2D quantum gravity at three loops: a counterterm investigation

Laetitia Leduc (1) , Adel Bilal (1)

1 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

We analyze the divergences of the three-loop partition function at fixed area in 2D quantum gravity. Considering the Liouville action in the Kähler formalism, we extract the coefficient of the leading divergence ∼AΛ2(ln⁡AΛ2)2 . This coefficient is non-vanishing. We discuss the counterterms one can and must add and compute their precise contribution to the partition function. This allows us to conclude that every local and non-local divergence in the partition function can be balanced by local counterterms, with the only exception of the maximally non-local divergence (ln⁡AΛ2)3 . Yet, this latter is computed and does cancel between the different three-loop diagrams. Thus, requiring locality of the counterterms is enough to renormalize the partition function. Finally, the structure of the new counterterms strongly suggests that they can be understood as a renormalization of the measure action.

Keywords: partition function; quantum gravity; nonlocal; renormalization; Liouville; Kaehler; higher-order: 3; dimension: 2

Domains: High Energy Physics - Theory [hep-th]

Laetitia Leduc, Adel Bilal. 2D quantum gravity at three loops: a counterterm investigation. Nuclear Physics B, 2016, 903, pp.226-261. ⟨10.1016/j.nuclphysb.2015.12.013⟩. ⟨hal-01554125⟩