14 05 imamura

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QCD Junctions from AdS/CFT Univ. of Tokyo Yosuke Imamura hep-th/0410138, hep-th/0512xxx 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 Baryon vertex We want to determine with AdS/CFT

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4-dim Minkowski gravitational force AdS blackhole background The same solution with that used in Sakai-Sugimoto model

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RR 4-form flux D-branes carry the RR charge.

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This turns out to be incorrect ! AdS dual of QCD junction (Witten, Ooguri & Vafa)

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QCD string tension T(k) depends on k T(k) satisfies T(0)=0 : 0-strings = no strings T(k+N)=T(k) : k is defined only mod N T(-k)=T(k) : A (-k)-string is a k-string in the opposite dir. k 0 N tension T(k) Tension of QCD strings

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Strings in RR flux expand to a D-brane tube Myers’ effect k fundamental strings D4-brane tube AdS dual of k-string (Herzog and Klebanov) electric flux

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The cross section behaves like a flexible superconducting ring with finite tension in a magnetic field background. 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. magnetic field = background RR flux current = electric flux on the D-brane (To make it easy to imagine) let’s lower the dimensions by 2.

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the ring would become stable when the current vanished. k-string The mod N nature of the string charge is geometrically understood k flux cross section If the tension were 0,…

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both the flux and the current contribute to the string charge 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 The tension is non-vanishing in reality differential form

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k 0 N tension T(k) QCD string tension reproduces the correct behavior of T(k)

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Numerical analysis of QCD string junctions Technical difficulty: We can’t solve the E.O.M. analytically Numerical method Myers’ effect electric flux D4-brane QCD junction

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The vertex contribution is unexpectedly small and negative. Result

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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. Summary 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.