Non-Abelian Strong-Weak Coupling Duality in (String-Derived) N=4 Supersymmetric Yang-Mills Theories

Abstract

We study strong-weak coupling duality (S-duality) in N=4 supersymmetric non-Abelian Yang-Mills theories. These theories arise naturally as the low-energy limit of four-dimensional toroidal compactifications of the heterotic string. Firstly, we define the free energy in the presence of electric and magnetic fluxes using 't Hooft's prescription, i.e. through functional integrals at finite volume in the presence of twisted boundary conditions. Then, we compute those free energies in two limiting cases: small and large coupling constant. Finally, we extend the free-energies to all values of the coupling constant (and the theta angle) by presenting a fully S-duality invariant ansatz. This ansatz obeys all relevant consistency conditions; in particular, it obeys 't Hooft duality equations and Witten's magnetic-electric transmutation. The existence of an S-duality invariant, consistent definition of free energies supports the claim made in the literature that S-duality is a duality symmetry of N=4 SUSY Yang-Mills. Our ansatz also suggests that N=4, irrespective of whether partially broken or not, is in a self-dual phase: no phase transitions occur between the strong and weak coupling regimes.

11 pages (minor misprints corrected, new references added; latex file), NYU-TH-94/06/02, IFUM/472/FT, SISSA 80/94/EP, RI-6-94

References in corpus (8)

• Duality Symmetric Actions
• Duality Symmetries of 4D Heterotic Strings
• Electric Magnetic Duality in String Theory
• Quantization of Dyon Charge and Electric-Magnetic Duality in String Theory
• Magnetic Monopoles, Bogomol'nyi Bound and SL(2,Z) Invariance in String Theory
• String and Fivebrane Solitons: Singular or Non-singular?
• SL(2, Z) Duality and Magnetically Charged Strings
• Low-Energy Dynamics of Supersymmetric Solitons

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• Strong/Weak Coupling Duality from the Dual String
• Global Aspects of Electric-Magnetic Duality
• Dual Pairs of Type II String Compactification
• Reducing $S$- duality to $T$- duality
• Dyons and S-Duality in N=4 Supersymmetric Gauge Theory
• S-duality in N=4 supersymmetric gauge theories
• On S-duality for Non-Simply-Laced Gauge Groups
• Evidence for Non-perturbative String Symmetries
• S-Duality in N=4 Yang-Mills Theories with General Gauge Groups,
• On the Existence of States Saturating the Bogomol'nyi Bound in N=4 Supersymmetry
• The Donaldson-Witten Invariants in Pure QCD with Order and Disorder 't Hooft-like Operators
• Exact Electric-Magnetic Duality in N=2 Supersymmetric QCD Theories
• The dyon spectra of finite gauge theories
• Generalized Abelian S-duality and coset constructions
• Dualities in Five Dimensions and Charged String Solutions
• $S$-duality in Vafa-Witten theory for non-simply laced gauge groups
• Superselection, Boundary Algebras and Duality in Gauge Theories
• Super Yang-Mills Theory as a Random Matrix Model
• Duality and Supersymmetric Monopoles
• Massless monopole clouds and electric-magnetic duality
• Aspects of Space-Time Dualities