Some Explorations in Holomorphy

In supersymmetric theories, one can obtain striking results and insights by exploiting the fact that the superpotential and the gauge coupling function are holomorphic functions of the model parameters. The precise meaning of this holomorphy is subtle, and has been explained most clearly by Shifman and Vainshtein, who have stressed the role of the Wilsonian effective action. In this note, we elaborate on the Shifman-Vainshtein program, applying it to examples in grand unification, supersymmetric QCD and string theory. We stress that among the ``model parameters" are the cutoffs used to define the Wilsonian action itself, and that generically these must be defined in a field-dependent manner to obtain holomorphic results.Comment: (26 pages and 2 figures as one uuencoded PostScript file) SCIPP 94/11. Important references added; typos correcte

Visible Effects of the Hidden Sector

The renormalization of operators responsible for soft supersymmetry breaking is usually calculated by starting at some high scale and including only visible sector interactions in the evolution equations, while ignoring hidden sector interactions. Here we explain why this is correct only for the most trivial structures in the hidden sector, and discuss possible implications. This investigation was prompted by the idea of conformal sequestering. In that framework hidden sector renormalizations by nearly conformal dynamics are critical. In the original models of conformal sequestering it was necessary to impose hidden sector flavor symmetries to achieve the sequestered form. We present models which can evade this requirement and lead to no-scale or anomaly mediated boundary conditions; but the necessary structures do not seem generic. More generally, the ratios of scalar masses to gaugino masses, the $\mu$-term, the $B\mu$-term, $A$-terms, and the gravitino mass can be significantly affected.Comment: 23 pages, no figure

Brane Junctions in the Randall-Sundrum Scenario

We present static solutions to Einstein's equations corresponding to branes at various angles intersecting in a single 3-brane. Such configurations may be useful for building models with localized gravity via the Randall-Sundrum mechanism. We find that such solutions may exist only if the mechanical forces acting on the junction exactly cancel. In addition to this constraint there are further conditions that the parameters of the theory have to satisfy. We find that at least one of these involves only the brane tensions and cosmological constants, and thus can not have a dynamical origin. We present these conditions in detail for two simple examples. We discuss the nature of the cosmological constant problem in the framework of these scenarios, and outline the desired features of the brane configurations which may bring us closer towards the resolution of the cosmological constant problem.Comment: 15 pages, LaTeX. 4 postscript figures included. Typo corrected and reference adde

The GUT Scale and Superpartner Masses from Anomaly Mediated Supersymmetry Breaking

We consider models of anomaly-mediated supersymmetry breaking (AMSB) in which the grand unification (GUT) scale is determined by the vacuum expectation value of a chiral superfield. If the anomaly-mediated contributions to the potential are balanced by gravitational-strength interactions, we find a model-independent prediction for the GUT scale of order $M_{\rm Planck} / (16\pi^2)$. The GUT threshold also affects superpartner masses, and can easily give rise to realistic predictions if the GUT gauge group is asymptotically free. We give an explicit example of a model with these features, in which the doublet-triplet splitting problem is solved. The resulting superpartner spectrum is very different from that of previously considered AMSB models, with gaugino masses typically unifying at the GUT scale.Comment: 17 page

Dynamical Supersymmetry Breaking

Supersymmetry is one of the most plausible and theoretically motivated frameworks for extending the Standard Model. However, any supersymmetry in Nature must be a broken symmetry. Dynamical supersymmetry breaking (DSB) is an attractive idea for incorporating supersymmetry into a successful description of Nature. The study of DSB has recently enjoyed dramatic progress, fueled by advances in our understanding of the dynamics of supersymmetric field theories. These advances have allowed for direct analysis of DSB in strongly coupled theories, and for the discovery of new DSB theories, some of which contradict early criteria for DSB. We review these criteria, emphasizing recently discovered exceptions. We also describe, through many examples, various techniques for directly establishing DSB by studying the infrared theory, including both older techniques in regions of weak coupling, and new techniques in regions of strong coupling. Finally, we present a list of representative DSB models, their main properties, and the relations between them.Comment: 113 pages, Revtex. Minor changes, references added and corrected. To appear in Reviews of Modern Physic

