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...tion (3.8) grows, and eventually the Unruh temperature (3.6) reaches the Hagedorn temperature of perturbative string theory in the linear dilaton throat (2.1), (2.2). The latter is given by (see e.g. =-=[45]-=-) 1 Th = 2π √ . (3.9) 4 − Q2 Thus, Tu = Th when Q 2 = 2. At that point, one expects the effect of the classical condensate of open strings to be large. Indeed, the exact boundary state has the propert...

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...bosonic SL(2, IR) WZW model of level k + 2, and three free fermions in the adjoint representation that contribute −2 to the level. In our case Q = 1, so k = 2. This value lies above the transition of =-=[28,20]-=-, so the black hole is a normalizable state in the near-horizon geometry. The Euclidean black hole is obtained by Wick rotating t → it in (2.7). This gives rise to a cigar geometry, and one can read o...

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...or the entropy only through their effect on the area. To recapitulate, we found that the correction to the entropy depends on the charges only through the horizon area. Previously, it was observed in =-=[18]-=- that the entropy of two dimensional charged black holes is proportional to the area of the horizon for any value of the charges and the mass. The entropy rather than being a more general function of ...

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... It can be shown using the (type B) boundary conditions on the N = 2 SCA generators. 15 Another way to reach this conclusion is to consider the effective linear dilaton CFT living on the long strings =-=[77]-=-. 21over the zero modes of S 3 × T 4 , the amplitude (4.42) for large N and P behaves like: ¯Nc ∼ 1 k ∞∑ w=1 1 ω e−π√ k 2 w {∫ ∞ 0 dP e −2π [√ 2 P k k 2 w −P ]} ∑ N N γ e −2π (√ 2 N k w −√ (2−1/k)N )...

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...ics in section 4, which is in close resemblance to the case in flat space. In section 5 we discuss some implication of our results to a conjectured strings/black hole correspondence in AdS3 space. In =-=[19]-=- some aspects on the correspondence between strings in AdS3 and BTZ black hole are uncovered by taking a different approach in that the parameter k is varied. Instead here we examine the theory by cha...

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...pproaches 1, when the 2D black hole (and correspondingly the zero-mode solution (4.6)) turn non-normalizable [19]. The critical k = 1 level is also where the black-hole/string phase transition occurs =-=[36]-=-. At k = 2 (when e2Φ(ρ) and T (ρ) have the same asymptotic behavior, (4.2)), it was conjectured [37] that string theory on the background (3.3) describes the type II string on a small 4D Schwarzschild...

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...ecisely at the point where the Hawking temperature of the black hole reaches the (limiting) fundamental string temperature. At the transition, the fundamental string and black hole entropies coincide =-=[5]-=-. In section 3, we study RN black holes in d ≥ 4 dimensions. Like in the Schwarzschild case, the exact CFT corresponding to these geometries in string theory is not known, but as in [1], we can test t...

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...ear dilaton charge QD is related to the bosonic level k ′ b of the S3 /ZN theory as where k ′ b = k′ s − 2 = NN ′ , if we assume k ′ s = NN ′ + 2. Q 2 D = 2 k ′ , (5.7) b + 2 Finally, as explained in =-=[40]-=-, there is a simple relation between linear dilaton and SL(2) models. Adding p D1-branes along the R 1,1 and taking the near-horizon limit amounts to replacing the factor R 1,1 × R φ by AdS3. The leve...

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...or the entropy only through their effect on the area. To recapitulate, we found that the correction to the entropy depends on the charges only through the horizon area. Previously, it was observed in =-=[18]-=- that the entropy of two dimensional charged black holes is proportional to the area of the horizon for any value of the charges and the mass. The entropy rather than being a more general function of ...