. To obtain concrete examples, we determine the N=4 action of M-theory on six-dimensional SU(2)-structure manifolds with background fluxes. Calabi-Yau threefolds with vanishing Euler number are examples of SU(2)-structure manifolds that yield N=2 Minkowski vacua. We find that that one-loop corrections to the Chern-Simons terms vanish trivially and thus do not impose constraints on identifying effective theories. This result is traced back to the absence of isometries on these geometries. Examples with isometries arise from type IIB supergravity on squashed Sasaki-Einstein manifolds. In this case the one-loop gauge Chern-Simons terms vanish due to non-trivial cancellations, while the one-loop gravitational Chern-Simons terms are non-zero.

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