Supersymmetry versus Gauge Symmetry on the Heterotic Landscape

One of the goals of the landscape program in string theory is to extract information about the space of string vacua in the form of statistical correlations between phenomenological features that are otherwise uncorrelated in field theory. Such correlations would thus represent predictions of string theory that hold independently of a vacuum-selection principle. In this paper, we study statistical correlations between two features which are likely to be central to any potential description of nature at high energy scales: gauge symmetries and spacetime supersymmetry. We analyze correlations between these two kinds of symmetry within the context of perturbative heterotic string vacua, and find a number of striking features. We find, for example, that the degree of spacetime supersymmetry is strongly correlated with the probabilities of realizing certain gauge groups, with unbroken supersymmetry at the string scale tending to favor gauge-group factors with larger rank. We also find that nearly half of the heterotic landscape is non-supersymmetric and yet tachyon-free at tree level; indeed, less than a quarter of the tree-level heterotic landscape exhibits any supersymmetry at all at the string scale.Comment: 29 pages, LaTeX, 4 figures, 7 table

Correlation Classes on the Landscape: To What Extent is String Theory Predictive?

In light of recent discussions of the string landscape, it is essential to understand the degree to which string theory is predictive. We argue that it is unlikely that the landscape as a whole will exhibit unique correlations amongst low-energy observables, but rather that different regions of the landscape will exhibit different overlapping sets of correlations. We then provide a statistical method for quantifying this degree of predictivity, and for extracting statistical information concerning the relative sizes and overlaps of the regions corresponding to these different correlation classes. Our method is robust and requires no prior knowledge of landscape properties, and can be applied to the landscape as a whole as well as to any relevant subset.Comment: 14 pages, LaTeX, 5 figure

Adventures in Thermal Duality (II): Towards a Duality-Covariant String Thermodynamics

In a recent companion paper, we observed that the rules of ordinary thermodynamics generally fail to respect thermal duality, a symmetry of string theory under which the physics at temperature T is related to the physics at the inverse temperature 1/T. Even when the free energy and internal energy exhibit the thermal duality symmetry, the entropy and specific heat are defined in such a way that this symmetry is destroyed. In this paper, we propose a modification of the traditional definitions of these quantities, yielding a manifestly duality-covariant thermodynamics. At low temperatures, these modifications produce "corrections" to the standard definitions of entropy and specific heat which are suppressed by powers of the string scale. These corrections may nevertheless be important for the full development of a consistent string thermodynamics. We find, for example, that the string-corrected entropy can be smaller than the usual entropy at high temperatures, suggesting a possible connection with the holographic principle. We also discuss some outstanding theoretical issues prompted by our approach.Comment: 31 pages, 6 figures, 1 conversatio

Free Fermion Orientifolds

We investigate a class of orientifold models based on tensor products of 18 Ising models. Using the same search criteria as for the comparable case of Gepner model orientifolds we find that there are no three-family standard model configurations with tadpole cancellation. Even if we do not impose the latter requirement, we only find one such configuration in the special case of complex free fermions. In order to allow a comparison with other approaches we enumerate the Hodge numbers of the type-IIB theories we obtain. We provide indications that there are fermionic IIB vacua that are not $Z_2\times Z_2$ orbifolds.Comment: 18 pages + Appendix; references adde

New Geometric Approaches to Finite Temperature String Theory

In quantum field theory a system at finite temperature can equivalently be viewed as having a compactified dimension. This situation carries over into string theory and leads to thermal duality, which relates the physics of closed strings at temperature T to the physics at the inverse temperature 1/T. Unfortunately, the classical definitions of thermodynamic quantities such as entropy and specific heat are not invariant under the thermal duality symmetry. We shall therefore pursue two different approaches. We shall investigate whether there might nevertheless exist special solutions for the string effective potential such that the duality symmetry will be preserved for all thermodynamic quantities. Imposing thermal duality covariance, we derive unique functional forms for the temperature-dependence of the string effective potentials.The second approach is to investigate self-consistent modifications to the rules of ordinary thermodynamics such that thermal duality is preserved. After all, methods of calculation should not break fundamental symmetries. We therefore propose a modification of the traditional definitions of these quantities, yielding a manifestly duality-covariant thermodynamics. At low temperatures, these modifications produce "corrections" to the standard definitions of entropy and specific heat which are suppressed by powers of the string scale. These corrections may nevertheless be important for the full development of a consistent string thermodynamics.One can also investigate the limitations of this geometric interpretation of temperature. Until recently, it appeared as though the temperature/geometry equivalence held in all string theories, but it appears to be broken for the heterotic string. We shall show this breaking by considering the SO(32) heterotic string in ten dimensions.The breaking of the geometric/finite temperature correspondence in the context of the heterotic string, leads to two different philosophical approaches when examining string systems at finite temperature. One approach is to discard the geometrical interpretation of temperature and ignore the string consistency conditions to follow the standard rules of statistical mechanics. This approach does not seem to lead to self-consistent string models. The second approach is to take the string consistency conditions as fundamental and explore their implications for systems at finite temperature. We shall examine some of the consequences of this approach