Duality between simple-group gauge theories and some applications

In this paper we investigate N=1 supersymmetric gauge theories with a product gauge group. By using smoothly confining dynamics, we can find new dualities which include higher-rank tensor fields, and in which the dual gauge group is simple, not a product. Some of them are dualities between chiral and non-chiral gauge theories. We also discuss some applications to dynamical supersymmetry breaking phenomena and new confining theories with a tree-level superpotential.Comment: 33 pages, LaTeX, references added, version to appear in PR

A Supersymmetric Composite Model with Dynamical Supersymmetry Breaking

We present a supersymmetric composite model with dynamical supersymmetry breaking. The model is based on the gauge group $SU(2)_S \times SU(2)_H \times SU(3)_c \times SU(2)_L \times U(1)_Y$. Supersymmetry is dynamically broken by the non-perturbative effect of the $SU(2)_S$ `supercolor' interaction. The large top Yukawa coupling is naturally generated by the $SU(2)_H$ `hypercolor' interaction as recently proposed by Nelson and Strassler. The supersymmetry breaking is mediated to the standard model sector by a new mechanism. The electroweak symmetry breaking is caused by the radiative correction due to the large top Yukawa coupling with the supersymmetry breaking. This is the `radiative breaking scenario', which originates from the dynamics of the supercolor and hypercolor gauge interactions.Comment: 30 pages, uses REVTEX macro, revised manuscript to appear in Phys. Rev.

Lectures on Supersymmetry Breaking

We review the subject of spontaneous supersymmetry breaking. First we consider supersymmetry breaking in a semiclassical theory. We illustrate it with several examples, demonstrating different phenomena, including metastable supersymmetry breaking. Then we give a brief review of the dynamics of supersymmetric gauge theories. Finally, we use this dynamics to present various mechanisms for dynamical supersymmetry breaking. These notes are based on lectures given by the authors in 2007, at various schools.Comment: 47 pages. v2: minor correction

A One-Scale Model of Dynamical Supersymmetry Breaking

A model of gauge-mediated supersymmetry breaking is constructed in which the low-energy physics depends on a single dynamical scale. Strong coupling dynamics of gauge theories plays an important role, in particular through its effects on beta functions and through confinement. The model does not have distinct messenger and supersymmetry-breaking sectors. The scale of supersymmetry breaking is of order 10-100 \TeV, implying that the decay of the next-to-lightest superpartner into the gravitino is prompt. Superoblique corrections are enhanced. A Dirac fermion and one complex scalar, in a 10 or \bar{10} of (global) SU(5), are predicted to be relatively light and to satisfy certain mass relations with the standard model squarks and sleptons.Comment: 28 pages, uses revtex, h-physrev.bs

Constraints on Astro-unparticle Physics from SN 1987A

SN 1987A observations have been used to place constraints on the interactions between standard model particles and unparticles. In this study we calculate the energy loss from the supernovae core through scalar, pseudo scalar, vector, pseudo vector unparticle emission from nuclear bremsstrahlung for degenerate nuclear matter interacting through one pion exchange. In order to examine the constraints on $d_{\cal U}=1$ we considered the emission of scalar, pseudo scalar, vector, pseudo vector and tensor through the pair annihilation process $e^+e^-\to {\cal U} \gamma$. In addition we have re-examined other pair annihilation processes. The most stringent bounds on the dimensionless coupling constants for $d_{\cal U} =1$ and $\Lambda_{\cal U}= m_Z$ are obtained from nuclear bremsstrahlung process for the pseudo scalar and pseudo-vector couplings $\bigl|\lambda^{\cal P}_{0,1}\bigr|\leq 4\times 10^{-11}$ and for tensor interaction, the best limit on dimensionless coupling is obtained from $e^+ e^-\to {\cal U} \gamma$ and we get $\bigl|\lambda^{\cal T}\bigr| \leq 6\times 10^{-6}$.Comment: 12 pages, 2 postscript figure