Chiral Lattice Gauge Theories Via Mirror-Fermion Decoupling: A Mission (im)Possible?

This is a review of the status and outstanding issues in attempts to construct chiral lattice gauge theories by decoupling the mirror fermions from a vectorlike theory. In the first half, we explain why studying nonperturbative chiral gauge dynamics may be of interest, enumerate the problems that a lattice formulation of chiral gauge theories must overcome, and briefly review our current knowledge. We then discuss the motivation and idea of mirror-fermion decoupling and illustrate the desired features of the decoupling dynamics by a simple solvable toy model. The role of exact chiral symmetries and matching of 't Hooft anomalies on the lattice is also explained. The second, more technical, half of the article is devoted to a discussion of the known and unknown features of mirror-decoupling dynamics formulated with Ginsparg-Wilson fermions. We end by pointing out possible directions for future studies.Comment: 53 pp; 6 figs; added table of contents, references, fixed typo

Continuity, Deconfinement, and (Super) Yang-Mills Theory

We study the phase diagram of SU(2) Yang-Mills theory with one adjoint Weyl fermion on R^3xS^1 as a function of the fermion mass m and the compactification scale L. This theory reduces to thermal pure gauge theory as m->infinity and to circle-compactified (non-thermal) supersymmetric gluodynamics in the limit m->0. In the m-L plane, there is a line of center symmetry changing phase transitions. In the limit m->infinity, this transition takes place at L_c=1/T_c, where T_c is the critical temperature of the deconfinement transition in pure Yang-Mills theory. We show that near m=0, the critical compactification scale L_c can be computed using semi-classical methods and that the transition is of second order. This suggests that the deconfining phase transition in pure Yang-Mills theory is continuously connected to a transition that can be studied at weak coupling. The center symmetry changing phase transition arises from the competition of perturbative contributions and monopole-instantons that destabilize the center, and topological molecules (neutral bions) that stabilize the center. The contribution of molecules can be computed using supersymmetry in the limit m=0, and via the Bogomolnyi--Zinn-Justin (BZJ) prescription in the non-supersymmetric gauge theory. Finally, we also give a detailed discussion of an issue that has not received proper attention in the context of N=1 theories---the non-cancellation of nonzero-mode determinants around supersymmetric BPS and KK monopole-instanton backgrounds on R^3xS^1. We explain why the non-cancellation is required for consistency with holomorphy and supersymmetry and perform an explicit calculation of the one-loop determinant ratio.Comment: A discussion of the non-cancellation of the nonzero mode determinants around supersymmetric monopole-instantons in N=1 SYM on R^3xS^1 is added, including an explicit calculation. The non-cancellation is, in fact, required by supersymmetry and holomorphy in order for the affine-Toda superpotential to be reproduced. References have also been adde

New Mechanisms of Dynamical Supersymmetry Breaking and Direct Gauge Mediation

We construct supersymmetric gauge theories with new mechanisms of dynamical supersymmetry breaking. The models have flat directions at the classical level, and different mechanisms lift these flat directions in different regions of the classical moduli space. In one branch of the moduli space, supersymmetry is broken by confinement in a novel manner. The models contain only dimensionless couplings and have large groups of unbroken global symmetries, making them potentially interesting for model-building. As an illustrative application, we couple the standard model gauge group to a model with an SU(5) global symmetry, resulting in a model with composite messengers and a non-minimal spectrum of superpartner masses.Comment: 18 pages, LaTeX2e, no figures. Minor corrections; version to be published in Phys. Rev.

