Non-Abelian vortices in dense QCD: quark hadron continuity and - PowerPoint PPT Presentation

Non-Abelian vortices in dense QCD: quark hadron continuity and non-Abelian statistics 2019/6/24@ Tokyo campus, Univ. of Tsukuba Muneto Nitta( 新田宗土 ) Chandrasekhar Chatterjee, Shigehiro Yasui( 安井 繁宏 ) Keio U.( 慶應義塾大学 )

Topic in this talk from Fukushima & Hatsuda Rept.Prog.Phys. 74 (2011) 014001

Quantum Chromo Dynamics (QCD) quarks Quark matter i = u,d,s flavor(global) SU(3) i q  α = r,g,b color(gauge) SU(3) Color-flavor locked (CFL) phase “Color superconductor” @ high density Bailin- Love(‘79), Iwasaki- Iwado(‘95) Alford-Rajagopal- Wilczek(‘98)  =   j k q q ~ 1      i ijk i 3x3 matrix Color superconductivity from Fukushima & Hatsuda as well as superfluidity Rept.Prog.Phys. 74 (2011) 014001

Superfluid Neutron Stars Neutron vortices superfluid Core Nuclear matter Rotation Magnetic field Proton Baym&Pines (‘60s) Anderson&Itoh (‘75) super- vortices conductor (Flux tubes)

Color superconductor    =   q q   i ijk j k  = = 1 , 2 , 3 ( r, g, b ) i 1 , 2 , 3 ( u, d, s )   = d s s u u d r gb   [ g b ] [ g b ] [ g b ]  = =   d s s u u d g br  i [ b r ] [ b r ] [ b r ]   = d s s u u d b rg   [ r g ] [ r g ] [ r g ] = = = u ds d sb s ud   →  =   i e g g G U ( 1 ) SU ( 3 ) SU ( 3 )   i color i flavor B C F

Iida&Baym(‘01) Landau-Ginzburg model from QCD Giannakis&Ren(‘02) Iida,Matsuura, Tachibana&Hatsuda(‘04) density GL of state parameters For a while we consider high density limit, where strange quark mass can be neglected. We also ignore E&M interaction. We can take into account these appropriately.

Color superconductor    =   q q   i ijk j k  = = 1 , 2 , 3 ( r, g, b ) i 1 , 2 , 3 ( u, d, s ) Ground  =   0 0 r gb state    =  =   0 0 g br  i    =   0 0 b rg color-flavor = = = locked (CFL) u ds d sb s ud =   G U ( 1 ) SU ( 3 ) SU ( 3 ) superfluidity U ( 1 ) B C F B → = − = g H SU ( 3 ) color superconductivity 1 SU ( 3 ) g + C F color flavor C

Color superconductor    =   q q   i ijk j k Integer  = = 1 , 2 , 3 ( r, g, b ) i 1 , 2 , 3 ( u, d, s ) quantized superfluid     = i ( r ) e 0 0 r gb   1 vortex   =  =   i 0 ( r ) e 0 g br  i 1     = i 0 0 ( r ) e b rg   1 = = = u ds d sb s ud Iida & Baym, Forbes & Zhitnitsky(‘02)

Color superconductor    =   q q   i ijk j k  = = 1 , 2 , 3 ( r, g, b ) i 1 , 2 , 3 ( u, d, s ) 1/3 quantized     = i ( r ) e 0 0 r gb   vortex 1  =  =   0 ( r ) 0 g br  i 0    = 0 0 ( r ) b rg   0 = = = u ds d sb s ud Balachandran, Digal & Matsuura (BDM) (‘05) Nakano, MN & Matsuura (‘07), Eto & MN (‘09)

1/3 quantized vortex     i ( r ) e 0 0   1  =    0 ( r ) 0  i 0    0 0 ( r )   0      2 0 0 ( r ) 0 0       1   i i = −        exp exp 0 1 0 0 ( r ) 0 0   3 3     −      0 0 1 0 0 ( r ) 1/3 quantized 0 SU(3) color   A Superfluid vortex F ~ rd  12 Non-Abelian vortex color flux tube

1/3 quantized vortex     i ( r ) e 0 0   1  =    0 ( r ) 0  i 0    0 0 ( r )   0   +  trace F 2 , 1 0 Profiles   −  G , traceless 1 0  0 Long tail of  a superfluid 1 vortex Gauge field confined color flux Eto & MN (‘09)

1/3 quantized vortex    ( r ) 0 0   0   =  i   0 ( r ) e 0  i 1      0 0 ( r ) 0 −      1 0 0 ( r ) 0 0       0   i i =        exp exp 0 2 0 0 ( r ) 0 1   3 3     −      0 0 1 0 0 ( r ) 1/3 quantized 0 SU(3) color   A Superfluid vortex F ~ rd  12 Non-Abelian vortex color flux tube

