Time-dependent heavy-quark potential at finite temperature from gauge-gravity duality

K. Nawa, T. Hayata and T. Hatsuda, in preparation

Cited in the paper.

For configuration I, there exist two real solutions, a local minimum (maximum) of S NG S_{\mathrm{NG}} . For large π ​ T ​ τ \pi T\tau , they undergo a pair annihilation and the real solution disappears. However, such an annihilation happens only after the configuration II takes over the configuration I. As for the configuration III, the real solution does not appear for π ​ T ​ τ < π − 1 \pi T\tau<\pi-1 . Furthermore, the configurations II and III take the same S NG S_{\mathrm{NG}} at π ​ T ​ τ = π − 1 \pi T\tau=\pi-1

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Similar situation has also been found in the weak-coupling perturbation, Eq.(3.10) of Ref. [ 9 ] : V ⁡ ( t , r ) V(t,r) behaves as i / t i/t for t ≪ r t\ll r , while it is highly suppressed as i ​ r 2 / t 3 ir^{2}/t^{3} for t ≫ r t\gg r

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By generalizing the box ansatz near the cusp, the potential from the cusp can be suppressed already at t ∼ 0.5 ​ ( π ​ T ) − 1 t\sim 0.5(\pi T)^{-1} . This is because the bottom of the world sheet touches the event horizon at τ ∼ 0.5 ​ ( π ​ T ) − 1 \tau\sim 0.5(\pi T)^{-1} and r ∼ 0.5 ​ ( π ​ T ) − 1 r\sim 0.5(\pi T)^{-1} . Such suppression is expected to occur for even smaller t t in the exact configuration for which the world sheet tends to hang deeper

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If we identify r dis r_{\rm dis} with the typical Q Q - Q ¯ \bar{Q} distances in the heavy quarkonia, we find the dissociation temperature T dis = 390 T_{\rm dis}=390 , 220 220 and 190 190 MeV for Υ \Upsilon ( 1 1 S), J / Ψ J/\Psi and Υ \Upsilon ( 2 2 S), respectively

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