Runaway Directions Research Articles

On the derivation of chiral symmetry breaking in QCD-like theories and S-confining theories

Recent works argue that the pattern of chiral symmetry breaking in QCD-like theories can be derived from supersymmetric (SUSY) QCD with perturbation of anomaly-mediated SUSY breaking (AMSB). Nevertheless, despite the fact that AMSB needs to be a small (but still exact) perturbation, two other major problems remain unsolved: first, in order to derive the chiral symmetry breaking pattern, one needs to minimize the potential along a certain specific direction, identifying this direction fully as an outcome is nontrivial given the moduli space of degenerate vacua in the SUSY limit; second, when SUSY is broken, non-holomorphic states might emerge and be relevant for determining the vacuum structure. In this work, we try to resolve these problems and discuss their physical implica- tions. For this purpose, we focus on SUSY QCD with Nf ≤ Nc + 1 and perturb the theories using AMSB. Without minimizing the potential along a certain specific direction in the moduli space, we successfully derive the expected chiral symmetry breaking pattern when Nf< Nc. However, when Nf = Nc and Nf = Nc + 1, we show that tree-level AMSB would induce runaway directions, along which baryon number is spontaneously broken, and the vacua with broken baryon number can be deeper while the field values are not far from the origin. This implies that phase transitions and/or non-holomorphic physics are necessary. In order to derive the expected chiral symmetry breaking pattern of non-SUSY QCD starting from the SUSY limit and AMSB, baryon number conservation is needed as an input rather than obtained as an output. Moreover, we perform explicit consistency checks on “ultraviolet insensitivity” for different Nf by adding the holomorphic mass term for the last flavor, we find that the “jump” of AMSB potential indeed matches the contribution from the holomorphic mass term. We also show in general that, when tree-level AMSB is not vanishing, the origin of the moduli space in s-confining theories does not persist as a minimum.

Runaway Directions in O’Raifeartaigh Models**Supported by the National Natural Science Foundation of China under Grant No. 11305110

R-symmetries, which are needed for supersymmetry (SUSY) breaking in O’Raifeartaigh models, often lead to SUSY runaway directions trough a complexified R-transformation. Non-R symmetries also lead to runaway directions in a similar way. This work investigates the occurrence of runaway directions of both SUSY and SUSY breaking types. We clarify previous issues on fractional charges and genericness, and make a refined statement on conditions for runaway directions related to either R-symmetries or non-R symmetries. We present a generic and anomaly-free model to show the existence of runaway directions related to non-R symmetries. We also comment on the possibility to combine the non-R symmetry case to the R-symmetry case by an R-charge redefinition.

Orientifolds and duality cascades: confinement before the wall

We consider D-branes at orientifold singularities and discuss two properties of the corresponding low energy four-dimensional effective theories which are not shared, generically, by other Calabi-Yau singularities. The first property is that duality cascades are finite and, unlike ordinary ones, do not require an infinite number of degrees of freedom to be UV-completed. The second is that orientifolds tend to stabilize runaway directions. These two properties can have interesting implications and widen in an intriguing way the variety of gauge theories one can describe using D-branes.

More stable de Sitter vacua fromS-dual nongeometric fluxes

Stable vacua obtained from isotropic tori compactification might not be fully stable provided the existence of runaway directions in the Kaehler directions of anisotropy. By implementing a genetic algorithm we report the existence of explicit flux configurations leading to stable de Sitter and Anti- de Sitter vacua, consisting on Type IIB compactifications on a 6-dimensional anisotropic torus threaded with standard and S-dual invariant non-geometric fluxes in the presence of orientifold 3-planes. In all dS vacua the masses of the complex structure moduli are heavier than the Hubble scale suggesting that the axio-dilaton and Kaeahler moduli are natural candidates for small-field inflation. In the way, we also report new solutions on isotropic and semi-isotropic tori compactifications. Finally, we observe that, since all our solutions are obtained in the absence of solitonic objects, they are good candidates to be lifted to stable solutions in extended supersymmetric theories.

Runaway, D term andR-symmetry breaking

We study the D-term effect on runaway directions of the F-term scalar potential. A minimal renormalizable model is presented where supersymmetry is broken without any pseudomoduli. The model is applied to the hidden sector of gauge mediation for spontaneously breaking R symmetry and generating nonvanishing gaugino masses at the one-loop order.

Precision determination of [formula omitted] using an unbiased global NLO parton set

We determine the strong coupling αs from a next-to-leading order analysis of processes used for the NNPDF2.1 parton determination, which includes data from neutral and charged current deep-inelastic scattering, Drell–Yan and inclusive jet production. We find αs(MZ)=0.1191±0.0006exp, where the uncertainty includes all statistical and systematic experimental uncertainties, but not purely theoretical uncertainties, which are expected to be rather larger. We study the dependence of the results on the dataset, by providing further determinations based respectively on deep-inelastic data only, and on HERA data only. The deep-inelastic fit gives the consistent result αs(MZ)=0.1177±0.0009exp, but the result of the HERA-only fit is only marginally consistent. We provide evidence that individual data subsets can have runaway directions due to poorly determined PDFs, thus suggesting that a global dataset is necessary for a reliable determination.

