52 research outputs found
The Monge-Amp\`ere operator and geodesics in the space of K\"ahler potentials
It is shown that geodesics in the space of K\"ahler potentials can be
uniformly approximated by geodesics in the spaces of Bergman metrics. Two
important tools in the proof are the Tian-Yau-Zelditch approximation theorem
for K\"ahler potentials and the pluripotential theory of Bedford-Taylor,
suitably adapted to K\"ahler manifolds.Comment: 25 pages, no figure, minor misprints correcte
The K\"ahler-Ricci flow with positive bisectional curvature
We show that the K\"ahler-Ricci flow on a manifold with positive first Chern
class converges to a K\"ahler-Einstein metric assuming positive bisectional
curvature and certain stability conditions.Comment: 15 page
Two-Loop Superstrings III, Slice Independence and Absence of Ambiguities
The chiral superstring measure constructed in the earlier papers of this
series for general gravitino slices is examined in detail for slices supported
at two points x_\alpha. In this case, the invariance of the measure under
infinitesimal changes of gravitino slices established previously is
strengthened to its most powerful form: the measure is shown, point by point on
moduli space, to be locally and globally independent from the points x_\alpha,
as well as from the superghost insertion points p_a, q_\alpha introduced
earlier as computational devices. In particular, the measure is completely
unambiguous. The limit x_\alpha = q_\alpha is then well defined. It is of
special interest, since it elucidates some subtle issues in the construction of
the picture-changing operator Y(z) central to the BRST formalism. The formula
for the chiral superstring measure in this limit is derived explicitly.Comment: 20 pages, no figure
Asyzygies, modular forms, and the superstring measure I
The goal of this paper and of a subsequent continuation is to find some
viable ansatze for the three-loop superstring chiral measure. For this, two
alternative formulas are derived for the two-loop superstring chiral measure.
Unlike the original formula, both alternates admit modular covariant
generalizations to higher genus. One of these two generalizations is analyzed
in detail in the present paper, with the analysis of the other left to the next
paper of the series.Comment: 30 page
Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
The Seiberg-Witten curve and differential for supersymmetric
SU(N) gauge theory, with a massive hypermultiplet in the adjoint representation
of the gauge group, are analyzed in terms of the elliptic Calogero-Moser
integrable system. A new parametrization for the Calogero-Moser spectral curves
is found, which exhibits the classical vacuum expectation values of the scalar
field of the gauge multiplet. The one-loop perturbative correction to the
effective prepotential is evaluated explicitly, and found to agree with quantum
field theory predictions. A renormalization group equation for the variation
with respect to the coupling is derived for the effective prepotential, and may
be evaluated in a weak coupling series using residue methods only. This gives a
simple and efficient algorithm for the instanton corrections to the effective
prepotential to any order. The 1- and 2- instanton corrections are derived
explicitly. Finally, it is shown that certain decoupling limits yield supersymmetric theories for simple gauge groups with
hypermultiplets in the fundamental representation, while others yield theories
for product gauge groups , with
hypermultiplets in fundamental and bi-fundamental representations. The spectral
curves obtained this way for these models agree with the ones proposed by
Witten using D-branes and M-theory.Comment: 45 pages, Tex, no figure
Strong Coupling Expansions of SU(N) Seiberg-Witten Theory
We set up a systematic expansion of the prepotential for
supersymmetric Yang-Mills theories with SU(N) gauge group in the region of
strong coupling where a maximal number of mutually local fields become
massless. In particular, we derive the first non-trivial non-perturbative
correction, which is the first term in the strong coupling expansion providing
a coupling between the different U(1) factors, and which governs for example
the strength of gaugino Yukawa couplings.Comment: 13 pages, Plain Tex, no macros needed, no figure
The Effective Prepotential of N=2 Supersymmetric SU(N_c) Gauge Theories
We determine the effective prepotential for N=2 supersymmetric SU(N_c) gauge
theories with an arbitrary number of flavors N_f < 2N_c, from the exact
solution constructed out of spectral curves. The prepotential is the same for
the several models of spectral curves proposed in the literature. It has to all
orders the logarithmic singularities of the one-loop perturbative corrections,
thus confirming the non-renormalization theorems from supersymmetry. In
particular, the renormalized order parameters and their duals have all the
correct monodromy transformations prescribed at weak coupling. We evaluate
explicitly the contributions of one- and two-instanton processes.Comment: 34 pages, Plain TeX, no macros needed, no figure
Carleson Measures and Toeplitz Operators
In this last chapter we shall describe an application of the Kobayashi distance to geometric function theory and functional analysis of holomorphic functions
The Box Graph In Superstring Theory
In theories of closed oriented superstrings, the one loop amplitude is given
by a single diagram, with the topology of a torus. Its interpretation had
remained obscure, because it was formally real, converged only for purely
imaginary values of the Mandelstam variables, and had to account for the
singularities of both the box graph and the one particle reducible graphs in
field theories. We present in detail an analytic continuation method which
resolves all these difficulties. It is based on a reduction to certain minimal
amplitudes which can themselves be expressed in terms of double and single
dispersion relations, with explicit spectral densities. The minimal amplitudes
correspond formally to an infinite superposition of box graphs on
like field theories, whose divergence is responsible for the poles in the
string amplitudes. This paper is a considerable simplification and
generalization of our earlier proposal published in Phys. Rev. Lett. 70 (1993)
p 3692.Comment: Plain TeX, 67 pp. and 9 figures, Columbia/UCLA/94/TEP/3
On the Construction of Asymmetric Orbifold Models
Various asymmetric orbifold models based on chiral shifts and chiral
reflections are investigated. Special attention is devoted to the consistency
of the models with two fundamental principles for asymmetric orbifolds :
modular invariance and the existence of a proper Hilbert space formulation for
states and operators. The interplay between these two principles is
non-trivial. It is shown, for example, that their simultaneous requirement
forces the order of a chiral reflection to be 4, instead of the naive 2. A
careful explicit construction is given of the associated one-loop partition
functions. At higher loops, the partition functions of asymmetric orbifolds are
built from the chiral blocks of associated symmetric orbifolds, whose pairings
are determined by degenerations to one-loop.Comment: 40 pages, no figures, typos correcte
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