Low Energy Supersymmetry from the Heterotic String Landscape

Abstract

We study possible correlations between properties of the observable and hidden sectors in heterotic string theory. Specifically, we analyze the case of the Z 6 -II orbifold compactification which produces a significant number of models with the spectrum of the supersymmetric standard model. We find that requiring realistic features does affect the hidden sector such that hidden sector gauge group factors SU(4) and SO(8) are favored. In the context of gaugino condensation, this implies low energy supersymmetry breaking. DOI: 10.1103/PhysRevLett.98.181602 PACS numbers: 11.25.Wx, 04.65.+e, 12.60.Cn, 12.60.Jv In the string theory landscape [1][2][3][4][5], the minimal supersymmetric standard model (MSSM) corresponds to a certain subset of vacua out of a huge variety. To obtain string theory predictions, one can first identify vacua with realistic properties, and then analyze their common features. In this Letter, we study possible implications of this approach for supersymmetry breaking. First, we look for models consistent with the MSSM at low energies, then we study common features of their hidden sectors which are responsible for supersymmetry breaking.We find that requiring realistic features affects the hidden sector such that, in the context of gaugino condensation, low energy supersymmetry breaking is favored. Since high energy supersymmetry is usually required by consistency of string models, this correlation provides a top-down motivation for low energy supersymmetry, which is favored by phenomenological considerations such as the gauge hierarchy problem and electroweak symmetry breaking.We base our study [6] on the orbifold compactifications [7,8] of the E 8 E 8 heterotic string [9]. Recent work on an orbifold GUT interpretation of heterotic models [10 -12] has facilitated construction of realistic models. In particular, the Z 6 -II orbifold (see [12]) has been shown to produce many models with realistic features [6,13,14]. These include the gauge group and the matter content of the MSSM, gauge coupling unification and a heavy top quark. Such models are generated using the gauge shifts These shifts are chosen due to their ''local grand unified theory (GUT)'' [13][14][15][16] properties. They lead to massless matter in the first twisted sector (T 1 ) forming a 16-plet of SO (10) the hypercharge will be that of standard 4D GUTs. These features facilitate construction of realistic models.We focus on models with one Wilson line of order 3 (W 3 ) and one Wilson line of order 2 (W 2 ), although we include all models with 2 Wilson lines in the statistics. These are the simplest constructions allowing for 3 MSSM matter families without chiral exotics. In this case, two matter generations have similar properties while the third family is different. Selection of realistic models proceeds as follows: (1) Steps (1)-(7) are described in detail in Ref. [6]. At the last step, we select models in which the decoupling of the SM exotic states is possible without breaking the largest gauge group in the hidden sector. ...

A Z2×Z2 standard model

“…Such a D 4 symmetry is known to be phenomenologically attractive as it can ameliorate supersymmetric flavor problems [34]. In this respect the structure of the model is very similar to the 6 -II models discussed in [10,12,35].…”

“…It is unknown whether a complete blow-down of the potentially realistic smooth compactifications, obtained so far [7,8,21], to an exact (free orbifold) CFT description exists. On the other hand, many phenomenologically attractive orbifold models [10][11][12] cannot be completely blown up without destroying the phenomenological viability of these settings, as the hypercharge or another part of the standard model gauge group gets broken in the complete blow-up [19].…”

“…This ensures that one has an ultra-violet complete framework in which couplings are accurately computable. The mini-landscape of 6 -II orbifolds [10][11][12] provides a large class of phenomenological appealing models of this kind: for example, the MSSM matter spectrum is reproduced, vector-like exotics can be decoupled and realistic features like a large top-Yukawa coupling, hierarchical couplings and non-trivial flavor mixing emerge.…”

The strings connection: MSSM-like models from strings

“…The construction principle for the models has been given in refs. [9][10][11]. One identifies models at the orbifold fixed points with enhanced gauge and discrete symmetries (in this construction we typically find several additional U (1)-symmetries).…”

“…A first attempt to do so was an analysis of heterotic E 8 × E 8 models within the orbifold compactification Z 6 I I . We will not repeat the details here, as they are explained in [9][10][11][32][33][34][35]. Meanwhile these investigations have been extended to the Z 2 × Z 2 case [13,36], Z 12 [37,38], Z 2 × Z 4 [39] and Z 8 [40].…”