D-brane Instantons in Type II String Theory Page: 4 of 70
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two-dimensional conformal field theory correlation functions on Riemannian sur-
faces of higher genus g. The expansion parameter is g --) with gQ the string
coupling and depends on the dilaton o via gQ = exp(c). Suppose we compact-
ify the ten-dimensional superstring on a six-dimensional background such that
N = 1 supersymmetry is preserved in four dimensions. One can then compute an
effective four-dimensional supergravity action for the massless modes. The non-
renormalization theorems for holomorphic couplings generalize naturally to the
string case. For the holomorphic couplings W and f we expect that beyond tree-
and one-loop level, respectively, non-perturbative corrections are present. Since
we still lack a complete second quantized version of string theory, one must argue
for the existence of these non-perturbative corrections by the analogy with field
theory. Stringent tests of their presence in decoupling limits, or in cases where
duality maps such effects to classical effects, provide overwhelming evidence that
this analogy is correct.
From the early days of the heterotic string, effects that are non-perturbative
from the worldsheet perspective have been a field of active interest. Such config-
urations arise as Euclidean closed strings wrapping topologially non-trivial two-
cycles of the compactification manifold [5, 6]. Being localized in four dimensions,
they are called worldsheet instantons, in analogy to the Euclidean topologically
non-trivial solutions of Yang-Mills theory. Their contribution to the couplings is
non-perturbative in the worldsheet expansion parameter a', but not in the string
coupling g .
However, the past one and a half decades have witnessed major progress in
the understanding of objects in string theory which are non-perturbative also
from the spacetime point of view. It has been shown that p-brane solutions of
the supergravity equations of motions are truly non-perturbative objects in string
theory. In particular for the large class of D-branes, the quantum theory around
the classical solution is known to be given by an open string theory with end-
points on the D-brane . These D-branes carry charge under certain Ramond-
Ramond p-forms and also have tension scaling like T, = g 1. Such objects
are indeed present in four-dimensional Type II string vacua preserving N = 1
space-time supersymmetry in two different ways. Firstly, D-branes can fill four-
dimensional space-time and wrap certain cycles of the internal manifold. These
D-branes carry both gauge fields and chiral matter fields which are observed as
physical fields on the four-dimensional effective theory localized on the D-brane.
The past years have seen many attempts to realize realistic gauge and matter
spectra on such intersecting D-brane models. This includes investigations of D-
branes on compact manifolds as well as on non-compact geometries. Beyond the
mere construction of models, a formalism has been developed to compute the
resulting N = 1 supersymmetric four-dimensional effective supergravity action.
Soon it was realized that D-branes play an important role not only as the
hosts of this effective field theory, but also as actors in it: Euclidean D-branes
wrapping entirely a topologically non-trivial cycle of the internal manifold appear
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Blumenhagen, Ralph; /Munich, Max Planck Inst.; Cvetic, Mirjam; U., /Pennsylvania; Kachru, Shamit; /Stanford U., Phys. Dept. /SLAC et al. D-brane Instantons in Type II String Theory, article, June 19, 2009; United States. (digital.library.unt.edu/ark:/67531/metadc926940/m1/4/: accessed January 17, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.