Mesons and Baryons in AdS/CFT (Short Introduction)
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Mesons and Baryons in AdS/CFT(Short Introduction)
Mesons and Baryons in AdS/CFT(Short Introduction)
Yunseok SeoHanyang University
Heavy Ion Meeting, Nov, 15, 2008
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IntroductionIntroduction
String theory
Fundamental object : one dimensional string
Open string Closed string
D-branes : p-dimensional extended object
5 different theory (type I, type IIA, type IIB, Heterotic SO(32), Heterotic )
Contains gauge field and gravity in the theory
Spacetime dimension : 10
Closed stringOpen string
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AdS/CFT CorrespondenceAdS/CFT Correspondence
Nc D3 branes
Duality
Low energy limit
Duality
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AdS/CFT CorrespondenceAdS/CFT Correspondence
Adding Flavour : Introducing probe D-brane
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Finite temperatureFinite temperature
Finite temperature : Introducing black hole
Temperature and horizon related by
DBI action
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Finite TemperatureFinite Temperature
Erdmenger et al.
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Finte DensityFinte Density
Boundary global symmetry
AdS/CFT
bulk guage symmetry
Gauge field on D-brane
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Finite DensityFinite Density
Minkowski Embedding Blackhole
Embedding
Black hole
Solution of DBI action
Blackhole embeddings have lower energy
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Adding sourceAdding source
LF1
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Witten’s Baryon VertexWitten’s Baryon Vertex
Chern-Simons coupling gives flux on D5(or D4) brane
To cancel the flux, we need Nc fundamental strings
F1’s
D3 or D4 brane
D5 or D4 brane
We need special background which provide confining phase
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Dilaton background geometry Dilaton background geometry
Gubser’s background
Deformation of D3 brane background
Supersymmetry and chiral symmetry are broken
Special limit of ‘Constable-Myers’ background (δ=2)
is proportional to the gluon condensation in boundary
theory
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Baryon vertexBaryon vertex
Baryons : D5 brane wrapped on an S5 on which Nc F1’s terminate The background 5-form field strength can couple to the world volume U(1)
gauge field via Chern-Simons term
DBI action for single D5 brane with Nc F1’s
Induced metric on D5 brane
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Baryon vertexBaryon vertex
Equation of motion
D5 brane solution
Force at cusp
D4/D6(D3/D5) YS, S Sin, JHEP 0804:010, 2008
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We consider D7 brane as a probe brane where the other end point of fundamental strings are attached
End point can be regarded as point source on D7 brane
Probe D7 braneProbe D7 brane
Induced metric on D7 brane
DBI action
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Probe D7 braneProbe D7 brane
Force at the cusp of D7 brane(Q≠0)
Solution of equation of motion for D7 brane(Q=0)
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Force balance conditionForce balance condition
Total configuration(Baryon D5 + F1’s +probe D7) can be stationary if there is force balance condition
Force balance condition
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Chiral condensationChiral condensation
Asymptotic behavior of D7 brane
Chiral condensation
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Baryon mass for Fixed quark massBaryon mass for Fixed quark mass
Deformation of D-brane
Deformation of D5 brane Baryon mass
Deformation of D7 brane Baryon-baryon interaction
Density dependence of baryon mass
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SummarySummary
AdS/CFT provides a method of calculating properties of gaue theories at strong couplingGauge theories at finite temperature can be studied by introducing black hole in the bulkDensity and chemical potentials can be easily introduced by turn on gauge field on probe brane
Meson spectrum : fluctuation of probe braneBaryon vertex: D5 brane wrapping D3 brane