topological current effect on hqcd at finite density and magnetic field pablo a. morales work in...
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![Page 1: Topological current effect on hQCD at finite density and magnetic field Pablo A. Morales Work in collaboration with Kenji Fukushima Based on Phys. Rev](https://reader030.vdocuments.us/reader030/viewer/2022032722/56649cdb5503460f949a59cc/html5/thumbnails/1.jpg)
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)
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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)
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Quantum Chromodynamics (QCD)
[Fukushima-Sasaki 2013]
Lattice QCD
PerturbativeQCD
?
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• 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...
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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
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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
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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!
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Towards a Holographic Representation of QCD
The Sakai-Sugimoto model
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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
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=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
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𝝉 𝑿𝟒
𝑼→∞
𝑼=𝑼 𝑲𝑲
𝝉 𝑿𝟒
𝑼→∞
𝑼=𝑼𝑻
Confined Deconfined
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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
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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
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Holographic QCD phase diagram
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[Bergman Lifschytz Lippert 2009]
• !• Second order PT to
nuclear matter• Constant
Holographic QCD phase diagram
...Still a question remains𝐁
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Magnetic field in hQCD and topological current
DBI Action Chern-Simons Action
Flavor sector action
Equations of motion
Density Magnetic Field Current
Asymptotic solutions
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[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
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Spacially modulated region in the phase diagram
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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)
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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
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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
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[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?!
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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
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[Fukushima-Morales 2013]
Surprising results!
However...
+𝐵
Topological current Less spirals!
dimensional reduction more spirals!
Shrinking of Inhomogeneous phase!
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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?)
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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
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