Comment on "Remark on the renormalization group equation for the Penner model"

Details Comment on "Remark on the renormalization group equation for the Penner model" Comment on "Remark on the renormalization group equation for the Penner model"

2007-12-17

arxiv.org/abs/0712.2686v1

Phys.Rev.D75:127901,2007

Physics

High Energy Physics

High Energy Physics - Theory

4 pages

Scientific paper

10.1103/PhysRevD.75.127901

We show explicitly that the sum over punctures for the three times derivative for the Penner free energy $F_{0}^{3}$, given by D.A. Johnston, Phys.Rev.D 51 (1995) is not correct. As a consequence, Eq.(21), the differentiated version for the renormalization group (RG) equation, is wrong. Also, his conclusion that the differentiated version of the (RG) equation for the three-times derivative of the free energy can be obtained from the higher genus (RG) equation can not be true. Finally, the differentiated version of the (RG) equation is extended to any $s$ derivative of the free energy $F_{0}$.

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