Gravitational instantons and anomalous chiral symmetry breaking

Yuta Hamada, J. Pawlowski, M. Yamada
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引用次数: 10

Abstract

We study anomalous chiral symmetry breaking in two-flavour QCD induced by gravitational and QCD-instantons within asymptotically safe gravity within the functional renormalisation group approach. Similarly to QCD-instantons, gravitational ones, associated to a K3-surface connected by a wormhole-like throat in flat spacetime, generate contributions to the 't~Hooft coupling proportional to $\exp(-1/g_N)$ with the dimensionless Newton coupling $g_N$. Hence, in the asymptotically safe gravity scenario with a non-vanishing fixed point coupling $g_N^*$, the induced 't Hooft coupling is finite at the Planck scale, and its size depends on the chosen UV-completion. Within this scenario the gravitational effects on anomalous $U(1)_A$-breaking at the Planck scale may survive at low energy scales. In turn, fermion masses of the order of the Planck scale cannot be present. This constrains the allowed asymptotically safe UV-completion of the Gravity-QCD system. We map-out the parameter regime that is compatible with the existence of light fermions in the low-energy regime.
引力瞬子与反常手性对称性破缺
利用功能重整化群的方法研究了引力和渐近安全引力下双味QCD的反常手性对称性破缺。与qcd -瞬子类似,与平坦时空中由虫洞状喉部连接的k3表面相关的引力瞬子,对与无因次牛顿耦合g_N成比例的t~Hooft耦合的贡献为$\exp(-1/g_N)$。因此,在具有非消失固定点耦合$g_N^*$的渐近安全重力场景中,诱导t - Hooft耦合在普朗克尺度上是有限的,其大小取决于所选择的uv补全。在这种情况下,引力对普朗克尺度上的异常U(1)_A$破缺的影响可能在低能量尺度上存在。反过来,普朗克尺度数量级的费米子质量也不可能存在。这限制了重力- qcd系统允许的渐近安全紫外补全。我们绘制了与低能量状态下存在的轻费米子相兼容的参数区。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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