QCD Junctions from AdSCFT

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QCD Junctions from AdS/CFT
hep-th/0410138, hep-th/0512xxx
Univ. of Tokyo Yosuke Imamura
12/14/2005 Workshop Flavor Physics and its
Origin
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Wilson loop
We consider SU(N) Pure Yang-Mills
(non-supersymmetric)
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Baryon vertex
We want to determine
Baryon vertex
with AdS/CFT
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AdS blackhole background
The same solution with that used in
Sakai-Sugimoto model
4-dim Minkowski
gravitational force
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D-branes carry the RR charge.
RR 4-form flux
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AdS dual of QCD junction
(Witten, Ooguri Vafa)
This turns out to be incorrect !
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Tension of QCD strings
QCD string tension T(k) depends on k
T(k) satisfies T(0)0 0-strings no
strings T(kN)T(k) k is defined only mod
N T(-k)T(k) A (-k)-string is a k-string in
the opposite dir.
tension T(k)
k
0
N
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AdS dual of k-string
(Herzog and Klebanov)
Strings in RR flux expand to a D-brane tube
electric flux
Myers effect
k fundamental strings
D4-brane tube
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(To make it easy to imagine) lets lower the
dimensions by 2.
The cross section behaves like a flexible
superconducting ring with finite tension in a
magnetic field background.
magnetic field background RR flux
current electric flux on the D-brane
If the ring shrinks by its tension, current on
the ring is induced by the electromagnetic
induction.
The brane configuration is determined by the
balance between the current and the tension.
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If the tension were 0,
the ring would become stable when the current
vanished.
k flux
cross section
k-string
The mod N nature of the string charge is
geometrically understood
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The tension is non-vanishing in reality
both the flux and the current contribute to the
string charge
differential form
The energy of the brane is
Given a string charge k, we determine brane
configuration so that it minimize the energy
under the Gauss constraint. The tension is
obtained as Energy/length
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QCD string tension
tension T(k)
k
0
N
reproduces the correct behavior of T(k)
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Numerical analysis of QCD string junctions
QCD junction
D4-brane
Myers effect
electric flux
Technical difficulty We cant solve the E.O.M.
analytically
Numerical method
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Result
The vertex contribution is unexpectedly small and
negative.
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Summary

• Energy of baryon vertices are computed by
  AdS/CFT.
• The absolute value is less than 4 of that of a
  wrapped brane and the signature is negative.

Questions
How can we explain it in QCD? How should we
treat endpoints of D4-tubes (quarks), which is
necessary to compute (high energy) baryon
spectrum.