257 research outputs found
One-dimensional fermions with incommensurate hopping close to dimerization
We study the spectrum of fermions hopping on a chain with a weak
incommensuration close to dimerization; both q, the deviation of the wave
number from pi, and delta, the strength of the incommensuration, are small. For
free fermions, we use a continuum Dirac theory to show that there are an
infinite number of bands which meet at zero energy as q approaches zero. In the
limit that the ratio q/delta ---> 0, the number of states lying inside the q =
0 gap is nonzero and equal to 2 delta / pi^2. Thus the limit q ---> 0 differs
from q = 0; this can be seen clearly in the behavior of the specific heat at
low temperature. For interacting fermions or the XXZ spin-1/2 chain, we use
bosonization to argue that similar results hold.Comment: Revtex, 9 pages including 2 epsf figure
The appearence of the resolved singular hypersurface {x_0}{x_1}-{{x_2}^n} =0 in the classical phase space of the Lie group SU(n)
A classical phase space with a suitable symplectic structure is constructed
together with functions which have Poisson brackets algebraically identical to
the Lie algebra structure of the Lie group SU(n). In this phase space we show
that the orbit of the generators corresponding to the simple roots of the Lie
algebra give rise to fibres that are complex lines containing spheres. There
are n-1 spheres on a fibre and they intersect in exactly the same way as the
Cartan matrix of the Lie algebra. This classical phase space bundle,being
compact,has a description as a variety.Our construction shows that the variety
containing the intersecting spheres is exactly the one obtained by resolving
the singularities of the variety {x_0}{x_1}-{{x_2}^n}=0 in {C^3}. A direct
connection between this singular variety and the classical phase space
corresponding to the Lie group SU(n) is thus established.Comment: 11 pages, 2 figures, LaTe
Entropy of Three-Dimensional Black Holes in String Theory
It is observed that the three-dimensional BTZ black hole is a supersymmetric
solution of the low-energy field equations of heterotic string theory
compactified on an Einstein space. The solution involves a non-zero dilaton and
NS-NS H-field. The entropy of the extreme black hole can then be computed using
string theory and the asymptotic properties of anti-de Sitter space, without
recourse to a D-brane analysis. This provides an explicit example of a black
hole whose entropy can be computed using fundamental string theory, as
advocated by Susskind.Comment: 7 pages, Latex, Two additional reference
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