1. T OPOLOGY CHANGE AND HADRON PROPERTIES IN COLD DENSE MATTER WCU-Hanyang Project Work in progress with Hyun Kyu Lee and Byung-Yoon Park

2. (February 2010)Ed. G.E. Brown & MR

4. Monte Carlo simulation Observation “Chiral magnetic spirals”

5. A RE THERE SUCH “ GEMS ” IN HADRONIC PHYSICS WITH THE SKYRMIONS ORIGINALLY DISCOVERED FOR BARYONS ?

6. L ESSONS FROM CONDENSED MATTER : “E MERGING ”( HIDDEN ) GAUGE SYMMETRY (HLS) L ESSONS FROM CONDENSED MATTER : “E MERGING ”( HIDDEN ) GAUGE SYMMETRY (HLS) Neel magnet Broken spin-rotation symmetry Valence bond solid (VBS) paramagnet Broken lattice-rotation symmetry Senthil et al, Science 303, 1490 (2004) Sigma model (skyrmion) HLS (½-skyrmion)

7. P OWER OF EFFECTIVE FIELD THEORY Both A (Neel magnet) and B (VBS) are captured by the Nonlinear  model + Berry phase. “Spinon” =order parameter in A ≠ order parameter in B While the  model describes A and B, the Berry phase plays no role in A but is crucial in B in giving the VBS order, so the phase transition does not involve the same order parameter. “Ginzburg-Landau-Wilson paradigm does not apply here.”

8. E MERGENT LOCAL SYMMETRY OR HLS Interplay of the emergent gauge field and the Berry phase leads to HLS theory between the A phase and the B phase Skyrmions replaced by 1/2-skyrmions Skyrmion number ~ CP 1

9. S. Sachdev State of ½-skyrmions (or merons)

10. Manifestation Manifestation in nuclear physics in nuclear physics Nuclear tensor forces and Nuclear tensor forces and (a)symmetry energy E sym in (a)symmetry energy E sym in compressed baryonic matter compressed baryonic matter Analogy (?) to “deconfined Quantum critical phenomenon”

11. S YMMETRY ENERGY E SYM S YMMETRY ENERGY E SYM

12. E SYM AT HIGH DENSITY IS A WILDERNESS

13. A ND AT HIGHER DENSITY

14. N ATURE : E SYM AT N ATURE : E SYM AT E SS Fit to FOPI/GSI data for      ratio → “supersoft” (E SS ) E ss A: “supersoft” E ss B: all others Xiao et al, PRL 102 (09) 062502 n > n 0 ?

15. 400 MeV/A Transport model analysis using IBUU04 Z. Xiao, B.A. Li, L.W. Chen, G.C. Yong and M. Zhang, PRL 102, 062502 (2009) Au+Au

16. “E SS ” COULD BE A DISASTER !!?? “E SS ” COULD BE A DISASTER !!?? There could be NO stable neutron stars unless …!! But Nature is full of neutron stars including the Hulse-Taylor binary pulsar. E SS If Nature chose the “supersoft” E SS

18. A VOIDING THE DISASTER A VOIDING THE DISASTER There could be NO stable neutron stars unless …!! But Nature is full of neutron stars including the Hulse-Taylor binary pulsar. Drastic wayout by D.H. Wen et al, PRL 103, 211102 (09): Modify Newtonian gravity. Why not? It could be emergent (E. Verlinde, arXiv:1001.0785). If Nature chose the “supersoft” E SS

19. “G RAVITY DOESN ’ T EXIST ” “G RAVITY DOESN ’ T EXIST ” The New York Times July 12, 2010

20. A VOIDING THE DISASTER A VOIDING THE DISASTER There could be NO stable neutron stars unless …!! But Nature is full of neutron stars including the Hulse-Taylor binary pulsar. Drastic wayout by D.H. Wen et al, PRL 103, 211102 (09): Modify Newtonian gravity. Why not? It could be emergent (E. Verlinde, arXiv:1001.0785). But kaons will not condense, and make Bethe and Brown very unhappy If Nature chose the “supersoft” E SS

