Abstract
We consider 5d Yang–Mills–Higgs theory with a compact ADE-type gauge group G and one adjoint scalar field on R3,1×R+, where R+=[0,∞) is the half-line. The maximally supersymmetric extension of this model, with five adjoint scalars, appears after a reduction of 6d N=(2,0) superconformal field theory on R3,1×R+×S1 along the circle S1. We show that in the low-energy limit, when momenta along R3,1 are much smaller than along R+, the 5d Yang–Mills–Higgs theory reduces to a nonlinear sigma model on R3,1 with a coset G/H as its target space. Here H is a closed subgroup of G determined by the Higgs-field asymptotics at infinity. The 4d sigma model describes an infinite tower of interacting fields, and in the infrared it is dominated by the standard two-derivative kinetic term and the four-derivative Skyrme–Faddeev term.
Highlights
Introduction and summaryQuantum chromodynamics (QCD) as well as Yang–Mills theory are strongly coupled in the infrared limit, and the perturbative expansion for them breaks down
We show that in the low-energy limit, when momenta along R3,1 are much smaller than along R+, the 5d Yang–Mills–Higgs theory reduces to a nonlinear sigma model on R3,1 with a coset G/H as its target space
In the absence of a quantitative understanding of non-perturbative QCD, convenient alternatives at low energy are provided by effective models among which nonlinear sigma models play an important role
Summary
Quantum chromodynamics (QCD) as well as Yang–Mills theory are strongly coupled in the infrared limit, and the perturbative expansion for them breaks down. A classical problem of the standard Skyrme model was its difficulty to incorporate other mesons besides pions This shortcoming was overcome recently with an extended 4d Skyrme model obtained from 5d Yang–Mills theory derived from D-brane configurations in string theory and the holographic approach [16] [17,18,19] for reviews and references) This extended Skyrme model can be reached from 6d N = (2, 0) superconformal field theory compactified on a circle to 5d super-Yang–Mills (SYM) theory on R3,1 × I, where I = [−R, R] is a finite-length interval [20], upon forgetting the five adjoint scalar fields. We show that, like the extended Skyrme model, an extended 4d Skyrme–Faddeev model can emerge in a low-energy limit of 5d SYM theory with Dirichlet boundary conditions [21, 22]. We demonstrate that the Skyrme model and the Skyrme–Faddeev model as well as their extended versions emerge from the M5-brane system of M-theory
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