Topological current effect on hQCD at finite density

and magnetic field

Pablo A. Morales

Work in collaboration with Kenji Fukushima

Based on Phys. Rev. Lett. 111, 051601 (2013)

Outline

INTRODUCTION• QCD Phase Diagram. AdS/CFT correspondance and

holography• The phase diagram according to the Sakai Sugimoto

model... And then introducing finite B?• Spatially Inhomogeneous phases• The Inhomogeneous phase according to the Sakai

Sugimoto model... And then introducing finite B?

Conclusions and Future Work (on the way)

Quantum Chromodynamics (QCD)

[Fukushima-Sasaki 2013]

Lattice QCD

PerturbativeQCD

?

• All contributions from the current-current interaction corresponding to the underlying symmetry must be included, not only (even when gauge fields are integrated out)

• Effects coming from vector-current , which gives rise to a density-density interactions, have been vastly studied in the phase diagram.

Crucial even at mean field approximation toliquid-gas phase transition of dense quark matter

• In order for Effective Field Theories to give an accurate description...

Complications in the QCD phase diagram go beyond inclusion of finite density

The inclusion of B in this picture is imperative:

• Early Universe• Neutron stars, Magnetars G • QGP in heavy ion collisions

• Chiral Magnetic Spirals• Magnetic Catalisys• Chiral Magnetic/Separation

Effect

Phenomenological and Experimental Theoretical side

𝑩𝒒𝑹 𝒒𝑳

momentum

spin

𝑩+¿

+¿

Quark Gluon Plasma

G

Magnetic field in the QCD phase diagram

Magnetic catalisys has been observed in effective field theories and lattice QCD (although with unphysical masses)

𝑩=𝟎

𝑩≫𝟎

Chemical PotentialCr

itica

l Tem

pera

ture

Chiral Boundary

Chirality is locked with the spinSo if we apply a magnetic field

𝑩𝒒𝑹

momentum

spin

𝒒𝑳

Just like vector-type interactions, even at mean field level the axial-vector interaction has a nonzero contribution, however it has been assummed to have no effect on the structure on the phase diagram

However, it is necessary to address on one importantphysical effect that has been overlooked up until now,

that is, the inevitable formation of the topological current!

Towards a Holographic Representation of QCD

The Sakai-Sugimoto model

The Gauge/Gravity Duality Weak Gravity

Strong GravityStrong CouplingWeak Coupling

Duality

difficult!easy!

Type IIB String Theoryon

CFT N=4Super Yang Mills

• The strong coupling limit (hard tosolve) in gauge theories happensto be dual to the weak gravity instring theory

• (Large ) limit of QCD. A theoryof gluon degrees of freedom

First step to QCD

=4 Super Yang Mills

0 1 2 3 4 5 6 7 8 9O O O O O

Minkowski CompactifyU

Holographic dim

𝑺𝑼 (𝑵 𝒄)𝑫𝟒

𝑫𝟒𝑋𝜇 , 𝑋 4

Properties:1. SUSY, Conformal2. No Chiral Symmetry3. No Confinement

Towards a holographic realizationof QCD

𝝉 𝑿𝟒

𝑼→∞

𝑼=𝑼 𝑲𝑲

𝝉 𝑿𝟒

𝑼→∞

𝑼=𝑼𝑻

Confined Deconfined

0 1 2 3 4 5 6 7 8 9O O O O O

O O O O O O O O O

Adding FlavorReceipt:Add Flavor branes and Distributed througout

𝜓𝐿𝜓𝑅

Close to QCD!1. SUSY broken2. Confinement3. Chiral Symmetry Breaking

Adding Flavor: Chiral Symmetry Breaking

L

When the two branes and are connectedin the interior of the bulk space. Fields do nottransform independently

𝑫𝟖

𝑿𝟒

𝑫𝟖

𝑿𝟒L

𝑼 (𝑵 𝒇 )𝑳

𝑼 (𝑵 𝒇 )𝑹

𝑼 (𝑵 𝒇 )𝑳×𝑼 (𝑵 𝒇 )𝑹

𝑫𝟒𝑫𝟒𝑼𝑻 𝑼 𝑼𝑻 𝑼

Holographic QCD phase diagram

[Bergman Lifschytz Lippert 2009]

• !• Second order PT to

nuclear matter• Constant

Holographic QCD phase diagram

...Still a question remains𝐁

Magnetic field in hQCD and topological current

DBI Action Chern-Simons Action

Flavor sector action

Equations of motion

Density Magnetic Field Current

Asymptotic solutions

[Preis, Rebhan, Schmidt 2013]

Topological current in the homogeneous chiral surface

Presence of quark matterneutron stars!

• Presence of topological current results in restoration of chiral symmetry at

• Whereas its absence results remains brokenFull chiral surface (ongoing reseach)

𝑩

𝝌 𝑺

Spacially modulated region in the phase diagram

Spatially Modulated PhasesInhomogeneous!

Effective Chiral models PNJL...

Lattice results

Chiral Spirals

[Bassar-Dunnes-Kharsheev][Hidaka-Kojo]

If the system the system atzero density has a condensate

Then the rotated system has the same condensate

This may be the case at high densities(Fermi surface realizes a pseudo (1+1)-dim system)

What should we expect at finite B?

Reduces the system effectively to a (1+1) dimensions.

Axial current is strengthened by strong B

Favors spiral configuration

Strong

Spatial Inhomogeneity + Topological axial current

Sakai Sugimoto model hQCD

Unperturbative QCD method

Inhomogeneous phase in hQCD

𝑘

𝜌=𝜌𝑐𝑟𝑖𝑡

𝜌<𝜌𝑐𝑟𝑖𝑡

𝜌>𝜌𝑐𝑟𝑖𝑡

• Imaginary dispersion relation Instability• Differential Equation dependant on

of

EOM decoupled in terms of dual fields

Sketch of calculations

[Ooguri-Park 2010]

A minimum value for the Chern-Simons coupling constant (at which instabilities can be found) can be determined analitically

However the corresponding critical density has to be found numerically

[Chuang-Dai-Kawamoto-Lin-Yeh 2011]

This instability can be predicted to occur in QGP

𝐁

...Then again what happens atfinite B?!

Addition of a magnetic field into the picture results into the breaking of rotational invariance of the EOM corresponding to the fluctuations and thus the system cannot be trivially decoupled in terms of the dual field as usual.

• So we solve numerically, from the condition that these fluctuations correspond to normalizable modes

[Fukushima-Morales 2013]

...presence of current changesresults drastically!

phase is enhanced with

[Fukushima-Morales 2013]

Surprising results!

However...

+𝐵

Topological current Less spirals!

dimensional reduction more spirals!

Shrinking of Inhomogeneous phase!

Conclusions/Future work• Holographic QCD provides us the means to study unpertubatively

the effect of the topological axial current in the phase diagram

• The role played the topological current in the phase diagram is critical to its homogeneous part and inhomogenous phase as well... ..(What happens in other effective chiral models? Universal Feature?)

• Could this Inhomogeneous phase be the dual of the ground state in QCD... (Chiral Spirals?)

Inhomogeneous Phases

[Ooguri-Nakamura 2011]

Chern-Simmons term in 5 dimensions can turn the Maxwell theory tachyonic through a magnetic field

When considering coupling to gravity, although the stability condition is modifiedin more complicated geometries, tachyonic modes can be found

Bottom-up approach