21. H OW TO CONCOCT THE E SS H OW TO CONCOCT THE E SS Possible mechanism: medium-scaling tensor forces  Tensor forces cancel: Exploit medium-enhanced cancelation to describe the C14 dating by J.W. Holt et al, PRL 100, 062501 (08) Assumed scaling: C. Xu & B.A. Li, arXiv:0910.4803

22. C14 DATING “ EXPLAINED ” J.W. Holt et al, PRL 100, 062501 (08)

23. A PPLY TO E SYM E sym n  i (n)=   (n/n 0 )    =0    mm   <  1 <  2 <  3 …<  m ≈ 0.2 n0n0 C. Xu & B.A. Li, arXiv:0910.4803 for all density (n)

24. B UT HALF - SKYRMION ( OR DYONIC *) PHASE ENTERS B UT HALF - SKYRMION ( OR DYONIC *) PHASE ENTERS Described in terms of skyrmions, baryonic matter has a “phase transition” at n deconf > n  n 1/2 > n 0 from a skyrmion matter to a ½-skyrmion matter *Sin, Zahed, R Ismail’s talk Drastic change

25. H LS IN DENSE MATTER H LS IN DENSE MATTER Mimic generic features of the Neel-VBS (though with different physics): Nonlinear sigma model: NL  Hidden gauge invariance: Promote to gauge theory with nonabelian gauge field     Harada/Yamawaki HLS theory: HLS NL  model is “gauge-equivalent” to HLS

26. I N NATURE  L,R decouple: L,R symmetries “restored” and  L,R and    are the relevant degrees of freedom as in the Neel-VBS transition (a)N c →  → a ≈ 1 & g ~ 0 : light-quark vector mesons tend to “vector limit” (HG) or “vector manifestation” (Harada-Yamawaki) (b) V(ector)D(ominance) is violated in medium (density & temperature) H. Georgi, 1990

27. G EORGI ’ S “ VECTOR MODE ” H. Georgi, 1990 At large N c,  (1-a) → 0, g ~ 0 Vector mesons (e.g.,  ) are light ~ 1/N c, become degenerate with   in the vector (or VM) limit. Cf: Weinberg’s “mended symmetry.” Baryons as matter field are massive ~ N c figuring in terms of two kinds of skyrmions Supports A variety of light-quark phenomena, e.g.   mass difference Heavy-light-quark phenomena, e.g., chiral doubler Nucleon form factor Etc etc.

28. VD VIOLATION IN NUCLEON FORM FACTOR Iachello, Jackson & Lande, 1973 Brown, Weise, R., 1986 Bijker & Iachello, 2004 + (1-z/2) z Cf: VD → z=2 Phenomenology: z ≈ 1 HLS: z =  

29. HLS 4 D “Core” & Cheshire Cat Holography I. Zahed “a” goes to 1: Vector dominance a la Sakurai violated in medium!!! V =  ’,  ”, …   HLS 5D

30. A PPEARANCE OF FRACTIONIZED SKYRMIONS skyrmion half-skyrmion Simulate dense matter by putting skyrmions in FCC crystals and squeeze them: ½-skyrmions in CC appear at n 1/2 B.Y. Park et al,1999 skyrmions Half-skyrmions

31. A LSO IN H QCD : “ DYONIC SALT ” A LSO IN H QCD : “ DYONIC SALT ” Increasing density Instantons: FCC ½ instantons (dyons): BCC Sin, Zahed, R., Phys. Lett. B689, 23 (2010) Dyons are bound by ~ 180 MeV.

