1. INSTANTON AND ITS APPLICATION Nam, Seung-il Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Japan YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007

2. 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: H|0  0 It also effects on QCD phase structure, represented by  qq ,  qq ,… Investigations on the vacuum itself: meron, dyon, vortex, instaton etc.. YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007

3. Instanton Named by t’Hooft (cf:Euclidean 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 YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007

4. 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 YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007

5. 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?) YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007

6. 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 U 5 YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007

7. Pion EM form factor at finite density VMD parameterization  -meson mass shift YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007

8. 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? YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007

9. Thank you very much for your attention and A bonus shot just for fun! YITP, Kyoto University YITP Lunch Seminar 19 Dec 2007