AbstractModuli 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 $$\mathscr {N}_{0}$$
N
0
of the open stratum depending explicitly on a choice of parabolic weights, a real-valued function $$\mathscr {S}$$
S
is defined as the regularized critical value of the non-compact Wess–Zumino–Novikov–Witten action functional. The definition of $$\mathscr {S}$$
S
depends on a suitable notion of parabolic bundle ‘uniformization map’ following from the Mehta–Seshadri and Birkhoff–Grothendieck theorems. It is shown that $$-\mathscr {S}$$
-
S
is a primitive for a (1,0)-form $$\vartheta $$
ϑ
on $$\mathscr {N}_{0}$$
N
0
associated with the uniformization data of each intrinsic irreducible unitary logarithmic connection. Moreover, it is proved that $$-\mathscr {S}$$
-
S
is a Kähler potential for $$(\Omega -\Omega _{\mathrm {T}})|_{\mathscr {N}_{0}}$$
(
Ω
-
Ω
T
)
|
N
0
, where $$\Omega $$
Ω
is the Narasimhan–Atiyah–Bott Kähler form in $$\mathscr {N}$$
N
and $$\Omega _{\mathrm {T}}$$
Ω
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 $$[\Omega ]$$
[
Ω
]
and tautological classes, which holds globally over certain open chambers of parabolic weights where $$\mathscr {N}_{0} = \mathscr {N}$$
N
0
=
N
.
Logarithmic Connections, WZNW Action, and Moduli of Parabolic Bundles on the Sphere
