Mannque Rho Saclay

What the Skyrmion Predicts inWhat the Skyrmion Predicts inDense Baryonic Matter thatDense Baryonic Matter thatPerturbation Theory Does NotPerturbation Theory Does Not

Changchun October, 2014

“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

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.

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.”

What’s accurately known at E 0 MeV

Current algebra: Soft pion theoremsFor pion-pion and pion-nucleon interactions

From soft pions to vector mesons

At E ≈ 0 , Soft pion/current algebra applies:

Invariance:

This local symmetry is “redundant” and arbitrary, sothere is no physics by itself. But power comes with a trick. (Emergent) Hidden Local Symmetry (HLS)

Observe

Going to the next energy scale, E ≈ mV , V=(and a1)

Pions interact with a strong coupling and the currentalgebra Lagrangian breaks down at a scale4mV/gV) ~ 4fsignaling 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

Most importantly local gauge invariance allows a systematicPT expansion for mV ≈ m≈ 0. Without it, no way to handlemassless vector mesons.

The strategy: Exploit the redundant degrees of freedomto render the vector mesons emergent as local gauge fieldsand have them propagate HLS theory

Caveat: Elevating EFT to a gauge field theory is NOTunique. Without gauge invariance it’s even worse!!

EFT Current algebra

a b c ……. z

E

a bc z

Which one is QCD?

HLS à la Harada-YamawakiHarada and Yamawaki 2001

Although the formulas look complicated, the idea is simpleand elegant and the prediction unambiguous.

Degrees of freedom: with NF=2 or 3.

HLS Lagrangian in the chiral limit: 3 parameters g (gauge coupling), F and For (g, Fa≡ (F/F)2)

(“Truncated tower”)

The crucial next step is to Wilsonian-match HLS correlatorsto 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??

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 theoryrequires fifth dimension”

Dimensional deconstruction Instead of restricting to one set of vectors as in HY, bringin towers of vector mesons as emergent gauge fields.

Do this using “moose construction”

One vector meson:

;

Georgi et al. 1999

Two vector mesons …

Many (K=) vector mesons in “open moose”:

where

“Theory space locality” ↔ “VM fixed point” (HY theory)

Let

And take continuum limit with K = , →0 : → 5D YM

with lattice size

o Extention in 5th dimension, i.e., dimensional deconstruction via infinite tower of vector mesonswhich are encapsulated in YM fields in “warped” metric.

o Global chiral symmetry in 4D is elevated to a local gauge symmetry in 5D

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 Nc QCD!?

Going top down from String theory

This is another story, Sakai-Sugimotoholographic QCD etc. Much to be worked out…

Y.L. Ma’s talk

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

Nuclear EFT

+

+

+ …

With

Heavy-mesons

Without

_

Relativistic Mean Field ↔ Landau-Fermi Liquid

Take or equivalently , do the mean-fieldapproximation ↔ 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 pointtheory.

What’s been accomplishedPions: interacting with the protons and neutrons subject to chiral symmetry with small symmetrybreaking.Derive KSDF from chiral Lagrangian Present industry in nuclear physics.

Aim: To go from chiral Lagrangian to nuclear forcesto nuclei to nuclear matter density (n0) then to >> n0

e.g. 1.97 Msun with density ~ 6n0

Success: ~ 2000 nuclei with RMS deviation ~ ½ MeV, up to ~ n0 Price to pay: ~ 50 parameters

Higher density: unknown, QCD uncontrollable.

At high density it is At high density it is totally totally wildwild

Example: “Symmetry energy”

A part of BW mass formula

Wilderness at n>nWilderness at n>n00

“Supersoft”

“Very Stiff”NuclearMatter (n0)

Even with hiddengauge symmetrythings go wild!!

“Supersoft”

“Very stiff”

Nature 1.97 Msun

Standard gravity does not work!

Causality?