1/3 quantized vortex    ( r ) 0 0   0  =    0 ( r ) 0  i 0     i   0 0 ( r ) e 1 −      1 0 0 ( r ) 0 0       0   i i = −        exp exp 0 1 0 0 ( r ) 0 0   3 3          0 0 2 0 0 ( r ) 1/3 quantized 1 SU(3) color   A Superfluid vortex F ~ rd  12 Non-Abelian vortex color flux tube

Comment 1/3 quantized vortex Non-Abelian vortices were discovered earlier    ( r ) 0 0 in the context of   0 Supersymmetry and  =    String theory (‘03) 0 ( r ) 0  i 0     i   0 0 ( r ) e 1 −      1 0 0 ( r ) 0 0       0   i i = −        exp exp 0 1 0 0 ( r ) 0 0   3 3          0 0 2 0 0 ( r ) 1/3 quantized 1 SU(3) color   A Superfluid vortex F ~ rd  12 Non-Abelian vortex color flux tube

Non-Abelian vortices Color Fluxes  i    ( r ) e 0 0   1    0 ( r ) 0 Abelian vortex 0    0 0 ( r )   0 No flux        ( r ) 0 0 i ( r ) e 0 0     0 1  i        i 0 ( r ) e 0 0 ( r ) e 0 1 1        i   0 0 ( r ) 0 0 ( r ) e   0 1    ( r ) 0 0   0  Which are   0 ( r ) 0 0     energetically i   0 0 ( r ) e 1 favored?

Non-Abelian vortices Color Fluxes  i    ( r ) e 0 0   1    0 ( r ) 0 Abelian vortex 0    0 0 ( r )   0 No flux        ( r ) 0 0 i ( r ) e 0 0     0 1  i        i 0 ( r ) e 0 0 ( r ) e 0 1 1        i   0 0 ( r ) 0 0 ( r ) e   0 1   Split    E ( r ) 0 0     1 E 0   =    0 ( r ) 0 E = 0       i 9   0 0 ( r ) e E 1 = Nakano, MN & Matsuura (‘07), simulation by Alford et.al (‘16)

Abrikosov vortex lattice

Colorful vortex lattice

= SU H ( 3 )     i + ( r ) e 0 0 C F    1  =    0 ( r ) 0 =   K [ SU ( 2 ) U ( 1 )] i 0   + C F  0 0 ( r )   @ vortex core 0 Nambu-Goldstone modes localized around the vortex Continuous family H SU ( 3 )  =  =  + 2 C F C C C C P of solutions exists  K SU ( 2 ) U ( 1 ) Eto,Nakano&MN(’09) = Gapless modes propagating along the vortex line “ground state” fluctuations 1+1 dim effective theory

Quark-hadron continuity

How do vortices connect? Hadron (hyperon) matter ??? Quark Matter (CFL) ??? Neutron star

Continuity of Quark and Hadron Matter Thomas Schäfer and Frank Wilczek Phys. Rev. Lett. 82 , 3956 – Published 17 May 1999 (continuity or crossover) No phase transition between hadron and CFL phases Matching of symmetries and excitations ( Nambu-Goldstone modes etc ) Three-flavor quarks with degenerate mass

Continuity of Quark and Hadron Matter Thomas Schäfer and Frank Wilczek Phys. Rev. Lett. 82 , 3956 – Published 17 May 1999 Colorful boojums at the interface of a color superconductor Mattia Cipriani, Walter Vinci, and Muneto Nitta Phys. Rev. D 86 , 121704(R) – Published 21 December 2012 Continuity of vortices from the hadronic to the color-flavor locked phase in dense matter Mark G. Alford, Gordon Baym, Kenji Fukushima, Tetsuo Hatsuda, Motoi Tachibana, Phys.Rev. D99 (2019) no.3, 036004 e-Print: arXiv:1803.05115 [hep-ph] Quark-hadron continuity under rotation: vortex continuity or boojum? Chandrasekhar Chatterjee, Muneto Nitta, Shigehiro Yasui Phys.Rev. D99 (2019) no.3, 034001, e-Print: arXiv:1806.09291 [hep-ph] Anyonic particle-vortex statistics and the nature of dense quark matter Aleksey Cherman, Srimoyee Sen, Laurence G. Yaffe e-Print: arXiv:1808.04827 [hep-th] Quark-hadron continuity beyond Ginzburg-Landau paradigm Yuji Hirono, Yuya Tanizaki Phys.Rev.Lett. 122 (2019) no.21, 212001, e-Print: arXiv:1811.10608 [hep-th]