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Large N c QCD

Towards a Holographic Dual of. Large N c QCD. ECT, Trento, July 2004. David Mateos Perimeter Institute. Based on:. Towards the Holographic Dual of Large N c QCD (hep-th/0311270) M. Kruczenski, DM, R. Myers and D. Winters The Holographic Life of the (hep-th/0404260)

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Large N c QCD

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  1. Towards a Holographic Dual of Large Nc QCD ECT, Trento, July 2004 David Mateos Perimeter Institute

  2. Based on: • Towards the Holographic Dual of Large Nc QCD (hep-th/0311270) • M. Kruczenski, DM, R. Myers and D. Winters • The Holographic Life of the (hep-th/0404260) • J. Barbon, C. Hoyos, DM and R. Myers Related work: • Meson Spectroscopy in AdS/CFT with Flavour (hep-th/0304032) M. Kruczenski, DM, R. Myers and D. Winters

  3. Nf D-brane probes = Open Strings Gravity = Closed Strings Mystery of strong interaction dynamics Dynamical Probes Phenomenology (mesons, baryons,…) QCD = SU(Nc) Yang-Mills + Nf quarks (especially in ‘t Hooft limit: Nc!1 , Nf fixed )

  4. Plan • AdS/CFT with Flavour • QCD from D4/D6 • Nc=1 , Nf=1: SSB and meson spectrum (goldstone boson) • Nc=1 , Nf >1: Holographic Vafa-Witten, and pions? • Baryons • Nc finite: 0 physics (Barbon’s talk)

  5. Gauge Theory Decoupling Limit Correspondence String Theory AdS/CFT with Flavour QCD Maldacena AFM, KR, KK SU(Nc) SYM in Mink4+1 Gluons + Adjoint Scalars and Fermions Fundamental Scalars and Fermions in Mink3+1 Interacting closed + open strings Nc D4-branes Holographic 4 Nf D6-branes Closed Stringsin `AdS’ + Nf D6 probes 0123 567 Nf¿ Nc D6 Mink4+1 =  AdS `AdS’ Nc!1

  6. U(1)A QCD from D4/D6 Nc D4: 0 1 2 3 4 _ _ _ _ _ Nf D6: 0 1 2 3 _ 5 6 7 _ _ • On D4-branes: 4+1 SU(Nc) SYM = Gluons + Adjoint Scalars and Fermions • Compactify 4-direction with antiperiodic boundary conditions for Adjoint Fermions Witten • Renders theory four-dimensional at E ¿ MKK = 1 / RKK • Breaks SUSY: Gives masses to Adjoint Fermions (tree level) and Adjoint Scalars (one-loop) • With D6-branes: Nf flavours of 3+1 Fundamental Scalars + Dirac Fermions L+ R • Fundamental Scalars aquire one-loop mass • Fundamental Fermions remain massless because protected by chiral U(1)A So do we have QCD at E ¿ MKK ?

  7. E # 2 e gYM (MKK) Nc QCD» MKK Decoupling String description has: Curvature » 1 2 2 gYM NcÀ 1 gYM Nc¿ 1 Supergravity approximation 2 gYM Nc So do we have strictly QCD ? No, but many features are captured, and confining theory in its own right. MKK QCD

  8. The Vacuum: D6-brane Embedding and SSB  567 D6 D6-brane probe in D4-brane background:  567  567 D6 D6 Nc D4: 0 1 2 3 4 _ Nf=1: D6: 0 1 2 3 _ 5 6 7 _ _  567 r (  ) D6 r ,   r r  () r Minimum energy  = const , r =r() Proportional mq Field/Operator Correspondence: r () Vacuum embedding: Choose a and adjust b for regularity Unbroken SUSY: r = mq Broken SUSY… 89-plane Asymptotically (!1): r = a + b /  + …

  9. The Vacuum: D6-brane Embedding and SSB mq mq SSB Finite bump remains r() mq! 0 

  10. The Vacuum: D6-brane Embedding and SSB as mq! 0 for large mq

  11. Meson Spectrum   D6 D6 r r    non-normalizable  normalizable = Regular, normalizable fluctuations: n» ei k ¢ x fn() , Mn2 = - k2 SSB Pseudo-scalar Goldstone boson, k2 = 0:

  12. Meson Spectrum Scalars Pseudo-scalars GMOR M2 (analytically!) M2KK Scale set by MKK Degeneracy?

  13. Meson Spectrum Supersymmetry restoration M2 M2 M2KK M2KK

  14. QCD with Nf flavours of mass mq >0 U(Nf)V is not spontaneously broken Nf D6-branes Nf D6-branes r r   Unbroken Spontaneously Broken Fij = [i Aj] + [Ai,Aj] • Gauge theory contains Holographic Vafa-Witten Theorem and Nf >1 Spectrum In brane picture U(Nf)V is gauge symmetry: Spectrum ¾ Nf2 massless pseudo-scalars Goldstone Bosons of U(Nf)V£ U(Nf)A! U(Nf)V ? Probably not: • Non-derivative interactions (from D6s action) Gauge theory reason? String mechanism: D=9+1 Gauge Invariance NA DBI = A DBI +[Xi,Xj]

  15. D4 = Baryonic Brane Baryon? Baryons: Constituent quarks vs Chiral Soliton Baryons: Constituent quarks vs Chiral Soliton Baryons: Constituent quarks vs Chiral Soliton Meson BIon D6 = Flavour Brane AdS

  16. Conclusions What is String Theory good for? Many things. As far as QCD is concerned, at the very least it provides a new, geometric way of looking at old problems.

  17. Finite Nc and Physics Massless quarks Physics depends only on  + Nf ED6() Calculable in pure D4 background (ie no D6) Exact agreement To quadratic order: Witten-Veneziano To linear order: Tadpole = YM Nf

  18. String corrections to propagator: Gauge theory Finite Nc and Physics String analog of de Rujula-Georgi-Glashow: Splits U(Nf) singlet from non-singlets… Provided -glueball coupling is non-zero at p=0 ! Shown in SUGRA limit from D6 couplings

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