32. “P HASE ” STRUCTURE Sigma model HLS model The ½-skyrmion phase at n  n 1/2 is characterized by Rough estimate: n 1/2 ~ (1.3 – 2) n 0 n 1/2 n deconf i.e. “vector mode”

33. W HAT DOES THE ½- SKYRMION PHASE DO TO E SYM ? Symmetry ener gy ∼ 1/N c Isospin rotation Collective-quantize the (neutron) skyrmion matter I. Klebanov, 1985 Moment of inertia

34. E SYM FROM HALF - SKYRMION MATTER H.K. Lee, B.Y. Park, R. 2010

35. H OW TO UNDERSTAND THE CUSP AT IN “ STANDARD ” NUCLEAR PHYSICS ? In-medium scaling n 1/2 H.K. Lee, B.Y. Park, R. 2010

36. A SSUMPTIONS 1. Skyrmion number Q is conserved, a baryon can be considered as a bound pair (B ~ 100-200 MeV) of 2 half-skyrmions in the half-skyrmion phase. 2.Half-baryons interact via exchange of pions and vector mesons, giving a meaning to “effective nuclear forces.” 3.Quasiparticle description with effective masses and coupling constants makes sense. Scaling in density

37. T ENSOR FORCES ARE DRASTICALLY MODIFIED IN THE ½- SKYRMION PHASE For density n  n 1/2 : n=n 0 n=2n 0 n=0  Above n 1/2, the  tensor gets “killed,” enabling the pions (   ’s) to condense → pionic crystal in dense neutron matter ( e.g., Pandharipande and Smith 74). Decreasing tensor Increasing tensor n 1/2 For density n < n 1/2 : “standard” nuclear physics,

38. H OW THE ½- SKYRMIONS ACT ON E SYM H OW THE ½- SKYRMIONS ACT ON E SYM

39. ½-skyrmion vs. scaling Scaling prediction This prediction could be checked or falsified at FAIR or even RIB (e.g., KoRIA) machines ½-skyrmion

40. A PPLICATION : S TRANGE GOINGS - ON IN COMPRESSED MATT ER A PPLICATION : S TRANGE GOINGS - ON IN COMPRESSED MATT ER Insert anti-kaon in half-skyrmion matter Skyrmion-1/2-skyrmion background Ignore kaon back-reaction onto (half-)skyrmion matter J.I. Kim, B.Y. Park, R. 2009

41. A NALOGY TO “ MAGNETIC SPIRALS ” W ITH SPIN → ISOSPIN ? A NALOGY TO “ MAGNETIC SPIRALS ” W ITH SPIN → ISOSPIN ? Pfleiderer & Rosche, Nature, 17 June 2010 Chiral magnetic spirals Dzyaloshinsky-Moriya interaction

42. A NTI - KAON “ ROAMING ” THROUGH ½- SKYRMION MATTER : W ESS -Z UMINO TERM A NTI - KAON “ ROAMING ” THROUGH ½- SKYRMION MATTER : W ESS -Z UMINO TERM How to measure isospin spirals?

43. ppnK - “Challenging problem” ! pp n K-K- 1.5 fm  N (0) = 9  0   av = 3  0 1.2 fm Exp.  B ｔｈ -ex ~ 60 MeV Chiral restoration ? Relativistic effect ? Y. Akaishi 2010

44. “M YSTERIOUS ” ATTRACTION IN ½- SKYRMION MATTER “M YSTERIOUS ” ATTRACTION IN ½- SKYRMION MATTER △ B ~ 50-60 MeV Is this what Akaishi and Yamazaki need for dense kaonic matter ? BB

45. D EDONFINED QUANTUM CRITICAL ? ss Crystal Density Sigma model Sigma model ½-skyrmions n 1/2 ~ (1.3-2)n 0 “ superqualiton ” Hong, Zahed, R. (99)

46. C ONCLUSION C ONCLUSION If the ½-skyrmion phase (in 4D) or the ½-instanton (or dyonic-salt) phase (in 5D) is present at a density not far above n 0, drastic effects are expected for a variety of low-temperature nuclear processes, in particular, in the EOS crucial for compact stars. So what is the real “doorway” to higher-density phase(s)?