Stationary points of the Yang‐Mills action

Sadun, Lorenzo; Segert, Jan

doi:10.1002/cpa.3160450405

Cited by 12 publications

(12 citation statements)

References 21 publications

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“…4 and 6.7 for x > 0 andu(x) − 2mx → 0 as x → −∞. Moreover, for x < 0, u(x) − 2mx < 0 and u ′ (x) − 2m < 0,and for x near −∞ we have the asymptotic estimates0 > u(x) − 2mx ≥ −C(ε)e min{ √ Λ,2m}(1−ε)x , (6.41) 0 > u ′ (x) − 2m ≥ −C(ε)e min{ √ Λ,2m}(1−ε)x ,(6 42). …”

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confidence: 98%

Domain wall equations, Hessian of superpotential, and Bogomol'nyi bounds

Chen

Yang

2016

Nuclear Physics B

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An important question concerning the classical solutions of the equations of motion arising in quantum field theories at the BPS critical coupling is whether all finiteenergy solutions are necessarily BPS. In this paper we present a study of this basic question in the context of the domain wall equations whose potential is induced from a superpotential so that the ground states are the critical points of the superpotential. We prove that the definiteness of the Hessian of the superpotential suffices to ensure that all finite-energy domain-wall solutions are BPS. We give several examples to show that such a BPS property may fail such that non-BPS solutions exist when the Hessian of the superpotential is indefinite. *

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confidence: 98%

Domain wall equations, Hessian of superpotential, and Bogomol'nyi bounds

Chen

Yang

2016

Nuclear Physics B

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“…To minimize S YM numerically, we use a finite mode approximation [23]. We write f 3 and f as polynomials in t obeying the symmetry and boundary conditions,…”

Section: Numerical Resultsmentioning

confidence: 99%

“…We need only minimize S YM on this class of invariant connections, which is quite easy to do numerically. There is a fairly extensive literature on minimizing S Y M over connections with specific prescribed symmetries [13,14,[18][19][20][21][22][23][24][25][26][27], but seemingly not the U (2) × Z 2 2 symmetry of interest here. The closest seems to be [25], which studies U (2) invariant connections on non-round S 4 and finds a solution of the Yang-Mills equation which degenerates, in the round limit, to a zero-size instanton/anti-instanton pair.…”

Section: Rationalementioning

confidence: 99%

A loop of SU(2) gauge fields stable under the Yang-Mills flow

Friedan

2010

Surveys in Differential Geometry

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Abstract. The gradient flow of the Yang-Mills action acts pointwise on closed loops of gauge fields. We construct a topologically nontrivial loop of SU (2) gauge fields on S 4 that is locally stable under the flow. The stable loop is written explicitly as a path between two gauge fields equivalent under a topologically nontrivial SU (2) gauge transformation. Local stability is demonstrated by calculating the flow equations to leading order in perturbations of the loop. The stable loop might play a role in physics as a classical winding mode of the lambda model, a 2-d quantum field theory that was proposed as a mechanism for generating spacetime quantum field theory. We also present evidence for 2-manifolds of SU (3) and SU (2) gauge fields that are stable under the Yang-Mills flow. These might provide 2-d instanton corrections in the lambda model.For Isidore M. Singer in celebration of his eighty-fifth birthday.

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“…La existencia de soluciones no autoduales con acción finita ha sido obtenida para diferentes números de enrrollamiento [9,10]. Esto implica que el vacío de Yang-Mills consiste de diferentes sectores con carga topológica relacionados entre sí, por tunelaje instantónico [7,11].…”

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