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Precise Quark-Mass Dependence of the Instanton Determinant
Dunne, Gerald V.,Hur, Jin,Lee, Choonkyu,Min, Hyunsoo American Physical Society 2005 Physical review letters Vol.94 No.7
<P>The fermion determinant in an instanton background for a quark field of arbitrary mass is determined exactly using an efficient numerical method to evaluate the determinant of a partial-wave radial differential operator. The bare sum over partial waves is divergent but can be renormalized in the minimal subtraction scheme using the result of WKB analysis of the large partial-wave contribution. Previously, only a few leading terms in the extreme small and large mass limits were known for the corresponding effective action. Our approach works for any quark-mass and interpolates smoothly between the analytically known small and large mass expansions.</P>
Instanton determinant with arbitrary quark mass: WKB phase-shift method and derivative expansion
Dunne, Gerald V.,Hur, Jin,Lee, Choonkyu,Min, Hyunsoo Elsevier 2004 Physics letters: B Vol.600 No.3
<P><B>Abstract</B></P><P>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.</P>
Higgs structures of dyonic instantons
Choi, Min-Young,Kim, Kyung Kiu,Lee, Choonkyu,Lee, Ki-Myeong IOP Publishing Ltd 2008 Journal of high energy physics Vol.2008 No.4
We study Higgs field configurations of dyonic instantons in spontaneously broken (4 + 1)-dimensional Yang-Mills theory. The adjoint scalar field solutions to the covariant Laplace equation in the ADHM instanton background are constructed in general noncanonical basis, and they are used to study explicitly the Higgs field configurations of dyonic instantons when the gauge fields are taken by Jackiw-Nohl-Rebbi instanton solutions. For these solutions corresponding to small instanton number we then consider in some detail the zero locus of the Higgs field, which describes the cross section of supertubes connecting parallel D4-branes in string theory. Also the information on the Higgs zeroes is used to discuss the residual gauge freedom concerning the Jackiw-Nohl-Rebbi solutions.