This research has been co-financed by the European Union (European Social Fund, ESF) and Greek national funds through the Operational Program ”Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF), under the grants schemes ”Funding of proposals that have received a positive evaluation in the 3rd and 4th Call of ERC Grant Schemes”, and under the action “ARISTEIA”, as well as the EU program “Thales” ESF/NSRF 2007-2013. Recent progress in holographic QCD

Matti J¨arvinen

University of Crete −→ Ecole´ Normale Sup´erieure,Paris

XIth confinement and spectrum St Petersburg – 11 September 2014

1/16 Outline

This talk: model construction 1. Introduction to holographic QCD

I Top-down approach

I Bottom-up approach 2. Improved holographic QCD

I Holographic model for Yang-Mills 3. V-QCD

I Holographic model for QCD with backreacted

2/16 AdS/CFT

Generic structure I Conformal field theory on the boundary ↔ in the bulk I Field theory at large Nc and λ ↔ Classical limit of string theory (supergravity) Dictionary I Operator Oi (x) on the bdry ↔ field φi in the bulk

ZCFT[Ji (x)] = Zsugra[φi ] φi (x)=Ji (x) @ bdry

I Here Ji (x) is the source for Oi (x) Apply to QCD? I Supported by QCD string picture (’t Hooft)? I Could shed on the strongly coupled IR I Duality however works only for certain field theories (typically conformal and SUSY) ⇒ QCD difficult! 3/16 Holographic QCD: Top-down approach

Constructions directly motivated by the original AdS/CFT duality

I Concrete, fixed string models in 10/11 d Quarks I Specific brane intersections

I Typically probe quarks in glue background

I Control on what dual field theory is However.. I Field theory not QCD (Light Kaluza-Klein modes..)

I Still works quite well!

E.g., Sakai-Sugimoto model: D4-D8-D8

4/16 Holographic QCD: Bottom-up approach

Holographic models constructed “by hand”

I Follow generic principles of holography

I Lots of freedom → effective 5d description, no link to specific dual theory

I (Surprisingly?) good description of QCD data

I Difficult to improve systematically

I Results often depend on the choice of boundary conditions

Examples

I Hard-wall and soft-wall models

I Light-front holography

5/16 Improved holographic QCD

IHQCD: bottom up model for pure Yang-Mills inspired by string theory [Gursoy, Kiritsis, Nitti] [Gubser, Nellore] Idea:

I Follow generic structure predicted by string theory as closely as possible → Ansatz for Lagrangian, better control on the model

I Explore all remaining degrees of freedom

Implementation:

I Five-dimensional noncritical string theory

I Brane construction, Nc D3 branes

6/16 Result: Z √  4 (∂λ)2  S = M3N2 d5x g R − + V (λ) g c 3 λ2 g

Issue:

I Vg has wrong UV behavior, “bad dictionary” (λ → 0, no surprise!)

I Fix by hand: map Vg to QCD beta function instead in the UV

Exploration of all choices of Vg in the IR ⇒ String theory prediction (power-law) + minor corrections (logarithmic) works

I “Good” IR singularity: all IR boundary conditions uniquely fixed

7/16 Good agreement with pure YM lattice data, both at zero and finite temperature [Gursoy, Kiritsis, Mazzanti, Nitti; Panero; . . . ]

Trace of the energy-momentum tensor

1.8

1.6 SU(3) 4

T SU(4)

/ 1.4 SU(5) p SU(6) 1.2 SU(8) improved holographic QCD model 1

0.8

0.6 , normalized to the SB limit of 4

T 0.4 / ∆ 0.2

0 0.5 1 1.5 2 2.5 3 3.5 T / Tc 8/16 Adding (probe) flavor in IHQCD

Framework: D4-D4 (space-filling) probe branes ⇒ Sen like brane action (Tachyonic Dirac-Born-Infeld) [Klebanov,Maldacena; Bigazzi,Casero,Cotrone,Kiritsis,Paredes]

Results in the probe limit (fundamental quarks):

I Confining asymptotics of the geometry triggers chiral symmetry breaking

I Gell-Mann-Oakes-Renner relation

I Linear Regge trajectories for

I A very good fit of the light masses

[Gursoy,Kiritsis,Nitti; Iatrakis,Kiritsis,Paredes]

9/16 V-QCD: motivation

Veneziano limit: large Nf , Nc with x = Nf /Nc fixed ⇒ backreaction

Backreaction ⇒ better modeling of (ordinary) QCD?

