Inverse magnetic catalysis in dense (holographic) matter

Transcription

1 BNL, June 27, Andreas Schmitt Institut für Theoretische Physik Technische Universität Wien 1040 Vienna, Austria Inverse magnetic catalysis in dense (holographic) matter F. Preis, A. Rebhan, A. Schmitt, JHEP 1103, 033 (2011); JPG 39, (2012) (Chiral) magnetic catalysis Chiral transition in the Sakai-Sugimoto model Inverse magnetic catalysis at finite chemical potential Add baryonic matter

2 BNL, June 27, Magnetic catalysis (page 1/2) K. G. Klimenko, Theor. Math. Phys. 89, (1992) V. P. Gusynin, V. A. Miransky, I. A. Shovkovy, PLB 349, (1995) (massless) fermions in Nambu-Jona-Lasinio (NJL) model L NJL = ψ iγ µ µ ψ + G [( ψψ) 2 + ( ψ iγ 5 ψ) 2] mean-field approximation: ψψ = ψψ + fluctuations Zero magnetic field: dynamical fermion mass M ψψ 0 for coupling g > g c = 1 dimensionless coupling g GΛ 2 /π 2

3 BNL, June 27, Magnetic catalysis (page 1/2) K. G. Klimenko, Theor. Math. Phys. 89, (1992) V. P. Gusynin, V. A. Miransky, I. A. Shovkovy, PLB 349, (1995) (massless) fermions in Nambu-Jona-Lasinio (NJL) model L NJL = ψ iγ µ µ ψ + G [( ψψ) 2 + ( ψ iγ 5 ψ) 2] mean-field approximation: ψψ = ψψ + fluctuations Nonzero magnetic field: M 0 for arbitrarily small g, M eb e const./ebg at weak coupling g 1 dimensionless coupling g GΛ 2 /π 2

4 BNL, June 27, Magnetic catalysis (page 2/2) Analogy to BCS Cooper pairing: BCS superconductor Magnetic catalysis Cooper pair condensate ψψ chiral condensate ψψ µ e const./gν F M eb e const./gν 0 (ν F : d.o.s. at E = µ Fermi surface) (ν 0 : d.o.s. at E = 0 surface) pairing dynamics effectively (1+1)-dimensional because of Fermi surface effectively (1+1)-dimensional in lowest Landau level (LLL) because of magn. field = µ2 G 2π 2 gap equation 0 dk (k µ) M = q BG 2π 2 gap equation (LLL) dk z M k 2 z + M 2

5 BNL, June 27, Magnetic catalysis in the real world and in holography 2 Experiment 0.8 M q Σ xy e 2 h Theory T ΧS Restored H Σ xy e 2 h b 0.04, T 30 mk Γ 18 K, Γ tr 6 K V g V V.P.Gusynin et al., PRB 74, (2006) graphene: appearance of additional plateaus in strong magnetic fields [B = 9 T (pink), B = 45 T (black)] ΧSB H C.V.Johnson, A.Kundu, JHEP 0812, 053 (2008) Sakai-Sugimoto: magnetic field enhances dynamical mass M q and critical temperature T c see also: J. Erdmenger et al., JHEP 0712, 091 (2007) V.G.Filev, R.C.Rashkov, AHEP (2010)

6 BNL, June 27, (Chiral) magnetic catalysis in QCD? T ~150 MeV heavy ion collisions < ψ ψ > = 0 R L < ψ ψ > ~ 0 R L _ compact stars chiral transition probed in heavyion collisions and compact stars in both instances huge magnetic fields are present! µ z=0 y inward moving ion b/2 B b/2 x outward moving ion quark gluon plasma heavy-ion collisions: temporarily B G magnetars: at surface B G

7 BNL, June 27, Chiral transition in the Sakai-Sugimoto model (p. 1/3) T. Sakai, S. Sugimoto, Prog. Theor. Phys. 113, (2005) T τ x 4 deconfined u L χs restored T c D8 D8 confined χs broken µ not unlike expectation from large-n c QCD in probe brane approximation: chiral transition unaffected by quantities on flavor branes (µ, B,...)

8 BNL, June 27, Chiral transition in the Sakai-Sugimoto model (p. 2/3) less rigid behavior for smaller L deconfined, chirally broken phase for L < 0.3 π/m KK O. Aharony, J. Sonnenschein, S. Yankielowicz, Annals Phys. 322, 1420 (2007) N. Horigome, Y. Tanii, JHEP 0701, 072 (2007) T deconfined χs broken L deconfined χs restored T c confined χ S broken µ

9 BNL, June 27, Chiral transition in the Sakai-Sugimoto model (p. 3/3) L π/m KK corresponds to (non-local) NJL model E. Antonyan, J. A. Harvey, S. Jensen, D. Kutasov, hep-th/ J. L. Davis, M. Gutperle, P. Kraus, I. Sachs, JHEP 0710, 049 (2007) T deconfined χs broken deconfined χs restored confined χ S broken T c µ this limit is considered in the following calculation...