Enter topologyEnter topology SkyrmionSkyrmion

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 =m0 + m0 as

Could lead to Fermi-liquid-to-non-Fermi liquid transition, invalidating RMF theory at high density?

Hot topic in condensed matter physics

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

Boundary conditions “trade” betweentopology and QCD degrees of freedom

G. Brown, H.B. Nielsen, A.D. Jackson,…, I. Zahed, M.R. early 1990’s

“Cheshire Cat” :Replace quark dynamicsby meson dynamics viaskyrmions

Skyrmion Crystal : half-skyrmion BCC

1987, A. S. Goldhaber & N. S. Manton

y

Y

z x

X

(E/B)min=1.076 at LC=5.56

Lb

=-1=+1(Lb/2 above)

Skyrmion Crystal : cubic half-skyrmion

Y

X

(E/B)min=1.038 at Lf=4.72

o

z

Y

z z

X

z

Lf y

x

x

y

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

Also in hQCD: “dyonic salt”Also in hQCD: “dyonic salt”

Increasing density

Instantons: FCC

½ instantons(dyons): BCC

Sin, Zahed, R. 2010

Topology change = Phase ChangeTopology change = Phase Change

Estimate: n1/2 ~ (1.3 – 2) n0

qq 0≠ 0

qq≠ 0≠ 0

qq= 0= 0

qq

“dilaton”

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 thesepredictions 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 asholographic dual, BPS etc.?

Anti-kaon “roaming” through Anti-kaon “roaming” through ½-skyrmion matter: Wess-Zumino term ½-skyrmion matter: Wess-Zumino termPrediction-IPrediction-I

B.-Y. Park et al 2010

B

△ B ~ 50-60 MeVIssues: (1) Brown-Bethe scenario (2) Dense kaon nuclei (3) 1.97 Msolar star

Prediction-IIB.Y. Park et al 2010

Nuclear symmetry energy

Prediction – III Where does the nucleon mass come from?

“Emergent” parity-doublet symmetry for nucleons: m* = m0 +

n1/2

m0

Y.L. Ma et al 2003

Also baryons as dyonic instantons

Generalized Ioffe mass formula

Gorsky et al: 1308.3362

EEsym sym in ½-skyrmion matter in ½-skyrmion matter

NC-1

Is the cusp real?

Answer: Yes

EEsymsym is dominated by the tensor forces is dominated by the tensor forces

N N

G.E. Brown and R. Machleidt 1994 … A. Carbone et al 2013

Tensor forces are drastically modified in Tensor forces are drastically modified in the ½-skyrmion phase the ½-skyrmion phase

n=n0

n=2n0

n=0

Above n1/2, the tensor gets “killed,” triggers the 0’s to condense → pionic crystal in dense neutron matter ( Pandharipande and Smith 74).

VT

Symmetry EnergySymmetry Energy

“Symmetry energy is dominated by the tensor forces”:

Esym

nn1/2n1/2

With nuclear correlations

Skyrmion

Predicts: Predicts: How the ½-skyrmionsHow the ½-skyrmions act on E act on Esymsym

C14 dating probes up to C14 dating probes up to nn00

J.W. Holt, G.E. Brown, T. Kuo … 2008

Can explain the long lifetime of carbon-14.

“Embed” in many-body correlations To go above n0

Dong, Kuo et al 2013

Topology change

Half-skyrmions

skyrmions

Similar “stiffening” when hadrons transform smoothlyInto strange quark matter at n ~ 2n0

Hatsuda et al 2013

Compact stars w/wo topology change

without

with

M=2.4 Msun

R=11 km

Observations: M=1.97±0.04, 2.01±0.04 Msun , R~ (11-15) km

Surprises

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

BPS NucleiBPS Nuclei

BPSSkyrmions

pions

And compact stars …But where are the deuteron, triton …??

C. Adam et al, PRL 111 (2013) 232501

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 ?

What this Changchun theory groupWhat this Changchun theory group Will do ? Will do ?

Solve the puzzles and Answer the fundamental questions!