Pseudoparticle solutions of the Yang-Mills equations

Belavin, A. A.; Polyakov, Alexander M.; Schwartz, Arthur S.; Tyupkin, Yu. S.

doi:10.1016/0370-2693(75)90163-x

Cited by 2,739 publications

(1,946 citation statements)

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“…2N f h is the number of fermion zero modes in the background of the Belavin-PolyakovSchwarz-Tyupkin (BPST) instanton [7] on R 4 . For the fermionic representations of interest 2h = {2, 2N + 4, 2N − 4, 2N} for R = {F, S, AS, BF}.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Multiflavor QCD∗ on R3×S1: Studying transition from Abelian to non-Abelian confinement

Shifman

Ünsal

2009

Physics Letters B

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The center-stabilized multiflavor QCD* theories formulated on R 3 × S 1 exhibit both Abelian and non-Abelian confinement as a function of the S 1 radius, similar to the Seiberg-Witten theory as a function of the mass deformation parameter. For sufficiently small number of flavors and small r(S 1 ), we show occurence of a mass gap in gauge fluctuations, and linear confinement. This is a regime of confinement without continuous chiral symmetry breaking (χSB). Unlike one-flavor theories where there is no phase transition in r(S 1 ), the multiflavor theories possess a single phase transition associated with breaking of the continuous χS. We conjecture that the scale of the χSB is parametrically tied up with the scale of Abelian to non-Abelian confinement transition.

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Section: Theoretical Frameworkmentioning

confidence: 99%

Multiflavor QCD∗ on R3×S1: Studying transition from Abelian to non-Abelian confinement

Shifman

Ünsal

2009

Physics Letters B

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“…To study instanton-related physics it is of fundamental importance to determine the oneloop tunnelling amplitude given by the Euclidean one-loop effective action in the background of a single (anti-)instanton [7]. 't Hooft [5] succeeded in calculating the corresponding contribution by massless scalar or quark fields exactly in the 1970s, but such an exact calculation is no longer possible if the fields have non-zero mass.…”

Section: Introductionmentioning

confidence: 99%

Instanton determinant with arbitrary quark mass: WKB phase-shift method and derivative expansion

2004

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The fermion determinant in an instanton background for a quark field of arbitrary mass is studied using the Schwinger proper-time representation with WKB scattering phase shifts for the relevant partial-wave differential operators. Previously, results have been obtained only for the extreme small and large quark mass limits, not for intermediate interpolating mass values. We show that consistent renormalization and large-mass asymptotics requires up to third-order in the WKB approximation. This procedure leads to an almost analytic answer, requiring only modest numerical approximation, and yields excellent agreement with the well-known extreme small and large mass limits. We estimate that it differs from the exact answer by no more than 6% for generic mass values. In the philosophy of the derivative expansion the same amplitude is then studied using a Heisenberg-Euler-type effective action, and the leading order approximation gives a surprisingly accurate answer for all masses.

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“…holds and as a result the curvature strength decays as the inverse power of r 4 , corresponding to an asymptotically pure gauge connection like the BPST [11] instanton. The problem here is that the finite action condition for the Higgs terms in (22) results in an asymptotic connection field that decays as one half times a pure gauge, which is inconsistent with the finite action requirement on the YM terms, namely that the connection be asymptotically pure gauge.…”

Section: Summary and Discussionmentioning

confidence: 99%