10 BNL, June 27, Setup of our calculation D8-brane action in deconfined geometry for N f = 1 O. Bergman, G. Lifschytz, M. Lippert, PRD 79, (2009) S = S DBI + S CS = N du u 5 + b 2 u fa 2 3 a u3 fx N u T 2 b du (a 3 a 0 a 0 a 3) u T a 0 accounts for µ magnetic field b = F 12 b, µ induce a 3 ( anisotropic condensate π 0 ) E.G.Thompson, D.T.Son, PRD 78, (2008) A. Rebhan et al., JHEP 0905, 084 (2009) x 4 (u) = { const. χs nontrivial χsb equations of motion: ( ) a 0 u5 + b 2 u 2 u 1 + fa 2 3 a u3 fx 2 4 ( ) f a 3 u5 + b 2 u 2 u 1 + fa 2 3 a u3 fx 2 4 ( ) u 3 f x 4 u5 + b 2 u 2 u 1 + fa 2 3 a u3 fx 2 4 = 3ba 3 = 3ba 0 = 0 solve for a 0 (u), a 3 (u), x 4 (u)

11 BNL, June 27, T = 0 phase diagram b mesonic "LLL" "hll" apparent Landau level transition G. Lifschytz, M. Lippert, PRD 80, (2009) (charge density exactly like in LLL for free fermions) non-monotonic behavior of critical µ (in apparent contrast to magnetic catalysis) Μ

12 BNL, June 27, Inverse magnetic catalysis Why does B restore chiral symmetry for certain µ? free energy gain from ψ ψ pairing increases with B (magnetic catalysis) µ induces free energy cost for pairing; this cost depends on B! weak coupling (NJL): E. V. Gorbar et al., PRC 80, (2009) Ω B[µ 2 M(B) 2 /2] just like Clogston limit δµ = 2 in superconductivity A. Clogston, PRL 9, 266 (1962) B. Chandrasekhar, APL 1, 7 (1962) Sakai-Sugimoto: large B: Ω B[µ M(B) 2 ] small B: Ω µ 2 B const M(B) 7/2 Inverse magnetic catalysis

13 BNL, June 27, Phase structure at nonzero temperature blue: chiral phase transition green: LLL transition b ΧSb t 0.13 t 0.1 t 0.05 t 0 ΧS Μ t ΧS Μ 0.2 Μ 0.25 Μ 0.3 Μ 0 ΧSb b t b 5 ΧSb b 0.12 b 0 ΧS Μ

14 BNL, June 27, Agreement with NJL calculation Sakai-Sugimoto: F. Preis, A. Rebhan and A. Schmitt, JHEP 1103, 033 (2011) b ΧSb t 0.13 t 0.1 t 0.05 t 0 ΧS Μ t ΧS Μ 0.2 Μ 0.25 Μ 0.3 Μ 0 ΧSb NJL: b t b 5 ΧSb b 0.12 b 0 ΧS T. Inagaki, D. Kimura, T. Murata, Prog. Theor. Phys. 111, (2004) Μ m [GeV] T = 0.01 T = 0.05 T = 0.03 Symmetric phase T = 0.10 Broken phase H [GeV 2 ] T = 0.15GeV H [GeV ] B. P. B. P. m = 0.34 m = 0.28 m = 0.31 m = 0.31 m = 0.34 m = 0.27 m = 0.24GeV Symmetric phase T [GeV] T [GeV] Broken phase Symmetric phase H = 0.60GeV m [GeV] (IMC also in quark-meson model J. O. Andersen and A. Tranberg, arxiv: [hep-ph]) H = 0.30 H = H = 0.0 H = 0.18

15 BNL, June 27, Homogeneous baryonic matter in Sakai-Sugimoto baryons in AdS/CFT: wrapped D-branes with N c strings E. Witten, JHEP 9807, 006 (1998); D. J. Gross, H. Ooguri, PRD 58, (1998) baryons in Sakai-Sugimoto: D4-branes wrapped on S 4 equivalently: instantons on D8-branes ( Skyrmions) T. Sakai, S. Sugimoto, Prog. Theor. Phys. 113, (2005) H. Hata, T. Sakai, S. Sugimoto, S. Yamato, Prog. Theor. Phys. 117, 1157 (2007) pointlike approximation for N f = 1: O. Bergman, G. Lifschytz, M. Lippert, JHEP 0711, 056 (2007) S = S from above + N 4 T 4 dω 4 dτ e Φ det g + N c A }{{} 8π 2 0 Tr F 2 R 4 U } {{} n 4 N c M q n 4 A 0 (u)δ(u u c ) (n 4 baryon density, M q constituent quark mass, u c location of D4-branes)

16 BNL, June 27, Effect of baryons on T = 0 phase diagram 0.4 ignoring baryonic matter 0.4 including baryonic matter b "LLL" b mesonic "LLL" mesonic 0.1 "hll" Μ small b: baryonic matter prevents the system from restoring chiral symmetry 0.1 baryonic baryon onset (2nd order!) intersects chiral phase transition large b: mesonic matter superseded by quark matter with baryonic matter, IMC plays an even more prominent role in the phase diagram Μ

17 BNL, June 27, Summary Dense matter in the NJL limit of the Sakai-Sugimoto model shows a transition reminiscent of LLL... shows a chiral phase transition with MC at large B and IMC at small B Baryonic matter changes the phase diagram dramatically for small B Agreement with NJL calculations only before including baryonic matter

18 BNL, June 27, Outlook Sakai-Sugimoto calculation: understand chiral non-restauration with baryons extend to N f = 2 more general: problem of large N c vs. N c = 3! inverse catalysis in QCD and NJL models how is IMC affected by the chiral shift? E. V. Gorbar, V. A. Miransky and I. A. Shovkovy, PRC 80, (2009) F. Preis, A. Rebhan, A. Schmitt, work in progress are recent lattice results for T c (B) related to IMC? G. S. Bali et al., JHEP 1202, 044 (2012)