TOPOLOGY CHANGE AND HADRON PROPERTIES IN COLD DENSE MATTER

WCU-Hanyang Project

Work in progress with Hyun Kyu Lee and Byung-Yoon Park

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

Monte Carlo simulation

Observation

“Chiral magnetic spirals”

ARE THERE SUCH“GEMS”IN HADRONIC PHYSICS WITH THE SKYRMIONS ORIGI-NALLY DISCOVERED FOR BARYONS?

LESSONS FROM CONDENSED MATTER : “EMERGING”(HIDDEN) GAUGE SYMMETRY (HLS)

Neel magnet Broken spin-rotation symmetry

Valence bond solid(VBS) paramagnetBroken lattice-rotation symmetry

Senthil et al, Science 303, 1490 (2004)

Sigma model (skyrmion)

HLS(½-skyrmion)

POWER OF EFFECTIVE FIELD THE-ORY

Both A (Neel magnet) and B (VBS) are captured by the Nonlinear s model + Berry phase.

“Spinon” =order parameter in A ≠ order parameter in B

While the s model describes A and B, the Berry phase playsno 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.”

EMERGENT LOCAL SYMMETRY OR HLS

Interplay of the emergent gauge field and the Berry phaseleads to HLS theory between the A phase and the B phase

Skyrmions replaced by 1/2-skyrmions

Skyrmion number ~

CP1

S. Sachdev

State of½-skyrmions (or merons)

Manifestation in nuclear physics Nuclear tensor forces and (a)symmetry energy Esym in compressed baryonic matter

Analogy (?) to “deconfined Quantum critical phenomenon”

SYMMETRY ENERGY ESYM

ESYM AT HIGH DENSITY IS A WILDERNESS

AND AT HIGHER DENSITY

NATURE: ESYM AT

Fit to FOPI/GSI data for p-/p+ ratio → “supersoft” (ESS)

A: “supersoft” Ess

B: all others

Xiao et al, PRL 102 (09) 062502

n > n0 ?

400 MeV/A

Transport model analysis using IBUU04Z. Xiao, B.A. Li, L.W. Chen, G.C. Yong and M. Zhang, PRL 102, 062502 (2009)

Au+Au

“ESS” 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.

If Nature chose the “supersoft” ESS

AVOIDING 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” ESS

“GRAVITY DOESN’T EXIST”The New York TimesJuly 12, 2010

AVOIDING 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, andmake Bethe and Brown very unhappy

If Nature chose the “supersoft” ESS

HOW TO CONCOCT THE ESS

Possible mechanism: medium-scaling tensor forces

, p r

Tensor forces cancel: Exploit medium-enhanced cancelationto describe the C14 dating by J.W. Holt et al, PRL 100, 062501 (08)

Assumed scaling:

C. Xu & B.A. Li, arXiv:0910.4803

C14 DATING “EXPLAINED”

J.W. Holt et al, PRL 100, 062501 (08)

APPLY TO ESYM

Esym

n

Fi(n)= 1-ai (n/n0)

a0 =0

a1

a2

a3

am

0=a0 < a1 < a2 <a3 …<am ≈ 0.2

n0

C. Xu & B.A. Li, arXiv:0910.4803

for all density (n)

BUT HALF-SKYRMION (OR DYONIC*) PHASE ENTERS

Described in terms of skyrmions, baryonic matterhas a “phase transition” at ndeconf > n n1/2 > n0 froma skyrmion matter to a ½-skyrmion matter

*Sin, Zahed, R Ismail’s talk

Drastic change

HLS IN DENSE MATTER

Mimic generic features of the Neel-VBS (though with different physics):

Nonlinear sigma model: NLs

Hidden gauge invariance:

Promote to gauge theory with nonabelian gauge field rm : Harada/Yamawaki HLS theory: HLS

NLs model is “gauge-equivalent” to HLS

IN NATURE

xL,R decouple: L,R symmetries “restored” and xL,R and rm arethe relevant degrees of freedom as in the Neel-VBS transition

(a) Nc → → 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

GEORGI’S “VECTOR MODE”

H. Georgi, 1990

At large Nc , k (1-a) → 0, g ~ 0

• Vector mesons (e.g., r) are light ~ 1/Nc , become degenerate with p in the vector (or VM) limit. Cf: Weinberg’s “mended symmetry.”• Baryons as matter field are massive ~ Nc figuring in terms of two kinds of skyrmions

Supports •A variety of light-quark phenomena, e.g. p mass difference• Heavy-light-quark phenomena, e.g., chiral doubler• Nucleon form factor• Etc etc.

