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Small Instantons and Weak Scale String Theory
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CERN-TH/99-308
hep-th/9910090
Small Instantons and Weak Scale String Theory
Karim Benakli and Yaron Oz
Theory Division, CERN
CH-1211, Geneva 23, Switzerland
Abstract
We consider heterotic string compactifications to four dimensions when instantons
shrink to zero size. If the standard model gauge group originates from the new
gauge symmetry associated with the small instantons singularity, then the weakly
or strongly coupled heterotic string scales can be taken to be arbitrarily low. The
SO(32) and E8×E8 gauge groups can then be very weakly coupled even at the string
scale and behave as non-abelian global symmetries. We comment on a possible role
of small instantons in supersymmetry breaking.
October 1999
1 Introduction
The string scale, compactification scale, and Planck scale and the relations between them,
are of great importance for understanding the dynamics of string theory and its phe-
nomenological applications. These relations depend strongly on the choice of the string
vacuum [1]. In this note we consider heterotic string compactifications to four dimensions
when instantons shrink to zero size [2, 3, 4] in weakly and strongly coupled [5] limits
of heterotic strings. We discuss some aspects of the resulting four-dimensional N = 1
supersymmetric gauge theories.
One of the main aims of our study is to illustrate how the heterotic string scale can
be made arbitrarily low. Lowering the compactification scale [6], the string scale [7] and
quantum gravity scale [8] to TeV or to intermediate energies [9, 10] allows new perspectives
on phenomenological applications of string theory. It was argued that this is possible for
Type I string theory in [11], for the Hor?ava–Witten compactifications of M-theory in [9]
and for Type II string theory in [12] (see also [13]).
The paper is organized as follows. In the next section we will briefly discuss heterotic
string compactification. In section 3 we will con
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