Small Instantons and Weak Scale String Theory.pdf

Small Instantons and Weak Scale String Theory.pdf

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Small Instantons and Weak Scale String Theory

a r X i v : h e p - t h / 9 9 1 0 0 9 0 v 1 1 1 O c t 1 9 9 9 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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