Crossover between Abelian and non-Abelian confinement in N=2 supersymmetric QCD

Journal Article · Fri May 15 04:00:00 EDT 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.79.105006· OSTI ID:21296369

Shifman, M ^[1]; Yung, A ^[1]

---

1. William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455 (United States)

In this paper we investigate the nature of the transition from Abelian to non-Abelian confinement (i.e. crossover vs phase transition). To this end we consider the basic N=2 model where non-Abelian flux tubes (strings) were first found: supersymmetric QCD with the U(N) gauge group and N{sub f}=N flavors of fundamental matter (quarks). The Fayet-Iliopoulos term {xi} triggers the squark condensation and leads to the formation of non-Abelian strings. There are two adjustable parameters in this model: {xi} and the quark mass difference {delta}m. We obtain the phase diagram on the ({xi},{delta}m) plane. At large {xi} and small {delta}m the world-sheet dynamics of the string orientational moduli is described by the N=2 two-dimensional CP(N-1) model. We show that as we reduce {xi} the theory exhibits a crossover to the Abelian (Seiberg-Witten) regime. Instead of N{sup 2} degrees of freedom of non-Abelian theory, now only N degrees of freedom survive in the low-energy spectrum. Dyons with certain quantum numbers condense, leading to the formation of the Abelian Z{sub N} strings whose fluxes are fixed inside the Cartan subalgebra of the gauge group. As we increase N this crossover grows exceedingly sharper, becoming a genuine phase transition at N={infinity}.

• OSTI ID: 21296369
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 10 Vol. 79; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CONFINEMENT
DEGREES OF FREEDOM
ENERGY SPECTRA
FLAVOR MODEL
MASS DIFFERENCE
MATTER
PHASE DIAGRAMS
PHASE TRANSFORMATIONS
QUANTUM CHROMODYNAMICS
QUANTUM NUMBERS
QUARKS
SUPERSYMMETRY
TWO-DIMENSIONAL CALCULATIONS