1. Mannque Rho Saclay What the Skyrmion Predicts in Dense Baryonic Matter that  Perturbation Theory Does Not Changchun October, 2014

2. “When you use quantum field theory to study low-energy phenomena, then according to the folk theorem you’re not really making any assumption that could be wrong, unless of course Lorentz invariance or quantum mechanics or cluster decomposition is wrong, provided you don’t say specifically what the Lagrangian is. As long as you let it be the most general possible Lagrangian consistent with the symmetries of the theory, you’re simply writing down the most general theory you could possibly write down. Weinberg Folk Theorem

3. Effective field theory was first used in this way to calculate processes involving soft  mesons, that is,  mesons with energy less than about  F  =1200 MeV. The use of effective quantum field theories has been extended more recently to nuclear physics, where although nucleons are not soft they never get far from their mass shell, and for that reason can be also treated by similar methods as the soft pions.

4. Nuclear physicists have adopted this point of view, and I gather that they are happy about using this new language because it allows one to show in a fairly convincing way that what they’ve been doing all along (using two-body potentials only, including one-pion exchange and a hard core) is the correct first step in a consistent approximation scheme.”

5. What’s accurately known at E  0 MeV Current algebra: Soft pion theorems For pion-pion and pion-nucleon interactions

6. From soft pions to vector mesons  At E ≈ 0, Soft pion/current algebra applies:  Invariance: This local symmetry is “redundant” and arbitrary, so there is no physics by itself. But power comes with a trick.  (Emergent) Hidden Local Symmetry (HLS) Observe

7.  Going to the next energy scale, E ≈ m V, V=  (and a 1 ) Pions interact with a strong coupling and the current algebra Lagrangian breaks down at a scale 4  m V /g V ) ~ 4  f   signaling that new degrees of freedom – the vector mesons – must figure.  How to bring in the vector degrees of freedom require an ingenuity.  Naively: But this is a mess and hopeless at high order.  Cleverly, implement local gauge invariance: e.g.  U

8. Most importantly local gauge invariance allows a systematic  PT expansion for m V ≈ m   ≈ 0. Without it, no way to handle massless vector mesons.  The strategy: Exploit the redundant degrees of freedom to render the vector mesons emergent as local gauge fields and have them propagate HLS theory  Caveat: Elevating EFT to a gauge field theory is NOT unique. Without gauge invariance it’s even worse!! EFT Current algebra a b c ……. z E ab cz  Which one is QCD?

9. HLS à la Harada-Yamawaki Harada and Yamawaki 2001 Although the formulas look complicated, the idea is simple and elegant and the prediction unambiguous.  Degrees of freedom:  with N F =2 or 3.  HLS Lagrangian in the chiral limit: 3 parameters g (gauge coupling), F  and F  or (g, F   a≡ (F  /F  ) 2 ) (“Truncated tower”)

10.  The crucial next step is to Wilsonian-match HLS correlators to QCD correlators (OPE) at the matching scale   ≥ m  The RGE flow picks the VM (“vector manifestation”) fixed point as rep. of QCD. “VM”=(g=0, a=1) We are sure that this theory has something to do with QCD! But is it complete?? Perhaps not??

11. Emergence of infinite tower of vector mesons  Bottom-up: Dimensional deconstruction  Top-down: Holographic dual gravity  Baryons as instantons or skyrmions-in-infinite-tower  Complete vector dominance “Strong coupled gauge theory requires fifth dimension”

12. Dimensional deconstruction Instead of restricting to one set of vectors as in HY, bring in towers of vector mesons as emergent gauge fields. Do this using “moose construction”  One vector meson: ; Georgi et al. 1999

13.  Two vector mesons …  Many (K=  ) vector mesons in “open moose”: where

14. “Theory space locality” ↔ “VM fixed point” (HY theory) Let And take continuum limit with K = ,  →0 : → 5D YM with lattice size  o Extention in 5 th dimension, i.e., dimensional deconstruction via infinite tower of vector mesons which are encapsulated in YM fields in “warped” metric. o Global chiral symmetry in 4D is elevated to a local gauge symmetry in 5D

15. o The pion field appears as a Wilson line The resulting theory, “ultraviolet completed” to QCD, is “dimensionally deconstructed QCD” Son/Stephanov 2004  infinite tower of hidden local gauge fields  baryons are instantons in 5D YM theory. Atiyah-Manton 1989  + Anomaly: Chern-Simons term Say “GHLS” Large N c QCD!?

