Nick J. Evans

Orientifolds, Branes, and Duality of 4D Gauge Theories

Recently, a D-brane construction in type IIA string theory was shown to yield the electric/magnetic duality of four-dimensional N = 1 supersymmetric U(Nc) gauge theories with Nf flavours of quark. We present here an extension of that construction which yields the electric/magnetic duality for the SO(Nc) and USp(Nc) gauge theories with Nf quarks, by adding an orientifold plane which is consistent with the supersymmetry. Due to the intersection of the orientifold plane with the NS-NS fivebranes already present, new features arise which are crucial in determining the correct final structure of the dualities.

An Effective field theory approach to color superconductivity at high quark density

Abstract We investigate the Fermi Liquid theory of high density QCD. Using the renormalization group (RG), we determine the behavior of effective fermion interactions near the Fermi surface. At sufficiently high densities the matching between the Fermi Liquid theory and QCD can be accomplished in perturbation theory and a reliable calculation of Cooper pair formation performed, modulo the existence of screening masses for the gluon. The presence of a chemical potential leads to different RG flows for sub-components of the effective interactions which would ordinarily be linked by Lorentz invariance. We also study instanton-induced operators and find that near the Fermi surface they are likely to be subdominant relative to operators induced by perturbative gluon exchange. We discuss the implications of our results for the phase structure of QCD at finite baryon density and temperature.

Non-perturbative couplings and color superconductivity

Abstract Quark matter at sufficiently high density exhibits color superconductivity, due to attractive gluonic interactions. At lower densities of order Λ QCD 3 , it has been proposed that instanton generated vertices may play an important role in the Cooper pair formation. We study the renormalization group flow to the Fermi surface of the full set of couplings generated by gluonic and instanton interactions. In earlier work we showed that if the gluonic interactions dominate at the matching scale, their running determines the scale of the Cooper pair formation Δ . Here we consider all possibilities, including the one in which the instanton interactions dominate all others at the matching scale. In the latter case we find that a number of additional induced couplings (including the gluonic ones) reach their Landau poles almost simultaneously with the instanton vertex. Presumably all contribute to the Cooper pair formation. The most important consequence of including all the couplings is a large increase in the gap size Δ .

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.

The field theory of non-supersymmetric brane configurations

Abstract 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 auxiliary 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.

Quark condensates in non-supersymmetric MQCD

Abstract A set of non-supersymmetric minimal area embeddings of an M-theory 5-brane are considered. The field theories on the surface of the 5-brane have the field content of N = 2 SQCD with fundamental representation matter fields. By suitable choice of curve parameters the N = 2 and N = 1 superpartners may be decoupled leaving a semi-classical approximation to QCD with massive quarks. As supersymmetry breaking is introduced a quark condensate grows breaking the low energy ZF flavour symmetry. At θ = (odd) π spontaneous CP violation is observed consistent with that of the QCD chiral lagrangian.

Duality in Non-Supersymmetric MQCD

The curves that describe the M-theoretic extension of type IIA string configurations with non-supersymmetric field theories on their surface exhibit a duality map. The map suggests a continued link between a SU(N) gauge theory with F flavours and an SU(F-N) gauge theory with F flavours (the duality of supersymmetric QCD) even when the gaugino mass is taken to infinity. Within the context of the field theory such a duality only continues to make sense if the scalar fields remain light. We discuss the difficulties of decoupling the scalars within this framework.

Duality in nonsupersymmetric M-theory QCD

The curves that describe the M-theoretic extension of type IIA string configurations with non-supersymmetric field theories on their surface exhibit a duality map. The map suggests a continued link between a SU(N) gauge theory with F flavours and an SU(F-N) gauge theory with F flavours (the duality of supersymmetric QCD) even when the gaugino mass is taken to infinity. Within the context of the field theory such a duality only continues to make sense if the scalar fields remain light. We discuss the difficulties of decoupling the scalars within this framework.

Softly broken SQCD: in the continuum, on the lattice, on the brane

Abstract We review progress in studying the solutions of SQCD in the presence of explicit, soft SUSY breaking terms. Massive N = 1 SQCD in the presece of a small gaugino mass leads to a controlled solution which has interesting phase structure with changing θ angle reminiscent of the QCD chiral Lagrangian. Current attempts to test the solutions of pure glue SQCD on the lattice require a theoretical understandinf of the theory with small gaugino mass in order to understand the approach to the SUSY point. We provide such a description making predictions for the gaugino condensate and lightest bound state masses. Finally we briefly review recent D-brane constructions of 4D gauge theories in string theory including a non-supersymmetric configuration. We identify this configuration with softly broken N = 2 SQCD.