Paper (*cross-listing*): hep-th/9311042 hep-th@xxx.lanl.gov
From: dmrrsn@math.duke.edu (David R. Morrison)
Date: Mon, 8 Nov 93 21:06:28 EST
Measuring Small Distances in N=2 Sigma Models, by Paul S. Aspinwall, Brian R.
Greene, and David R. Morrison, 62 pp. with 6 figs., LaTeX and epsf.tex,
IASSNS-HEP-93/49
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We analyze global aspects of the moduli space of K\"ahler forms for $N$=(2,2)
conformal $\sigma$-models. Using algebraic methods and mirror symmetry we
study extensions of the mathematical notion of length (as specified by a
K\"ahler structure) to conformal field theory and calculate the way in which
lengths change as the moduli fields are varied along distinguished paths in
the moduli space. We find strong evidence supporting the notion that, in the
robust setting of quantum Calabi-Yau moduli space, string theory restricts the
set of possible K\"ahler forms by enforcing ``minimal length'' scales,
provided that topology change is properly taken into account. Some lengths,
however, may shrink to zero. We also compare stringy geometry to classical
general relativity in this context.
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Paper (*cross-listing*): hep-th/9311049 hep-th@xxx.lanl.gov
From: dmrrsn@math.duke.edu (David R. Morrison)
Date: Mon, 8 Nov 93 21:08:06 EST
Where is the large radius limit?, by David R. Morrison, 5 pages with 2 figures,
LaTeX and epsf.tex, IASSNS-HEP-93/68
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By properly accounting for the invariance of a Calabi-Yau sigma-model under
shifts of the $B$-field by integral amounts (analagous to the $\theta$-angle in
QCD), we show that the moduli spaces of such sigma-models can often be enlarged
to include ``large radius limit'' points. In the simplest cases, there are
holomorphic coordinates on the enlarged moduli space which vanish at the limit
point, and which appear as multipliers in front of instanton contributions to
Yukawa couplings. (Those instanton contributions are therefore suppressed at
the limit point.) In more complicated cases, the instanton contributions are
still suppressed but the enlarged space is singular at the limit point. This
singularity may have interesting effects on the effective four-dimensional
theory, when the Calabi-Yau is used to compactify the heterotic string. (Talk
presented at the ``Strings '93'' conference, May 24--29, 1993, Berkeley.)