Surveying Pseudomoduli: the Good, the Bad and the Incalculable

We classify possible types of pseudomoduli which arise when supersymmetry is dynamically broken in infrared-free low-energy theories. We show that, even if the pseudomoduli potential is generated only at higher loops, there is a regime where the potential can be simply determined from a combination of one-loop running data. In this regime, we compute whether the potential for the various types of pseudomoduli is safe, has a dangerous runaway to the UV cutoff of the low-energy theory, or is incalculable. Our results are applicable to building new models of supersymmetry breaking. We apply the results to survey large classes of models.Comment: 34 page

On Exact Superpotentials, Free Energies and Matrix Models

We discuss exact results for the full nonperturbative effective superpotentials of four dimensional $\mathcal{N}=1$ supersymmetric U(N) gauge theories with additional chiral superfield in the adjoint representation and the free energies of the related zero dimensional bosonic matrix models with polynomial potentials in the planar limit using the Dijkgraaf-Vafa matrix model prescription and integrating in and out. The exact effective superpotentials are produced including the leading Veneziano-Yankielowicz term directly from the matrix models. We also discuss how to use integrating in and out as a tool to do random matrix integrals in the large $N$ limit.Comment: 14 pages; v2: typos corrected; v3: the scheme for computing exact superpotentials including both the Veneziano-Yankielowicz term and all instanton corrections directly using matrix models is emphasized and references added, to appear in JHE

Effective Gauge Degrees of Freedom and the (Non)existence of the Glueball Superpotential

We propose an efficient way to obtain a correct Veneziano-Yankielowicz type integration constant of the effective glueball superpotential $W_{eff}(S,g,\Lambda)$, even for massless theories. Applying our method, we show some $\mathcal{N} = 1$ theories do not have such an effective glueball superpotential, even though they have isolated vacua. In these cases, $S = 0$ typically.Comment: 17 pages, v2: Footnote added, typos corrected, v3: Reference adde

Tree level spontaneous R-symmetry breaking in O'Raifeartaigh models

We show that in O'Raifeartaigh models of spontaneous supersymmetry breaking, R-symmetries can be broken by non-zero values of fields at tree level, rather than by vacuum expectation values of pseudomoduli at loop level. As a complement of the recent result by Shih, we show that there must be a field in the theory with R-charge different from zero and two in order for R-symmetry breaking to occur, no matter whether the breaking happens at tree or loop level. We review the example by CDFM, and construct two types of tree level R-symmetry breaking models with a wide range of parameters and free of runaway problem. And the R-symmetry is broken everywhere on the pseudomoduli space in these models. This provides a rich set of candidates for SUSY model building and phenomenology.Comment: 8 pages; v2: major revision to section 6; v3: minor revision and typos; v4: typos, published version; v5: fix Latex syntax error, published versio

Exact Superpotentials for Theories with Flavors via a Matrix Integral

We extend and test the method of Dijkgraaf and Vafa for computing the superpotential of N=1 theories to include flavors in the fundamental representation of the gauge group. This amounts to computing the contribution to the superpotential from surfaces with one boundary in the matrix integral. We compute exactly the effective superpotential for the case of gauge group U(N_c), N_f massive flavor chiral multiplets in the fundamental and one massive chiral multiplet in the adjoint, together with a Yukawa coupling. We compare up to sixth-order with the result obtained by standard field theory techniques in the already non trivial case of N_c=2 and N_f=1. The agreement is perfect.Comment: 7 pages, v2: typos involving signs fixed; v3: version to appear in Phys.Rev.

Notes on SUSY and R-Symmetry Breaking in Wess-Zumino Models

We study aspects of Wess-Zumino models related to SUSY and R-symmetry breaking at tree-level. We present a recipe for constructing a wide class of tree-level SUSY and R-breaking models. We also deduce a general property shared by all tree-level SUSY breaking models that has broad application to model building. In particular, it explains why many models of direct gauge mediation have anomalously light gauginos (even if the R-symmetry is broken spontaneously by an order one amount). This suggests new approaches to dynamical SUSY breaking which can generate large enough gaugino masses.Comment: 23 pages. v2: references added, minor changes. v3: comment on non-renormalizable case adde

Note on the pseudo-Nambu-Goldstone Boson of Meta-stable SUSY Violation

Many models of meta-stable supersymmetry (SUSY) breaking lead to a very light scalar pseudo-Nambu Goldstone boson (PNGB), P, associated with spontaneous breakdown of a baryon number like symmetry in the hidden sector. Current particle physics data provide no useful constraints on the existence of P. For example, the predicted decay rates for both K --> pi + P, b--> s + P and Upsilon --> photon + P are many orders of magnitude below the present experimental bounds. We also consider astrophysical implications of the PNGB and find a significant constraint from its effect on the evolution of red giants. This constraint either rules out models with a hidden sector gauge group larger than SU(4), or requires a new intermediate scale, of order at most 10^{10} GeV, at which the hidden sector baryon number is explicitly broken.Comment: 17 pages, 3 figures. Version 2: minor typographical errors fixed. Version 3: a more reliable estimate for the decay rate of K-->pi+PNGB is provided, and the predicted rate for b-->s+PNGB is now include

Dynamical SUSY Breaking in Meta-Stable Vacua

Dynamical supersymmetry breaking in a long-lived meta-stable vacuum is a phenomenologically viable possibility. This relatively unexplored avenue leads to many new models of dynamical supersymmetry breaking. Here, we present a surprisingly simple class of models with meta-stable dynamical supersymmetry breaking: N=1 supersymmetric QCD, with massive flavors. Though these theories are strongly coupled, we definitively demonstrate the existence of meta-stable vacua by using the free-magnetic dual. Model building challenges, such as large flavor symmetries and the absence of an R-symmetry, are easily accommodated in these theories. Their simplicity also suggests that broken supersymmetry is generic in supersymmetric field theory and in the landscape of string vacua.Comment: 48 pages, 1 figure, added discussion about the spectrum and some cosmological implication

Classical self-dual strings in d=6, (2,0) theory from afar

We show how one can get solitonic strings in a six-dimensional (2,0) supersymmetric theory by incorporating a nonlinear interaction term. We derive a zero force condition between parallel strings, and compute a metric on a moduli space which is $R^4$ when the strings are far apart. When compactifying the strings on a two-torus we show that, in the limit of vanishing two-torus, one regains the moduli space of two widely separated dyons of equal magnetic charges in four dimensions.Comment: 13 pages, clarifications and added reference

Loop space, (2,0) theory, and solitonic strings

We present an interacting action that lives in loop space, and we argue that this is a generalization of the theory for a free tensor multiplet. From this action we derive the Bogomolnyi equation corresponding to solitonic strings. Using the Hopf map, we find a correspondence between BPS strings and BPS monopoles in four-dimensional super Yang-Mills theory. This enable us to find explicit BPS saturated solitonic string solutions.Comment: 29 pages, v3: section 5 is rewritten and string solutions are found, v4: a new section on general covariance in loop spac