Wilson - Polyakov Loop at Finite Temperature in Large N Gauge Theory

Aspects of d = 4,N = 4 superconformal U(N) gauge theory are studied at finite temperature. Utilizing the dual descriptions of the large N and strong coupling limit via Type IIB string theory compactification on Schwarzschild anti-de Sitter spacetime, we study correlations of Wilson-Polyakov loops and the static quark anti-quark potential thereof. We find two branches of macroscopic string representing the Polyakov-Wilson loop. On the outer horizon branch the loop is timelike and behaves similar to zero temperature counterpart. The interquark potential interpolates Coulomb and confinement behavior as the temperature is varied. On the inner horizon branch the loop is spacelike and terminates its quark ends at finite distance on Schwarzschild horizon. This implies dissipation of electric flux over Schwarzschild horizon, which is responsible for confinement behavior at finite temperature. To gain further insight, single quark state on probe D3-brane world-volume is also studied. Interpreting the Schwarzschild redshift function as dielectric constant, we find that it becomes purely imaginary as the D3brane falls inside Schwarzschild horizon, accounting possibly for the dissipative behavior in a way reminiscent to black hole membrane paradigm. 1 Work supported in part by KOSEF SRC-Program,Ministry of Education Grant BSRI 97-2418, SNU Faculty Research Fund and Korea Foundation for Advanced Studies Faculty Fellowship, by GIF the German-Israeli Foundation for Scientific Reseach and by the European Commission TMP Programme ERBFMRX-CT96-0045.