Skyrmions Revisited 2006 Mannque Rho PNU Saclay Quarks

Skyrmions Revisited 2006 Mannque Rho PNU & Saclay Quarks, Nuclei and Universe Daejon 2006

Happy Birthday ! DPM 60

Outline • The skyrme model with pion fields only does not work • Hidden local fields, possibly an infinite tower of them, must be taken into account. • QCD meets string theory. New look at baryons. Points to a new direction to nuclear and hadronic physics

Skyrmions as QCD Baryons A history: • 1962: Skyrme model • 1983: Witten (Adkins, Nappi): QCD at large Nc • 2000 -2005: “Everybody” (except MR …) agrees “Skyrme model works well, say, within ~ 20%” This is a lie. Skyrme model requires for ~20% accuracy • fp (p)/fp(p) ~1/2 • mp(p)/mp(p) ~ 2 • “Nuclei” do not at all look like nuclei Then what’s OK with the Skyrme model? • The idea • The topological structure • 2006: “Holographic skyrmion”: nucleon of R < 1/MKK

Pion mass crucial? Battye and Sutcliffe 2006 Chiral symmetry irrelevant in nuclear physics? ?

Battye, Manton and Sutcliffe 2006 B=12 “We expect the parameters to be considerably different from those which emerge by fitting the proton mass, proton size and proton-delta mass difference …. . for modeling nuclei. ”

Personal View Since many years, it has been argued that vector mesons have to be included for a realistic description of baryons as skyrmions. • Scoccola, Min et al: Hyperons 1989 • BYPark, Min, R: Q+ pentaquark 2004 And now I am convinced more than ever the vector mesons should be there…

Sakai-Sugimoto Model Sakai and Sugimoto 2005 Full story at low energy What’s important for this talk is that baryons must emerge as Instantons in 5 D skyrmions in 4 D in an tower of vector mesons

Holographic dual skyrmion Work in progress now • Hong, Yee, Yi, R. (HRYY) • Hata, Sakai, Sugimoto, Yamato I shall use the general idea and map it to Harada-Yamawaki hidden local symmetry theory. Then apply to the nucleon structure, e. g. nucleon form factors, vector dominance, the pentaquark structure … And a pseudogap skyrmion-1/2 skyrmion transitions in dense matter.

Holographic dual skyrmion predicts: The 5 D instanton size is tiny R< 1/m. N. This means that in 4 D the infinite tower of vector mesons shrink the skyrmion from R ~ 0. 6 to R ~ 0. 2 fm. Therefore the nucleon EM form factor must be largely vector dominated. This works fine for the JLab result The Jlab can be fit with VD by r, r’, …, w, w’, . . . This explains the long-standing puzzle why the nucleon form factors cannot be understood with VD by the lowest r and w while the VD works well for the pion form factor. Enter Harada-Yamawaki HLS theory …

Violation of VD in HY’s HLS Harada and Yamawaki 2001 HY’s HLS theory can be viewed as HLS with an infinite tower with all vector mesons other than the lowest ones Integrated out and then matched to QCD correlators at the matching scale EM current g p r, w p g Mocks up “Tower”

Harada and Yamawaki found the “vector manifestation” (VM) fixed point (a, g)=(1, 0) and Nature tends to flow away from a=2 at which VD holds. The VD with a=2 is an “accident”. E. g. , matter in heat bath or in density tends to move to a=1. In some sense a “knows” about the tower. Proton favors a 1 Known since a long time!! • Iachello, Jackson and Lande 1973 ½ and ½ model Bijker • Brown, Rho and Weise 1986 Chiral bag at magic angle q=p/2 • Bijker 2005 Multi-parameter fit Iachello et al

Physics with a 1 The nucleon and nuclear structure favor a near 1. Holographic skyrmion says it’s natural. This means that the everybody in the tower plays an important role in the baryon sector. This has a remarkable ramification on the structure of the Q+ pentaquark, never mind whether it is seen in experiments or not. We use 2 characteristics of skyrmions with vector mesons: (1) Topology and (2) a is near 1 in baryonic environment.

Pentaquark as a bound K+-skyrmion Park, Min, R. 2004 String theorists Klebanov, Itzhaki et al argued that the bound K+- soliton picture is consistent with large Nc and the chiral limit. I agree. In fact in 1988, Scoccola, Min et al argued for the bound-state model but with the vector mesons r and w. In 2004, BYPark, Min and R. applied to the pentaquark problem the same Lagrangian as that of Scoccola et al which is just HY’s hidden local symmetry Lagrangian, with one element which made the calculation incomplete, which makes the result untrustworthy and the outcome inconclusive.

However the qualitative result is most likely valid because it has to do with the importance of the infinite tower of vector mesons. What was wrong in BYPark et al? The holographic dual QCD dictates that Lanomalous is completely vector dominated. In terms of HY’s HLS, this means that the w 3 p does not have the direct coupling , p w p 0 p This means that some of the coefficients that appear in the “induced” WZ terms used by Park et al are not consistent with HY’s HLS.

This “correction work” has not been done; one of the terms appears to be very arduous though straightforward… This (I believe) does not disturb the qualitative structure of theory. In short, what must happen is the following K+ binds to the skyrmion in the infinite tower of the vector mesons. The latter is approximated in HY’s HLS theory (i. e. , in Scoccola et al’s Lagrangian) by a 1 Roughly, the infinite tower corresponds to a ~ 4/3

a = 4/3

Skyrmion-1/2 skyrmion transition Topology is most probably the same for the Skyrme soliton and holographic skyrmion. Topology is robust (e. g. , quantum computers (a la Sarma et al ) are being built on topology) Assume that topology is preserved when skyrmions are put on crystals. Study of topology of skyrmions on crystal: Work by BYPark, Min, H. J. Lee, Vento, R. at KIAS 1999 -2004 Found: Phase transition from skyrmions to half-skyrmions at some density, identified as chiral transition

Skyrmion U=exp (i 2 p/fp) “deconfine” Half skyrmion U=x. L+x. R Pseudo-gap phase

HLS (emergent) gauge field Vector mesons rmemerge as hidden gauge bosons; Back with Harada and Yamawaki again. Redundant field to be eaten up to make the r massive Invariance SU(NF) local gauge theory with rm SU(NF) This is hidden local symmetry theory of Harada and Yamawaki BR scaling

An analogy to condensed matter Perhaps a generic feature in All strongly correlated matter ?

A: magnetic Néel ground state Sigma model B: VBS quantum paramagnet Phase change takes place through deconfinement of a skyrmion into 2 half-skyrmions at the boundary. The ½-skyrmions are confined to each other in both phases by hedgehog gauge field (HGF). Deconfinement occurs when HGF is “decoupled”. Senthil et al, Nature 303 (2004) 1490

Sigma model CP 1 parameterization Hidden gauge symmetry Invariance: Local gauge symmetry with U(1) gauge field Am

z = fractional spinon =1/2 - skyrmion = “meron” Topological charge (skyrmion number) Q ~ 1/2 -skyrmions are confined by topology At the phase transition, the “monopole” (topology) becomes irrelevant and the 1/2 -skyrmions get deconfined, the integer skyrmion number becoming non-conserved. Senthil et al’s “deconfined quantum critical points”

Deconfined up-meron-down-antimeron 1/2 - skyrmion

“skyrmion” “half-skyrmion” “skyrmion” superqualiton

The future looks great for the Next generation in this field!!