Varieties of vacua in classical supersymmetric gauge theories

We give a simple description of the classical moduli space of vacua for supersymmetric gauge theories with or without a superpotential. The key ingredient in our analysis is the observation that the lagrangian is invariant under the action of the complexified gauge group \Gc. From this point of view the usual $D$-flatness conditions are an artifact of Wess--Zumino gauge. By using a gauge that preserves \Gc invariance we show that every constant matter field configuration that extremizes the superpotential is \Gc gauge-equivalent (in a sense that we make precise) to a unique classical vacuum. This result is used to prove that in the absence of a superpotential the classical moduli space is the algebraic variety described by the set of all holomorphic gauge-invariant polynomials. When a superpotential is present, we show that the classical moduli space is a variety defined by imposing additional relations on the holomorphic polynomials. Many of these points are already contained in the existing literature. The main contribution of the present work is that we give a careful and self-contained treatment of limit points and singularities.Comment: 14 pages, LaTeX (uses revtex.sty

Flavor in Supersymmetry with an Extended R-symmetry

We propose a new solution to the supersymmetric flavor problem without flavor-blind mediation. Our proposal is to enforce a continuous or a suitably large discrete R-symmetry on weak scale supersymmetry, so that Majorana gaugino masses, trilinear A-terms, and the mu-term are forbidden. We find that replacing the MSSM with an R-symmetric supersymmetric model allows order one flavor-violating soft masses, even for squarks of order a few hundred GeV. The minimal R-symmetric supersymmetric model contains Dirac gaugino masses and R-symmetric Higgsino masses with no left-right mixing in the squark or slepton sector. Dirac gaugino masses of order a few TeV with vanishing A-terms solve most flavor problems, while the R-symmetric Higgs sector becomes important at large tan(beta). epsilon_K can be accommodated if CP is preserved in the SUSY breaking sector, or if there is a moderate flavor degeneracy, which can arise naturally. epsilon'/epsilon, as well as neutron and electron EDMs are easily within experimental bounds. The most striking phenomenological distinction of this model is the order one flavor violation in the squark and slepton sector, while the Dirac gaugino masses tend to be significantly heavier than the corresponding squark and slepton masses.Comment: 15 pages, REVTEX4, 9 figure files, typos fixed, refs added, published versio

Next-to-Minimal Supersymmetric Standard Model with the Gauge Mediation of Supersymmetry Breaking

We study the Next-to-Minimal Supersymmetric Standard Model (NMSSM) as the simplest candidate solution to the $\mu$-problem in the context of the gauge mediation of supersymmetry breaking (GMSB). We first review various proposals to solve the $\mu$-problem in models with the GMSB. We find none of them entirely satisfactory and point out that many of the scenarios still lack quantitative studies, and motivate the NMSSM as the simplest possible solution. We then study the situation in the Minimal Supersymmetric Standard Model (MSSM) with the GMSB and find that an order 10% cancellation is necessary between the $\mu$-parameter and the soft SUSY-breaking parameters to correctly reproduce $M_Z$. Unfortunately, the NMSSM does not to give a phenomenologically viable solution to the $\mu$-problem. We present quantitative arguments which apply both for the low-energy and high-energy GMSB and prove that the NMSSM does not work for either case. Possible modifications to the NMSSM are then discussed. The NMSSM with additional vector-like quarks works phenomenologically, but requires an order a few percent cancellation among parameters. We point out that this cancellation has the same origin as the cancellation required in the MSSM.Comment: 36 pages, LaTeX, epsf.sty, 5 figures, references added, comments on some other papers based on our misundestanding corrected, none of our results change

Gauge/Anomaly Syzygy and Generalized Brane World Models of Supersymmetry Breaking

In theories in which SUSY is broken on a brane separated from the MSSM matter fields, supersymmetry breaking is naturally mediated in a variety of ways. Absent other light fields in the theory, gravity will mediate supersymmetry breaking through the conformal anomaly. If gauge fields propagate in the extra dimension they, too, can mediate supersymmetry breaking effects. The presence of gauge fields in the bulk motivates us to consider the effects of new messenger fields with holomorphic and non-holomorphic couplings to the supersymmetry breaking sector. These can lead to contributions to the soft masses of MSSM fields which dramatically alter the features of brane world scenarios of supersymmetry breaking. In particular, they can solve the negative slepton mass squared problem of anomaly mediation and change the predictions of gaugino mediation.Comment: 4 pages, RevTe