Important new features can be captured in the Veneziano limit:

I Phase diagram of QCD (at zero temperature, density, and quark mass), varying x = Nf /Nc I The QCD thermodynamics as a function of x

I Phase diagram as a function of baryon density

I Effect of turning on a finite quark mass at finite x

10/16 V-QCD: the fusion

The fusion: 1. IHQCD: model for glue by using dilaton 2. Adding flavor and chiral symmetry breaking via tachyon brane actions Consider1 . +2 . in the Veneziano limit with full backreaction ⇒ V-QCD models [MJ, Kiritsis]

11/16 Defining V-QCD

Degrees of freedom 2 I The tachyon τ ↔ qq¯ , and the dilaton λ ↔ TrF φ 2 I λ = e is identified as the ’t Hooft coupling g Nc

Z √  4 (∂λ)2  S = N2M3 d5x g R − + V (λ) V−QCD c 3 λ2 g Z 3 5 p −Nf Nc M d xVf (λ, τ) − det(gab + κ(λ)∂aτ∂bτ)

2 2 2A(r) 2 µ ν Vf (λ, τ) = Vf 0(λ) exp(−a(λ)τ ); ds = e (dr +ηµνx x )

Need to choose Vf 0, a, and κ ... The same strategy as for IHQCD works (!): I Match to perturbative QCD in the UV I Logarithmically modified string theory predictions in the IR 12/16 Phase diagram of V-QCD

At zero quark mass and temperature, constructing numerically all vacua, QCD phase diagram reproduced:

0 ChS x c~4 ChS x BZ =11/2

QCD-like IR-Conformal QED-like

Running Walking IRFP Banks- Zaks

I Conformal transition (BKT) at x = xc ' 4 [Kaplan,Son,Stephanov;Kutasov,Lin,Parnachev] h 2K i I Miransky scaling, hqq¯ i ∼ exp − √ , in walking regime xc −x

13/16 T

1000 Phase diagram at finite T Tcrossover 10 x [Alho,MJ,Kajantie,Kiritsis,Tuominen] c 0.1 Th > Tend

0.001 Tend > Th x 0 1 2 3 4

T 0.20

Example at finite T and µ 0.15 Chirally symmetric plasma [Alho,MJ,Kajantie, 0.10 Kiritsis,Rosen,Tuominen] Hadron ΧSB plasma 0.05 gas

Μ 0.0 0.1 0.2 0.3 0.4 0.5 14/16 Spectra etc in V-QCD

mLUV òà òà òà òà òà òà òà æ æ æ æ æ æ æ òà ì æ ì ì ì ì ì ì ì òà 1 æ ì

òà 0.1 æ Masses of lowest modes ì Spectrum of light mesons æ Vectors 0.01 à Axial vectors (nothing fitted to data yet) ì Scalars 0.001 ò Pseudoscalars òà æ ì - 10 4 æ x S-parameter 1 2 3 4 SHNcN f L

0.30 xc xBZ Axial anomaly 0.25 [Arean,Iatrakis,MJ,Kiritsis; MJ] 0.20 0.15 0.10 0.05 0.00 x 1 2 3 4 5 15/16

T 0.20

Example at finite T and µ 0.15 Chirally symmetric plasma [Alho,MJ,Kajantie, 0.10 Kiritsis,Rosen,Tuominen] Hadron ΧSB plasma 0.05 gas

Μ 0.0 0.1 0.2 0.3 0.4 0.5 Conclusion

I An ongoing program for constructing holographics duals for QCD with backreacted quarks

I Qualitative agreement with QCD data/expectations

I Next step: quantitative fit to experimental/lattice data

16/16 Extra slides

17/16 Improved holographic QCD

IHQCD: well-tested string-inspired bottom-up model for pure Yang-Mills

Z √  4 (∂λ)2  S = M3N2 d5x g R − + V (λ) g c 3 λ2 g with the metric

2 2A(r) 2 µ ν ds = e (dr + ηµνx x )

I A → log µ energy scale φ 2 I λ = e → ’t Hooft coupling g Nc 2 I φ ↔ Tr(F ) gµν ↔ Tµν

18/16