Gravitational instantons and anomalous chiral symmetry breaking

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 $g_N^{\ast }$, 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.

14 pages, 7 figures

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• Fate of chiral symmetry in Riemann-Cartan geometry
• Asymptotically Safe Gravity-Fermion systems on curved backgrounds