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arXiv 1203.3191hep-thmath-phmath.MP
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Galileons Wess-Zumino Terms

Galileons as Wess-Zumino Terms

Garrett Goon, Kurt Hinterbichler, Austin Joyce, Mark Trodden

摘要:

我们表明,伽利略可以被认为是Wess-Zumino条款的时空对称性的自发破缺。Wess-Zumino项是对称性破缺的唯象拉格朗日量的陪集构造中不包含的项。相反,在d时空维度上,它们是(d+1)-形式的d-形式势,这些形式是相对于未破缺对称群的完全对称群的李代数上同调中的非平凡余循环。我们引入了伽利略代数,并构造了非平凡的(d+1)-形式余圈,证明了在所有维中伽利略代数和多重伽利略代数的存在性是由特定的李代数上同调群的维数来计算的.我们还讨论了DBI和共形伽利略从这个角度来看,表明他们不是Wess-Zumino条款,在每种情况下有一个例外。

英文摘要:

We show that the galileons can be thought of as Wess-Zumino terms for the spontaneous breaking of space-time symmetries. Wess-Zumino terms are terms which are not captured by the coset construction for phenomenological Lagrangians with broken symmetries. Rather they are, in d space-time dimensions, d-form potentials for (d+1)-forms which are non-trivial co-cycles in Lie algebra cohomology of the full symmetry group relative to the unbroken symmetry group. We introduce the galileon algebras and construct the non-trivial (d+1)-form co-cycles, showing that the presence of galileons and multi-galileons in all dimensions is counted by the dimensions of particular Lie algebra cohomology groups. We also discuss the DBI and conformal galileons from this point of view, showing that they are not Wess-Zumino terms, with one exception in each case.

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