arXiv subjects

Pascal Tran-Ngoc-Bich

Publications and source records attributed to Pascal Tran-Ngoc-Bich.

3 recordsLinked to original sources

arXiv2001

Canonical quantization of the boundary Wess-Zumino-Witten model

We present an analysis of the canonical structure of the WZW theory with untwisted conformal boundary conditions. The phase space of the boundary theory on a strip is shown to coincide with the phase space of the Chern-Simons theory on a solid cylinder (a disc times a line) with two Wilson lines. This reveals a new aspect of the relation between two-dimensional boundary conformal field theories and three-dimensional topological theories. A decomposition of the Chern-Simons phase space on a punctured disc in terms of the one on a punctured sphere and of coadjoint orbits of the loop group easily lends itself to quantization, providing at the same time a quantization of the boundary WZW model.

hep-th↗

arXiv1998

Hitchin Systems at Low Genera

The paper gives a quick account of the simplest cases of the Hitchin integrable systems and of the Knizhnik-Zamolodchikov-Bernard connection at genus 0, 1 and 2. In particular, we construct the action-angle variables of the genus 2 Hitchin system with group SL(2) by exploiting its relation to the classical Neumann integrable systems.

hep-th↗

arXiv1998

Self-duality of the SL_2 Hitchin integrable system at genus two

We revisit the Hitchin integrable system whose phase space is the bundle cotangent to the moduli space $N$ of holomorphic $SL_2$-bundles over a smooth complex curve of genus two. $N$ may be identified with the 3-dimensional projective space of theta functions of the second order, We prove that the Hitchin system on $T^*N$ possesses a remarkable symmetry: it is invariant under the interchange of positions and momenta. This property allows to complete the work of van Geemen-Previato which, basing on the classical results on geometry of the Kummer quartic surfaces, specified the explicit form of the Hamiltonians of the Hitchin system. The resulting integrable system resembles the classic Neumann systems which are also self-dual. Its quantization produces a commuting family of differential operators of the second order acting on homogeneous polynomials in four complex variables. As recently shown by van Geemen-de Jong, these operators realize the Knizhnik-Zamolodchikov-Bernard-Hitchin connection for group SU(2) and genus 2 curves.

solv-int↗