Simplices in Newton-Okounkov bodies and the Gromov width of coadjoint orbits

Abstract We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

Download Full-text

The Darboux coordinate system and Holstein–Primakoff representations on Kähler manifolds

Canadian Journal of Physics ◽

10.1139/p06-081 ◽

2006 ◽

Vol 84 (10) ◽

pp. 891-904

Author(s):

J R Schmidt

Keyword(s):

Coordinate System ◽

Lie Groups ◽

Lie Algebra ◽

Poisson Structure ◽

Kähler Manifolds ◽

Coadjoint Orbits ◽

Kahler Manifolds ◽

Canonical Transformations ◽

Kahler Geometry

The Kahler geometry of minimal coadjoint orbits of classical Lie groups is exploited to construct Darboux coordinates, a symplectic two-form and a Lie–Poisson structure on the dual of the Lie algebra. Canonical transformations cast the generators of the dual into Dyson or Holstein–Primakoff representations.PACS Nos.: 02.20.Sv, 02.30.Ik, 02.40.Tt

Download Full-text

Some remarks on the Gromov width of homogeneous Hodge manifolds

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887814600299 ◽

2014 ◽

Vol 11 (09) ◽

pp. 1460029 ◽

Cited By ~ 3

Author(s):

Andrea Loi ◽

Roberto Mossa ◽

Fabio Zuddas

Keyword(s):

Line Bundle ◽

Upper Bound ◽

Ample Line Bundle ◽

Seshadri Constant ◽

Gromov Width

We provide an upper bound for the Gromov width of compact homogeneous Hodge manifolds (M, ω) with b2(M) = 1. As an application we obtain an upper bound on the Seshadri constant ϵ(L) where L is the ample line bundle on M such that [Formula: see text].

Download Full-text