Myckola Schwetz

Exact results in softly broken supersymmetric models

Abstract We show how recent exact results in supersymmetric theories can be extended to models which include explicit soft supersymmetry breaking terms. We thus derive new exact results for non-supersymmetric models.

Exact results and soft breaking masses in supersymmetric gauge theory

Abstract We give an explicit formalism connecting softly broken supersymmetric gauge theories (with QCD as one limit) to N = 2 and N = 1 supersymmetric theories possessing exact solutions, using spurion fields to embed these models in an enlarged N = 1 model. The functional forms of effective lagrangian terms resulting from soft supersymmetry breaking are constrained by the symmetries of the enlarged model, although not well enough to fully determine the vacuum structure of generic softly broken models. Nevertheless, by perturbing the exact N = 1 model results with sufficiently small soft breaking masses, we show that there exist nonsupersymmetric models that exhibit monopole condensation and confinement in the same modes as the N = 1 case.

Controlled soft breaking of N = 1 SQCD

Abstract We discuss the introduction of soft breaking terms into the exact solutions of N = 1 SQCD using a spurion analysis. The spurion symmetries are not sufficient to determine the behavior of models in which squark or gaugino masses alone are introduced. However, a controlled approximation is obtained in some cases if a supersymmetric mass is first introduced for the matter fields. We present low-energy solutions for two models with perturbing soft breaking terms, one with a gaugino mass and one with squark mixing. These models have non-trivial theta angle dependence and exhibit phase transitions at non-zero theta angle analogous to those found in the chiral Lagrangian description of QCD.

Topological charge and U(1)A symmetry in the high temperature phase of QCD

Abstract We discuss the global symmetries of the high temperature phase of QCD with N f massless quarks. We show that the U ( N f ) × U ( N f ) symmetries are only violated by operators of dimension ≥ 3 N f . For N f > 2 this implies that the thermal two-point correlation functions of the η′ and π a s are identical. We discuss the implications of this for the chiral phase transition at finite temperature.

QCD at large θ-angle axion cosmology

We use the chiral Lagrangian to investigate the global properties of the N-flavor QCD vacuum as a function of the θ parameter. In the case of exact quark degeneracy we find evidence for first-order phase transitions at θ = π · (odd integer). The first-order transitions are smoothed by quark mass splittings, although interesting effects remain at realistic quark masses. We emphasize the role of the η′ condensate in our analysis. Finally, we discuss the implications of our results on the internal hadronic structure of axion domain walls and axion cosmology.

Chiral perturbation theory, large-Nc and the η′ mass

Abstract Using chiral perturbation theory and the large- N c expansion, we obtain expressions for the η′ mass and η - η′ mixing in terms of low-energy chiral Lagrangian parameters. This is accomplished through an intermediate step of “matching” the topological susceptibility in the large- N c and chiral Lagrangian descriptions. By inserting the values of well-measured parameters we obtain predictions involving the the second order parameters L 6 , L 7 and L 8 . The prediction for L 6 is quite restrictive even after allowing for 1 N c corrections.

A strongly first order electroweak phase transition from strong symmetry-breaking interactions.

We argue that a strongly first order electroweak phase transition is natural in the presence of strong symmetry-breaking interactions, such as technicolor. We demonstrate this using an effective linear scalar theory of the symmetry-breaking sector.

A note on supersymmetry breaking

Abstract Using a simple observation based on holomorphy, we argue that any model which spontaneously breaks supersymmetry for some range of a parameter will do so generically for all values of that parameter, modulo some isolated exceptional points. Conversely, a model which preserves supersymmetry for some range of a parameter will also do so everywhere except at isolated exceptional points. We discuss how these observations can be useful in the construction of new models which break supersymmetry and discuss some simple examples. We also comment on the relation of these results to the Witten index.

Exact results in softly broken SUSY theories

Soft SUSY breaking parameters may be introduced into SUSY theories through non-zero F-components of spurion fields. We discuss the resulting solutions of softly broken N =2 SQCD close in parameter space to the SUSY limit.