16. Going top down from String theory This is another story, Sakai-Sugimoto holographic QCD etc. Much to be worked out… Y.L. Ma’s talk

17. How to approach dense baryonic system à la W theorem” 1. Baryons as skyrmions: multi-skyrmion system (e.g., skyrmion crystal) 2. Put baryon fields as explicit degrees of freedom, coupled to GHLS meson fields à la Weinberg (e.g., nucl-EFT)  chiral perturbation theory (  PT) With GHLS

18. Nuclear EFT + + + … With Heavy-mesons Without _

19. Relativistic Mean Field ↔ Landau-Fermi Liquid Take or equivalently, do the mean-field approximation ↔ Landau-Fermi-liquid theory. Reasoning: The mean field of the Lagrangian corresponds to a “Kohn-Sham” density functional (KSDF) which gives the Fermi-liquid fixed point theory.

20. What’s been accomplished Pions: interacting with the protons and neutrons subject to chiral symmetry with small symmetry breaking. Derive KSDF from chiral Lagrangian  Present industry in nuclear physics. Aim: To go from chiral Lagrangian to nuclear forces to nuclei to nuclear matter density (n 0 ) then to >> n 0 e.g. 1.97 M sun with density ~ 6n 0 Success: ~ 2000 nuclei with RMS deviation ~ ½ MeV, up to ~ n 0 Price to pay: ~ 50 parameters Higher density: unknown, QCD uncontrollable.

21. At high density it is totally wild Example: “Symmetry energy” A part of BW mass formula

22. Wilderness at n>n 0 Wilderness at n>n 0 “Supersoft” “Very Stiff” Nuclear Matter (n 0 ) Even with hidden gauge symmetry things go wild!!

23. “Supersoft” “Very stiff” Nature 1.97 M sun Standard gravity does not work! Causality?

24. Enter topology Skyrmion Enter topology Skyrmion

26. What  PT cannot do: Topology Skyrmions on Crystal Topology changes at high density, with the skyrmion fractionizing into ½- skyrmions. Drastic effect on the nuclear tensor forces: Dispute between Brown and Weinberg (1990). Parity-doublet symmetry “emerges” at high density: Nucleon mass in medium has two components, i.e., m * N =m 0 +    m 0 as     Could lead to Fermi-liquid-to-non-Fermi liquid transition, invalidating RMF theory at high density? Hot topic in condensed matter physics

27. Topology Change on Crystal Topology Change on Crystal When solitonic baryons are put on crystals, be they skrymions (4D) or instantons (5D), ½- skyrmions (4D) or dyons (5D) can appear at certain density: A.S. Goldhaber and N.S. Manton 1987 L. Castillejo et al 1989 …. and others S.-J. Sin, I. Zahed, MR 2010 Not captured in nucl-EFT based on chiral perturbation theory

28. Boundary conditions “trade” between topology and QCD degrees of freedom G. Brown, H.B. Nielsen, A.D. Jackson, …, I. Zahed, M.R. early 1990’s “Cheshire Cat” : Replace quark dynamics by meson dynamics via skyrmions

29. Skyrmion Crystal : half-skyrmion BCC 1987, A. S. Goldhaber & N. S. Manton y Y zx X (E/B) min =1.076 at L C =5.56 LbLb  =-1  =+1 (L b /2 above)

30. Skyrmion Crystal : cubic half-skyrmion Y X (E/B) min =1.038 at L f =4.72 o z Y z z X z LfLf y x x y

31. Appearance of ½-skyrmions is robust Appearance of ½-skyrmions is robust skyrmion half-skyrmion B.Y. Park, V. Vento, MR et al since 1999 skyrmions Half-skyrmions