VD VIOLATION IN NUCLEON FORM FACTOR

Iachello, Jackson & Lande, 1973 Brown, Weise, R., 1986Bijker & Iachello, 2004

+ (1-z/2)z + (1-z/2)

Cf: VD → z=2 Phenomenology: z ≈ 1

HLS: z =

g g

HLS4D

“Core” &Cheshire Cat

Holography

I. Zahed

“a” goes to 1: Vector dominance a la Sakurai violated in medium!!!

V = , r r’,r”, …r

HLS5D

APPEARANCE OF FRACTIONIZED SKYRMIONS

skyrmion

half-skyrmion

Simulate dense matter by putting skyrmions in FCC crystals and squeeze them: ½-skyrmions in CC appear at n1/2

B.Y. Park et al,1999

skyrmions Half-skyrmions

ALSO IN HQCD: “DYONIC SALT”

Increasing density

Instantons: FCC

½ instantons(dyons): BCC

Sin, Zahed, R., Phys. Lett. B689, 23 (2010)

Dyons are bound by ~ 180 MeV.

“PHASE”STRUCTURE

Sigma model

HLS model

The ½-skyrmion phase at n n1/2 is characterized by

Rough estimate: n1/2 ~ (1.3 – 2) n0

n1/2ndeconf

i.e. “vector mode”

WHAT DOES THE ½-SKYRMION PHASE DO TO ESYM ?

Symmetry energy 1/N∼ c

Isospin rotation

Collective-quantize the (neutron) skyrmion matterI. Klebanov, 1985

Moment of inertia

ESYM FROM HALF-SKYRMION MATTER H.K. Lee, B.Y. Park, R. 2010

HOW TO UNDERSTAND THE CUSP AT IN “STANDARD”NUCLEAR PHYSICS?

In-medium scaling

n1/2

H.K. Lee, B.Y. Park, R. 2010

ASSUMPTIONS 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

TENSOR FORCES ARE DRASTICALLY MODIFIED IN THE ½-SKYRMION PHASE

For density n n1/2 :

n=n0

n=2n0

n=0+p r

Above n1/2, the r tensor gets “killed,” enabling the pions (p0’s) to condense → pionic crystal in dense neutron matter ( e.g., Pandharipande and Smith 74).

Decreasing tensor Increasing tensor

n1/2

For density n < n1/2 :

“standard” nuclear physics

,

HOW THE ½-SKYRMIONS ACT ON ESYM

½-skyrmion vs. scaling

Scaling prediction

This prediction could be checked or falsified atFAIR or even RIB (e.g., KoRIA) machines

½-skyrmion

APPLICATION: STRANGE GOINGS-ON IN COMPRESSED MATTER

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

ANALOGY TO “MAGNETIC SPIRALS” WITH SPIN → ISOSPIN?

Pfleiderer & Rosche,Nature, 17 June 2010

Chiral magnetic spiralsDzyaloshinsky-Moriya interaction

ANTI-KAON “ROAMING” THROUGH ½-SKYRMION MATTER: WESS-ZUMINO TERM

How to measure isospin spirals?

ppnK-

“Challenging problem” !

pp

n

K-

1.5 fm

rN(0) = 9r0

rNav= 3r0

1.2 fm

MeV20,MeV108 E

MeV25,MeV6169 EExp.

DB ｔｈ -ex ~ 60 MeV

Chiral restoration ?

Relativistic effect ?

Y. Akaishi 2010

“MYSTERIOUS” ATTRACTION IN ½-SKYRMION MATTER

△B ~ 50-60 MeV

Is this what Akaishiand Yamazaki need for dense kaonic matter ?

DB

DEDONFINED QUANTUM CRITICAL?

ss Crystal

Density

Sigmamodel

Sigmamodel

½-skyrmions

n1/2 ~ (1.3-2)n0

“superqualiton”

Hong, Zahed, R. (99)

CONCLUSION

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 n0 , 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)?