Affiliation:
1. University of Pretoria
Abstract
We discuss integrable aspects of the logarithmic contribution of the
partition function of cosmological critical topologically massive
gravity. On one hand, written in terms of Bell polynomials which
describe the statistics of set partitions, the partition function of the
logarithmic fields is a generating function of the potential Burgers
hierarchy. On the other hand, the polynomial variables are solutions of
the Kadomtsev-Petviashvili equation, and the partition function is a KP
\tauτ
function, making more precise the solitonic nature of the logarithmic
fields being counted. We show that the partition function is a
generating function of Hurwitz numbers, and derive its expression. The
fact that the partition function is the generating function of branched
coverings gives insight on the orbifold target space. We show that the
logarithmic field \psi^{new}_{\mu \nu}ψμνnew
can be regarded as a branch point field associated to the branch point
\mu l =1μl=1.
Subject
General Physics and Astronomy
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献