Koebe 1/4 theorem and inequalities in {ital N}=2 supersymmetric QCD

Journal Article · Sat Jun 01 04:00:00 EDT 1996 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.53.7354· OSTI ID:284842

Matone, M ^[1]

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1. Department of Physics ``G. Galilei``-Istituto Nazionale di Fisica Nucleare, University of Padova, Via Marzolo, 8-35131 Padova (Italy)

The critical curve C on which Im{cflx {tau}}=0, {cflx {tau}}={ital a}{sub {ital D}}/{ital a}, determines hyperbolic domains whose Poincar{acute e} metric can be constructed in terms of {ital a}{sub {ital D}} and {ital a}. We describe C in a parametric form related to a Schwarzian equation and prove new relations for {ital N}=2 supersymmetric SU(2) Yang-Mills theory. In particular, using the Koebe 1/4 theorem and Schwarz{close_quote}s lemma, we obtain inequalities involving {ital u}, {ital a}{sub {ital D}}, and {ital a}, which seem related to the renormalization group. Furthermore, we obtain a closed form for the prepotential as a function of {ital a}. Finally, we show that {partial_derivative}{sub {cflx {tau}}}{l_angle}tr{phi}{sup 2}{r_angle}{sub {cflx {tau}}}=1/8{pi}{ital ib}{sub 1}{l_angle}{phi}{r_angle}{sub {cflx {tau}}}{sup 2}, where {ital b}{sub 1} is the one-loop coefficient of the beta function. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 284842
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 12 Vol. 53; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
QUANTUM CHROMODYNAMICS
RENORMALIZATION
SCHWARZSCHILD METRIC
SU-2 GROUPS
SUPERSYMMETRY
YANG-MILLS THEORY