INSTANTON

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• INSTANTON
• AND
• ITS APPLICATION
• Nam, Seung-il
• Yukawa Institute for Theoretical Physics (YITP),
  Kyoto University, Japan

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Introduction Strongly interacting particles
governed by QCD Difficulties in QCD in low
energy region Developing models guided in terms
of symmetries A powerful guidance Spontaneous
Breakdown of Chiral Symmetry SBCS ?
Nambu-Goldstone (NG) bosons (pion) Chiral bag,
NJL, Skyrmion, HLS etc But what is the origin
of this interesting phenomena? Highly nontrivial
QCD vacuum H0??0 It also effects on QCD phase
structure, represented by ?qq?,
?qq?, Investigations on the vacuum itself
meron, dyon, vortex, instaton etc..
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Instanton Named by tHooft (cfEuclidean Gauge
Soliton) Classical ground state solution of the
QCD in Euclidean space Analogy QED ? electron
phonon vs. QCD ? quark instanton Minimizing
the QCD YM action Self-dual condition (Singular
gauge) instanton solution Nonperturbative part
of gluons replaced by instantons (Anti)quarks
moving around this effective potential-like
ensemble
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Instanton Quark propagator in the instanton
effects Momentum-dependent quark
mass Playing a role of a intrinsic UV
regularator Non-zero chiral condensate (?qq?) ?
natural interpretation of SBCS
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• Instanton
• Advantageous features of this approach
• ? Preserving all relevant QCD symmetries
• ? U(1)A included via nonzero topological
  susceptibility
• ? Natural scale parameter average instanton size
  inter-distance
• ? No adjustable free parameters (at least for
  light quarks in leading Nc)
• ? Natural UV regulator M(k)
• ? Highgly nonlocal interaction between quarks
• ? Natural derivations of (almost) NJL and Skyrme
  mode
• No confinement (a PNJL-like approach possible?)

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Applications For baryonic sector Chiral Quark
Soliton Model For mesonic sector Nonlocal Chiral
Quark Model Quark Instanton ? Quark NG boson
by bosonization Effective chiral action at finite
density Nonlocal pseudoscalar meson background
field For mesonic sector, we pick up meson
fields directly by expanding U5
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Pion EM form factor at finite density VMD
parameterization
?-meson mass shift
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Summary and outlook Nontrivial QCD vacuum
configuration instanton Beautiful
interpretations on nonperturbative hadronic
properties Widely applied to various
problems Next steps ? extension to baryonic
sector ? extension to finite temperature ? A
possible relation with the hQCD? ? and 5th
z-direction ? Confinement in the instanton
model? eff. thermodynamic potential? ? Complex
constituent quark mass bounded at time-like
region?
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Thank you very much for your attention and A
bonus shot just for fun!