On the QCD Phase Transition at Finite Baryon Density

We investigate the QCD chiral phase transition at finite chemical potential $\mu$, using the renormalization group (RG) to characterize the infrared behavior of sigma models constrained by the flavor and spacetime symmetries. The results are similar to those obtained from RG analysis of the finite temperature transition at zero baryon density. When there are more than two massless flavors of quarks, a first order transition is predicted for the entire phase boundary. In the two flavor case, a boundary with first and second order regions separated by a tricritical point seems most likely. We discuss the real-world case with two light quarks and an intermediate mass strange quark. Improved lattice data on the temperature transition will strongly constrain the possibilities for the phase boundary.Comment: 10 pages, 2 figures, Latex. Added discussion on realistic strange quark mass and recent lattice dat

Magnetic Interactions, the Renormalization Group and Color Superconductivity in High Density QCD

We investigate the effect of long range magnetic interactions on the renormalization group (RG) evolution of local Cooper pairing interactions near the Fermi surface in high density QCD. We use an explicit cut-off on momentum modes, with special emphasis on screening effects such as Landau damping, to derive the RG equations in a gauge invariant, weak coupling expansion. We obtain the Landau pole $\Delta \sim \mu g^{-5} \exp(- \frac{3 \pi^2}{\sqrt{2} g})$, although the structure of our equations differs from previous results. We also investigate the gap equation, including condensates of higher angular momentum. We show that rotational invariance is unbroken at asymptotically high density, and verify that $\Delta$ is the correct value of the gap when higher modes are included in the analysis.Comment: 17 pages, 3 figures, late

A Note on Supersymmetry Breaking

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.Comment: 10 pages, LaTeX. Additional reference added, minor change to last subsectio

Controlled Soft Breaking of N=1 SQCD

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.Comment: 10 pages, Latex, one eps figur

Phase Transitions in Softly Broken N=2 SQCD at Non-zero Theta Angle

We investigate the behavior of softly broken $N=2$ SQCD at non-zero bare theta angle $\theta_0$, using superfield spurions to implement the SUSY breaking. We find a first-order phase transition as $\theta_0$ is varied from zero to $2 \pi$, in agreement with a prediction of `t Hooft. The low-energy theta angle $\theta_{eff}$, which determines the effective charges of dyonic excitations, has a complicated dependence on $\theta_0$ and breaking parameters.Comment: 18 pages, LaTeX, 10 epsf figure

Exact Results And Soft Breaking Masses In Supersymmetric Gauge Theory

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.Comment: Final version to appear in Nucl. Phys. B; LaTex, 19 pgs, no figures. Corrected references and some formulae, with no effect on conclusion

Chiral Perturbation Theory, Large-N_c and the eta' Mass

Using chiral perturbation theory and the large-$N_c$ expansion, we obtain expressions for the $\eta'$ mass and $\eta - \eta'$ 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.Comment: 11 pages, Latex, 3 figures using eps

The Field Theory of Non-Supersymmetric Brane Configurations

We identify the 4D field theories living on the world volume of D4 branes in non-supersymmetric type IIA string theory constructions. They are softly broken N=2 SQCD with the breakings introduced through vevs of the auxilliary fields in the spurion coupling field. Exact solutions of these theories for perturbing soft breakings exist in the literature. We calculate the ratios of string tensions in softly broken N=2 SU(N) gauge theory testing the recently proposed M-theory prediction. The semi-classical result of M-theory is renormalized in the non-supersymmetric models.Comment: 15 pages, Latex, clarified discussion and updated reference

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.Comment: LaTex, 15 pages, 3 figures in EPS format. Phys. Rev. D approved Typographically Correct version, minor grammatical change