Gauge mediation with D terms

I propose implementing General Gauge Mediation using the class of SU(N) × U(1) SUSY breaking models. As an existence proof, I have utilized the 4–1 model in building multi-parameter gauge mediation. These hidden sectors are relatively easy to use and avoid several model building pitfalls such as runaway directions. In addition models require no special tuning and may produce as many parameters as general gauge mediation allows.

Explicit R-symmetry breaking and metastable vacua

We consider O'Raifeartaigh-like models with explicit R-symmetry breaking and analyze the vacuum landscape. Taking such models as candidates for the hidden sector, we analyze the gauge mediation of the supersymmetry breaking, focusing on the effects produced by R-symmetry breaking. First, we construct families of non-R-symmetric models containing only singlet chiral superfields, and determine the conditions under which SUSY vacua, runaway directions and (longlived) metastable vacua exist. We then extend the results to the case in which some of the chiral fields are in the 5 ⊕ representation of SU(5). Gauging this symmetry, we compute soft masses for gauginos and sfermions, and analyze several issues such as doublet/triplet splitting, unification of coupling constants and CP violation phases.

Supersymmetry and R-symmetry breaking in models with non-canonical Kähler potential

We analyze several aspects of R-symmetry and supersymmetry breaking in generalized O'Raifeartaigh models with non-canonical Kähler potential. Some conditions on the Kähler potential are derived in order for the non-supersymmetric vacua to be degenerate. We calculate the Coleman-Weinberg (CW) effective potential for general quiral non-linear sigma models and then study the 1-loop quantum corrections to the pseudo-moduli space. For R-symmetric models, the quadratic dependence of the CW potential with the ultraviolet cutoff scale disappears. We also show that the conditions for R-symmetry breaking are independent of this scale and remain unchanged with respect to those of canonical models. This is, R-symmetry can be broken when generic R-charge assignments to the fields are made, while it remains unbroken when only fields with R-charge 0 and 2 are present. We further show that these models can keep the runaway behavior of their canonical counterparts and also new runaway directions can be induced. Due to the runaway directions, the non-supersymmetric vacua is metastable.

O'Raifeartaigh models with spontaneous R-symmetry breaking

O'Raifeartaigh models can have non-supersymmetric vacua with broken R-symmetry if they contain fields with R-charges different from 0 and 2. Runaway directions often occur in these models. We outline the relation between these runaway directions and R-symmetry.

R-symmetry breaking, runaway directions and global symmetries in O'Raifeartaigh models

We discuss O'Raifeartaigh models with general R-charge assignments, introduced by Shih to break R-symmetry spontaneously. We argue that most of these models have runaway directions related to the R-symmetry. In addition, we study the simplest model with a U(N) global symmetry and show that in a range of parameters R-symmetry is spontaneously broken in a metastable vacuum.

Runaway in the landscape

We consider flux compactifications of type IIB string theory on the mirror of a rigid Calabi-Yau. In special cases, these models are dual to the type IIA flux vacua with runaway direction in flux space. We show that new weak coupling AdS solutions can be found for large complex structure, while Minkowski solutions with all moduli stabilized are confined to be at strong coupling. The existence of these solutions, as found in a previous work, is nevertheless guaranteed by a nonrenormalization theorem of the type IIB flux superpotential. Based on our results, we are led to the conjecture that supersymmetric runaway directions in flux space are always accompanied by a spectrum of moduli masses reaching down to the AdS scale. This could be violated in a nonsupersymmetric situation.

Stringy instantons at orbifold singularities

We study the effects produced by D-brane instantons on the holomorphic quantities of a D-brane gauge theory at an orbifold singularity. These effects are not limited to reproducing the well known contributions of the gauge theory instantons but also generate extra terms in the superpotential or the prepotential. On these brane instantons there are some neutral fermionic zero-modes in addition to the ones expected from broken supertranslations. They are crucial in correctly reproducing effects which are dual to gauge theory instantons, but they may make some other interesting contributions vanish. We analyze how orientifold projections can remove these zero-modes and thus allow for new superpotential terms. These terms contribute to the dynamics of the effective gauge theory, for instance in the stabilization of runaway directions.

Building models of gauge-mediated supersymmetry breaking without a messenger sector

We propose a general scheme for constructing models in which the Standard Model (SM) gauge interactions are the mediators of supersymmetry breaking to the fields in the supersymmetric SM, but where the SM gauge groups couple directly to the sector which breaks supersymmetry dynamically. Despite the direct coupling, the models preserve perturbative unification of the SM gauge coupling constants. Furthermore, the supergravity contributions to the squark and slepton masses can be naturally small, typically being much less than 1% of the gauge-mediated (GM) contributions. Both of these goals can be achieved without need of a fine-tuning or a very small coupling constant. This scheme requires run-away directions at the renormalizable level which are only lifted by non-renormalizable terms in the superpotential. To study the proposed scheme in practice, we develop a modified class of models based on SU(N) × SU(N − 1) which allows us to gauge an SU(N − 2) global symmetry. However, we point out a new problem which can exist in models where the dynamical supersymmetry breaking sector and the ordinary sector are directly coupled - the two-loop renormalization group has contributions which can induce negative (mass)2 for the squarks and sleptons. We clarify the origin of the problem and argue that it is likely to be surmountable. We give a recipe for a successful model.