Logarithmic Connections, WZNW Action, and Moduli of Parabolic Bundles on the Sphere

被引:1
作者
Meneses, Claudio [1 ]
Takhtajan, Leon A. [2 ,3 ]
机构
[1] Christian Albrechts Univ Kiel, Math Seminar, Heinrich Hecht Pl 6, D-24118 Kiel, Germany
[2] SUNY Stony Brook, Dept Math, Stony Brook, NY 11794 USA
[3] Euler Int Math Inst, St Petersburg, Russia
关键词
VECTOR-BUNDLES; FORMALISM; SURFACES;
D O I
10.1007/s00220-021-04183-y
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Moduli spaces of stable parabolic bundles of parabolic degree 0 over the Riemann sphere are stratified according to the Harder-Narasimhan filtration of underlying vector bundles. Over a Zariski open subset N-0 of the open stratum depending explicitly on a choice of parabolic weights, a real-valued function S is defined as the regularized critical value of the non-compactWess-Zumino-Novikov-Witten action functional. The definition of S depends on a suitable notion of parabolic bundle 'uniformization map' following from the Mehta-Seshadri and Birkhoff-Grothendieck theorems. It is shown that -S is a primitive for a (1,0)-form theta on N-0 associated with the uniformization data of each intrinsic irreducible unitary logarithmic connection. Moreover, it is proved that -S is a Kahler potential for (Omega - Omega(T))vertical bar(N0), where Omega is the Narasimhan-Atiyah-Bott Kahler form in N and Omega(T) is a certain linear combination of tautological (1, 1)-forms associated with the marked points. These results provide an explicit relation between the cohomology class [Omega] and tautological classes, which holds globally over certain open chambers of parabolic weights where N-0 = N.
引用
收藏
页码:649 / 680
页数:32
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