The Hagedorn transition, deconfinement and SYM theory

Phase transitions of largeNorbifold gauge theories

“…This case is almost the same as the R × S 3 case analyzed in [2,3]. The solution is given by the form of the Gross-Witten ansatz [17] as…”

“…The critical temperatures x c and T c are summarized for small k in Table 1. We should note that for k = 1 the critical temperature reduces to the one for R × S 3 case [2,3] as x c = 7 − 4 √ 3 = 0.071797 or T c = 0.379663. Another interesting case may be with the Z k symmetric holonomy n I = N/k for all I.…”

“…In general, the counting of gauge invariant operator is an involved task. Fortunately, it was shown in [2,3] that the partition function of gauge invariant operator can be written in terms of single-particle partition functions as…”

“…Moreover, the large N gauge theories may have their dual description in terms of string theory on an asymptotic Anti-de Sitter (AdS) space [1]. For example, the partition function for a large N gauge theory on R × S 3 was computed in [2,3], and it was shown that the partition function is of order O(1) at low temperature and of order O(N 2 ) above a critical temperature. In the dual gravity theory, the phase transition corresponds to the HawkingPage transition [4,5], where the thermal AdS space is dominant at low temperature and the AdS-Schwarzschild black hole is dominant at high temperature.…”

“…In the next section, we define the orbifold gauge theories on R × S 3 /Z k with generic holonomy by utilizing the standard orbifold method as in [18]. We compute the partition function for the orbifold gauge theories by following [2,3]. In section 3 we analyze the partition function and discuss the phase structure.…”