arXiv 1702.061472017-02-20hep-th

陈-西蒙斯大流行病

A Chern-Simons Pandemic

Miguel Montero, Angel M. Uranga, Irene Valenzuela

备注：: 60 pages, 2 figures
DOI：: 10.1007/JHEP07(2017)123

摘要：

本文研究了量子引力理论，特别是弦论中广义整体对称性的相容性。这种整体对称性出现在具有$(p+1)$形式规范场的理论中，而对于时空维度$d\leq p+3$，带电物体的量子效应会阻碍它们的平衡。在具有2-形式规范场（或轴子标量）的4d理论中，这些场赋予史瓦西黑洞量子头发，这是一种全局电荷，导致通常的残余问题。我们描述了精确的机制，并从弦紧化和全息对的例子，在这些问题是回避要么计量或打破全球对称性，通过（合适的版本）Stuckelberg或Kaloper-Sorbo耦合。我们认为，即使在没有这种耦合的情况下，弦论中的一般解决方案是由涉及不同反对称张量场的三次陈-西蒙斯项打破整体对称性。我们猜想，任何具有（标准或更高次的反对称张量）规范场的理论都在沼泽地中，除非它的有效作用量包括这样的陈-西蒙斯项。这个猜想意味着许多熟悉的理论，如QED（甚至包括弱引力猜想所需要的带电粒子）或四维中的$\mathcal{N}=8$超引力，在量子引力中是不一致的，除非它们被这些陈-西蒙斯项所补充。

英文摘要：

In this paper we study the consistency of generalized global symmetries in theories of quantum gravity, in particular string theory. Such global symmetries arise in theories with $(p+1)$-form gauge fields, and for spacetime dimension $d\leq p+3$ there are obstructions to their breaking even by quantum effects of charged objects. In 4d theories with a 2-form gauge field (or with an axion scalar), these fields endow Schwarzschild black holes with quantum hair, a global charge leading to usual trouble with remnants. We describe precise mechanisms, and examples from string compactifications and holographic pairs, in which these problems are evaded by either gauging or breaking the global symmetry, via (suitable versions of) Stuckelberg or Kaloper-Sorbo couplings. We argue that even in the absence of such couplings, the generic solution in string theory is the breaking of the global symmetries by cubic Chern-Simons terms involving different antisymmetric tensor fields. We conjecture that any theory with (standard or higher-degree antisymmetric tensor) gauge fields is in the Swampland unless its effective action includes such Chern-Simons terms. This conjecture implies that many familiar theories, like QED (even including the charged particles required by the Weak Gravity Conjecture) or $\mathcal{N}=8$ supergravity in four dimensions, are inconsistent in quantum gravity unless they are completed by these Chern-Simons terms.

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英文摘要：

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