32. Also in hQCD: “dyonic salt” Also in hQCD: “dyonic salt” Increasing density Instantons: FCC ½ instantons (dyons): BCC Sin, Zahed, R. 2010

33. Topology change = Phase Change Topology change = Phase Change Estimate: n 1/2 ~ (1.3 – 2) n 0  qq  0  ≠ 0  qq  ≠ 0  ≠ 0  qq  = 0  = 0  qq   “dilaton”

34. Predictions Skyrmions on crystal make certain predictions that are not in standard nuclear field theory based on chiral symmetry. We would like to see whether these predictions are (1) trustworthy (or falsifiable) and (2) presaging new physics. Can be tested in future accelerators, “RAON” (Korea), FAIR (Darmstandt) …and LIGO (GW), … What about other skyrmion approaches, such as holographic dual, BPS etc.?

35. Anti-kaon “roaming” through ½-skyrmion matter: Wess-Zumino term Anti-kaon “roaming” through ½-skyrmion matter: Wess-Zumino term Prediction-I B.-Y. Park et al 2010 BB △ B ~ 50-60 MeV Issues: (1) Brown-Bethe scenario (2) Dense kaon nuclei (3) 1.97 M solar star

36. Prediction-II B.Y. Park et al 2010 Nuclear symmetry energy

37. Prediction – III Where does the nucleon mass come from? “Emergent” parity-doublet symmetry for nucleons: m * = m 0 +    n 1/2 m0m0 Y.L. Ma et al 2003

38. Also baryons as dyonic instantons Generalized Ioffe mass formula Gorsky et al: 1308.3362

39. E sym in ½-skyrmion matter E sym in ½-skyrmion matter  N C -1 Is the cusp real? Answer: Yes

40. E sym is dominated by the tensor forces E sym is dominated by the tensor forces  NN G.E. Brown and R. Machleidt 1994 … A. Carbone et al 2013

41. Tensor forces are drastically modified in the ½-skyrmion phase n=n 0 n=2n 0 n=0  Above n 1/2, the  tensor gets “killed,” triggers the  0 ’s to condense → pionic crystal in dense neutron matter ( Pandharipande and Smith 74).  VT VT

42. Symmetry Energy “Symmetry energy is dominated by the tensor forces”: E sym n n 1/2 With nuclear correlations Skyrmion

43. Predicts: How the ½-skyrmions act on E sym Predicts: How the ½-skyrmions act on E sym

44. C14 dating probes up to n 0 J.W. Holt, G.E. Brown, T. Kuo … 2008 Can explain the long lifetime of carbon-14.

45. “Embed” in many-body correlations To go above n 0 Dong, Kuo et al 2013 Topology change Half-skyrmions skyrmions Similar “stiffening” when hadrons transform smoothly Into strange quark matter at n ~ 2n 0 Hatsuda et al 2013

46. Compact stars w/wo topology change without with M=2.4 M sun R=11 km Observations: M=1.97±0.04, 2.01±0.04 M sun, R~ (11-15) km

47. Surprises

48. Hoyle state: carbon 12 Hoyle state: carbon 12 P.H.C. Lau and N.S. Manton, 1408.6680

49. BPS Nuclei BPS Nuclei BPS Skyrmions pions And compact stars … But where are the deuteron, triton …?? C. Adam et al, PRL 111 (2013) 232501

50. Puzzles and Questions  Where does the proton mass come from?  Cheshire Cat: Topology (skyrmion, half-skyrmion), quark-bag, BPS, … Who does the “translation”?  How does the skyrmion know about shell model? e.g., Hoyle state.  BPS puzzle: In Walecka picture, the small BE of nuclear matter is given by This is supported by the QCD sum rules. How does the BPS encapsulate this huge cancellation ?

51. What this Changchun theory group Will do ? Solve the puzzles and Answer the fundamental questions!