来自正弦标量的全息RG流与虫洞
Holographic RG flows and wormholes from sinusoidal scalars
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中文总结 AI 辅助
研究在双AdS边界施加正弦标量源诱导的半经典几何，发现大虫洞始终主导引力路径积分，其对应多值β函数的奇异全息RG流，不连通几何与虫洞对应不同红外行为。
中文摘要 AI 辅助
我们研究了在两个渐近反德西特（AdS）边界上施加相同正弦标量源所诱导的半经典几何。通过改变源强度，我们发现在某一阈值之外会出现大、小两种虫洞解。在该阈值之上，大虫洞始终是双边界引力路径积分中的主导鞍点；不存在虫洞处于次主导地位的区域。根据引力路径积分的系综解释，这意味着一旦虫洞解存在，所推测的系综相对于均值会呈现指数级大的涨落。这与此前研究的非均匀物质源虫洞例子不同，后者在参数空间存在虫洞处于次主导地位的区域，因此系综会集中在均值附近。将体几何解释为全息重整化群（RG）流时，我们还发现标量边界源的正弦调制会产生多值的有效全息β函数，这对应着奇异的RG流。具体而言，不连通几何对应于在红外区回到初始不动点的流，而虫洞则描述流向红外区有能隙相的流。
英文摘要
We study semiclassical geometries induced by turning on identical sinusoidal scalar sources on two asymptotic anti-de Sitter (AdS) boundaries. Varying the source strength, we find that large and small wormhole solutions appear beyond a certain threshold. Above this threshold, the large wormhole is always the dominant saddle in the two-boundary gravitational path integral; there is no regime where wormholes are subdominant. Under the ensemble interpretation of the gravitational path integral, this implies that once wormhole solutions exist, the putative ensemble has exponentially large fluctuations relative to the mean. This is unlike previously studied examples of wormholes sourced by inhomogeneous matter which have a region in parameter space where wormholes are subdominant, and therefore the ensemble is sharply concentrated around the mean. Interpreting the bulk geometries as holographic renormalization group (RG) flows, we also find that the sinusoidal modulation of scalar boundary sources results in effective holographic $β$-functions which are multivalued, indicating exotic RG flows. In particular, disconnected geometries correspond to flows that return to the starting fixed point in the infrared, while wormholes describe flows to a gapped phase in the infrared.
