12 research outputs found
Basic gerbe over non simply connected compact groups
We present an explicit construction of the basic bundle gerbes with
connection over all connected compact simple Lie groups. These are geometric
objects that appear naturally in the Lagrangian approach to the WZW conformal
field theories. Our work extends the recent construction of E. Meinrenken
\cite{Meinr} restricted to the case of simply connected groups.Comment: 27 pages, latex, 8 incorporated figure
Parallel Transport and Band Theory in Crystals
We show that different conventions for Bloch Hamiltonians on non-Bravais
lattices correspond to different natural definitions of parallel transport of
Bloch eigenstates. Generically the Berry curvatures associated with these
parallel transports differ, while physical quantities are naturally related to
a canonical choice of the parallel transport.Comment: 5 pages, 1 figure ; minor updat
Unitarity of the Knizhnik-Zamolodchikov-Bernard connection and the Bethe Ansatz for the elliptic Hitchin systems
We work out finite-dimensional integral formulae for the scalar product of
genus one states of the group Chern-Simons theory with insertions of Wilson
lines. Assuming convergence of the integrals, we show that unitarity of the
elliptic Knizhnik-Zamolodchikov-Bernard connection with respect to the scalar
product of CS states is closely related to the Bethe Ansatz for the commuting
Hamiltonians building up the connection and quantizing the quadratic
Hamiltonians of the elliptic Hitchin system.Comment: 24 pages, latex fil
SU(2) WZW Theory at Higher Genera
We compute, by free field techniques, the scalar product of the SU(2)
Chern-Simons states on genus > 1 surfaces. The result is a finite-dimensional
integral over positions of ``screening charges'' and one complex modular
parameter. It uses an effective description of the CS states closely related to
the one worked out by Bertram. The scalar product formula allows to express the
higher genus partition functions of the WZW conformal field theory by
finite-dimensional integrals. It should provide the hermitian metric preserved
by the Knizhnik-Zamolodchikov-Bernard connection describing the variations of
the CS states under the change of the complex structure of the surface.Comment: 44 pages, IHES/P/94/10, Latex fil
Construction and properties of a topological index for periodically driven time-reversal invariant 2D crystals
We present mathematical details of the construction of a topological
invariant for periodically driven two-dimensional lattice systems with
time-reversal symmetry and quasienergy gaps, which was proposed recently by
some of us. The invariant is represented by a gap-dependent -valued index that is simply related to the Kane-Mele invariants of
quasienergy bands but contains an extra information. As a byproduct, we prove
new expressions for the two-dimensional Kane-Mele invariant relating the latter
to Wess-Zumino amplitudes and the boundary gauge anomaly.Comment: published version ; 56 pages, 15 figure