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1 Nambu-Goldstone Fermion in Quark-Gluon Plasma and Bose-Fermi Cold Atom System ( /BNL! ECT* ") : Jean-Paul Blaizot (Saclay CEA #) ( )
2 (SUSY) = b f b f 2
3 (SUSY) Q: supercharge b f b f SUSY: [Q, H]=0 Supercharge : 3
4 SUSY ( ) SUSY SUSY nf nb E E -Goldstone (NG)? 4
5 V. V. Lebedev and A. V. Smilga, Nucl. Phys. B 318, 669 (1989) SUSY NG -Goldstone : ik µ (fermion ver.) d 4 xe ik (x y) TJ µ (x)o(y) = {Q, O} J µ : supercurrent Q=J 0 : supercharge NG k 0 5
6 SUSY NG ik µ NG V. V. Lebedev and A. V. Smilga, Nucl. Phys. B 318, 669 (1989) d 4 xe ik (x y) TJ µ (x)o(y) = {Q, O} { } (µ=0) O=Q NG mode <QQ >. (T 0ν γν). SUSY. Wess-Zumino ε, T µν =diag(ρ,p,p,p), SUSY NG (Goldstino) 6
7 QED/QCD goldstino V. V. Lebedev and A. V. Smilga, Annals Phys. 202, 229 (1990) SUSY. = q g 7
8 QED/QCD goldstino V. V. Lebedev and A. V. Smilga, Annals Phys. 202, 229 (1990) QED/QCD. Y. Hidaka, D. S., and T. Kunihiro, Nucl. Phys. A 876, 93 (2012) D. S., PRD 87, (2013). J. P. Blaizot and D. S., Phys. Rev. D 89, (2014). Reω p/3 Im g 2 144π 2 QED g 2 (4 + N f ) 2 48π 2 QCD (Type-I NG mode). 8
9 ( ) Wess-Zumino model: Y. Yu, and K. Yang, PRL 105, (2010) Dense QCD: K. Maeda, G. Baym and T. Hatsuda, PRL 103, (2009) QED: Kapit and Mueller, PRA 83, (2011) 9
10 Motivation SUSY simulate goldstino!! 10
11 T. Shi, Y. Yu, and C. P. Sun, PRA 81, (R) (2010) 2 f, F b b f F 11
12 H α = t α a α i aj α µ α a α i ai α ij i ( ) T. Shi, Y. Yu, and C. P. Sun, PRA 81, (R) (2010) f b = (tf =tb) (µf =µb) t : M. Snoek, S. Vandoren, and H. T. C. Stoof, PRA 74, (2006) 12
13 U bb 2 i n b i ( n b i 1 ) + U bf = T. Shi, Y. Yu, and C. P. Sun, PRA 81, (R) (2010) i n b i nf i, (Ubb =Ubf) tf =tb, Ubb =Ubf, µf =µb Q =bf. F decouple. 13
14 SUSY NG ik µ d 4 xe ik (x y) TJ µ (x)o(y) = {Q, O} Q =bf Q =b f NG O=Q NG mode <QQ >. (ρ). SUSY ρ. 14
15 d=2 BEC. a << (kf) -1, (T) -1 ( a=1.) Δµ=µf -µb 0 Explicit SUSY breaking 15
16 resummed perturbation T. Shi, Y. Yu, and C. P. Sun, PRA 81, (R) (2010) Goldstino (<Q (x)q(0)>) Q =bf 1 <Q (x)q(0)>= b f SUSY ω-δµ, p 0 ( )= (Δµ=µf -µb) d 2 k n F (ϵ f k ) (2π) 2 ω µ t(2k p + p 2 ), 2 16
17 resummed perturbation T. Shi, Y. Yu, and C. P. Sun, PRA 81, (R) (2010) (1) resum : Uρb Uρf + 2Uρb : d 2 k n F (ϵ f k ) (2π) 2 ω ( µ + t(2k p + p 2 )+Uρ), ( )= U -1 17
18 resummed perturbation T. Shi, Y. Yu, and C. P. Sun, PRA 81, (R) (2010) ring U -1 U -1 U U -1 =U -1 ring 18
19 resummed perturbation T. Shi, Y. Yu, and C. P. Sun, PRA 81, (R) (2010) (2) Random Phase Approximation self-consistent explicit. 19
20 (1), (2) Goldstino.. p <<kf, Uρ/(kf t) 20
21 goldstino ω 1 (sum rule ) Type-II NG mode ( Type-I). α 1 ρ ( 4πt 2 ρ 2 f Uρ (T=0 ) t(ρ f ρ b ) ) NG p=0 0. p: 21
22 T 0 17 U/t=0.1, f =0.5, b = /t T/t α T. 22
23 Goldstino : Q, Q, ρ : m +, m -, m z Q m + Q m - b Q 2 =Q 2 =0 f up m +2 =m -2 =0 down m ± =m x ± im y 23
24 h :! = h + p 2 Type-II 24
25 NG mode type-i II. NII=rank<[Qa, Qb]>/2 NI=NBS -2NII H. Watanabe and H. Murayama, PRL 108, (2012) Y. Hidaka, PRL 110, (2013) ( <[m ±, m z ]>=0 ) <[m +, m - ]>=2m0 rank<[qa, Qb]>/2=1 NII =1 NI =0 NBS =2 25
26 Goldstino ( ). <[Q, ρ]>=0 <{Q, Q }>=ρ ( <[m ±, m z ]>=0 ) <[m +, m - ]>=2m0 Q, Q m+, m- ρ mz. 26
27 ! = µ p 2 Δµ h p: Dp 4. D T. Hayata, Y. Hidaka (2014) 27
28 QGP goldstino ( ). goldstino ( ). 28
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F [ ] F [ ] Nambu( 60), Goldstone(61), Nambu Jona-Lasinio( 61), Goldstone, Salam, Weinberg( 62). N NG = N BS NG : CC by-sa Aney CC by Zouavman Le Zouave CC by-sa Roger McLassus U(1) CC by-sa Aney -Goldstone
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3 3. 3.. H H = H + V (t), V (t) = gµ B α B e e iωt i t Ψ(t) = [H + V (t)]ψ(t) Φ(t) Ψ(t) = e iht Φ(t) H e iht Φ(t) + ie iht t Φ(t) = [H + V (t)]e iht Φ(t) Φ(t) i t Φ(t) = V H(t)Φ(t), V H (t) = e iht V (t)e
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