Topology Change and EoS for Compressed Baryonic Matter WCU-APCTP 2013

Topics Topology change in physics Nucleon with and without topology Proton decay with topology Topology in chiral bag and Cheshire Cat Skyrmion-half-skyrmion transition Georgi vector mode and HLS Translate topology change to parameters in EFT Lagrangian EoS for dense matter Compact stars And where does the nucleon mass come from?

“Models of Topology Change” : Shapere and Wilczek, arXiv: Topology change

“Topology change amounts to no more than a smooth change of boundary conditions in Hilbert space Or equivalently a change of parameters in the Hamiltonian” Shapere and Wilczek

Chain of equivalence via topology in nuclear/hadron physics Gauge equivalence Soliton/skyrmion Cheshire Cat ∞ tower

The Cheshire Cat Dual description of QCD in terms of hadronic variables In (1+1) dimensions, there is an exact bosonization of fermions: Illustration in 2D and generalization to (3+1) D. Consider fermion theory External fields Mass terms etc can be added … “How hadrons transform to quarks” Damgaard, Nielsen & Sollacher 1992 Nadkarni, Nielsen, Zahed 85

Enlarge Gauge Invariance:

 Gauge fix:  Concerned with chiral symmetry: choose “Cheshire cat gauge” “quarks”“pions”   is totally arbitrary, so physics should be independent of  “CCP”  Original fermion theory  with Boson theory: Fermions arise as topological solitons

Pick (Brown-Rho 1979) with The “Chiral Bag” Example: Fermion number VRV inside outside Mapping “volume” physics to “surface” with boundary conditions See later: AdS/QCD Holography

Equation of motion:  Inside  Outside  At the boundary Generates an axial vector field on the surface and gives rise to “vector anomaly” causing the fermion charge leakage.  Fermion charge: conserved VRV

Magic angle ½ fermion in the presence of magnetic monopole ½ baryon in the presence of a hedgehog pion at magic angle Jackiw, Rebbi 1976 Vento et al 1980 Dirac sea Magic angle Baryon charge divided half inside the bag half in hedgehog pion

Nature: 3+1 dimensions QCD could in principle be “bosonized” But  Nobody so far succeeded to accomplish it  It will have infinite number of bosons and the Lagrangian will have infinite number of terms → effective field theory  An EFT must break down at some scale and has to be “ultraviolet-completed” to a fundamental theory→ “matching”  Cheshire Cat can be only approximate in Nature with the exception of topological quantities Nonetheless there are intriguing predictions: e.g., “Proton spin”

The Cheshire Cat “How hadrons transform to quarks” Baryon charge: GEB, Goldhaber, R 1983 Goldstone, Jaffe 1983

Proton spin: CC in action Flavor singlet axial current (FSAC) U(1) A Anomaly: Naively: J proton = a 0 ≡ g A 0

quark sector gluon sector exp Total Vento, R G A 0 : FSAC Proton spin problem?

Pion Cloud uud

Where does Cheshire Cat break down “Core” in the proton Brown, Rho and Weise 1986 Look at Dirac form factor “Inside” “Outside” Shrink the core to zero gives “Sakurai VD” This does not work!!

Chiral bag at magic angle  magic angle) → R core ~ 0.38 fm Deep inelastic electron scattering → ~ (0.2  0.1) fm

Cheshire cat must break down if the proton decays Martin & Stavenga arXiv: At grand unification scale, proton can decay e.g. Proton structure Baryon-number violation (BNV)

Martin-Stavenga proposal: “The core in the chiral bag structure could suppress the square of the hadronic matrix element by ~ ” “Consequence: M GUT could be < times the “standard” bound ~ 5x10 15 GeV” Core size: R GUT ~ 0.05 fm: Beyond which topological twist makes no sense!!

Topology change in dense matter

Skyrmions on crystal Simulate dense matter by putting skyrmions in FCC crystals and squeeze them: ½-skyrmions in CC appear at n 1/2  ( ) n 0 skyrmions Half-skyrmions

Half-skyrmion phase “Topological phase transition”

Half-Skyrmions f*f* Lee, Park, Rho and Vento 2004

Tensor Forces  NN

Without ½ skymionWith ½ skymion Tensor forces w/wo topology change “Parameter change”

C14 dating probes scaling for n~n 0 J.W. Holt et al, PRL 100, (08)

Symmetry energy probes n>n 0 “Symmetry energy is dominated by the tensor forces”: E sym n (a) Without ½-s(b) With ½-s Schematically predicts

n 1/2 = ( ) n 0 Symmetry Energy E sym Dong, Kuo, Lee, Rho

Monopole matrix element Evolution of single-particle energy Nuclear physics at “RAON”

T. Otsuka 05

No nuclear renormalization of the fundamental tensor force

Duality?  Skyrmion cross over to half-skyrmion at n ~ ( )n 0  Hadron cross over to strong-coupled quark matter at n ~(2-4)n 0 Masuda, Hatsuda, Takatsuka: arXiv:

Skyrmion- Half-skyrmion Hadron- Squark top change No top change

The models predict M max ~ 2.3 M sun ~ 2.4 M sun R ~ 11km ~ 10.5km n max ~ 5.5 n 0 < n causality ~ 5 n 0 Skyrmion-half-skyrmion Hadron-Squark matter

Nucleon mass Molecules, Atoms, Nuclei: Masses =sum of masses of constituents + tiny binding energy Constituents: protons, neutrons, electrons Nuclear BE < 1%

Half-skyrmion phase “Topological phase transition” Chiral symmetry still broken with pion and massive hadrons

Nucleon mass in skyrmion matter with  with  Byung-Yoon Park’s talk Topology change

Nucleon mass with dilaton limit fixed point Won-Gi Paeng’s talk

Source for nucleon mass  Emergent  Intrinsic in QCD Parity-doublet model DeTar and Kunihiro 1989

Parity-doublet model

Where does m 0 come from? Conclusion