Boundary conditions for scalars in Lifshitz
Boundary conditions for scalars in Lifshitz
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DOI：
10.1088/0264-9381/30/6/065009
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发表时间：
2012-12
影响因子：
3.5
通讯作者：
T. Andrade;S. Ross
中科院分区：
文献类型：
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作者：
T. Andrade;S. Ross
我们考虑了Lifshitz背景下标量场的量子化，探索了替代边界条件的可能性，允许慢衰减模式波动。我们证明了与ADS情形相比，具有不同边界条件的标量场在更大的质量范围内是可归一化的。然而，我们随后发现了另一种边界条件的新不稳定性，这意味着定义良好对偶理论的另一种边界条件的质量范围是m2BF<；m2<；m2BF+1，类似于ADS情形。这种不稳定性是一种新的类型，具有随时间指数增长的任意大动量的模；因此，它本质上是一种UV效应，并意味着在它出现的地方根本没有定义双场理论。我们讨论了对偶场理论中的解释，并给出了标量算符维数的一个下界。
We consider the quantization of scalar fields on a Lifshitz background, exploring the possibility of alternative boundary conditions, allowing the slow falloff mode to fluctuate. We show that the scalar field with alternative boundary conditions is normalizable for a larger range of masses than in the AdS case. However, we then find a new instability for alternative boundary conditions, implying that the range of masses where alternative boundary conditions define a well-behaved dual theory is m2BF < m2 < m2BF + 1, analogously to the AdS case. The instability is of a novel type, with modes of arbitrarily large momentum which grow exponentially in time; it is therefore essentially a UV effect, and implies that the dual field theory is simply not defined where it appears. We discuss the interpretation in the dual field theory, and give a proposed lower bound on the dimension of scalar operators.