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On the Hypermultiplet Moduli Space of Heterotic Compactifications with Small Instantons
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hep-th/9812253
December 31, 1998
On the Hypermultiplet Moduli Space
of Heterotic Compactifications with Small Instantons
Eugene Perevalov
1
Department of Mathematics
Harvard University
Camdridge, MA 02138, USA
ABSTRACT
We explore a relation between four-dimensional N = 2 heterotic vacua induced by Mirror
Symmetry via Heterotic/Type II duality. It allows us to compute the α′ corrections to the
hypermultiplet moduli space of heterotic compactifications on K3×T 2 in the limit of large
base of the elliptic K3. We concentrate on the case of point-like instantons on orbifold
singularities leading to low-dimensional hypermultiplet moduli spaces.
1 pereval@math.harvard.edu
1. Introduction
When a heterotic string is compactified on a K3 × T 2 manifold the result is an N = 2
supergravity coupled to Yang-Mills with matter. The moduli space of the above theory is
parametrized by the VEVs of scalar components of vector and hypermultiplets and locally
has the following form.
M ～= MH ×MV ,
where MH is a quaternionic manifold and MV is a special Ka?hler manifold. The geometry
of the moduli space encodes the information about the effective low-energy theory and is
of primary interest. In general, it receives corrections of two types: due to finite size
of the compactification manifold and to nonzero string coupling (α′ and gs corrections,
respectively). However, since the string coupling is determined by the VEV of the dilaton
which is a scalar component of a vector multiplet in heterotic compactifications, MH
is unaffected by gs corrections. MV on the other hand is expected to be corrected by
the quantum effects. What allows one to compute these corrections and obtain exact
expressions for the geometry of MV are two kinds of dualities believed to hold in string
theory: Mirror Symmetry (see e.g.,[1] and Heterotic/Type II duality[2,3].
Heterotic/Type II duality relates heterotic strings compactified on K3× T 2 to Type
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