Abstract
It is well known that non-perturbative α′ corrections to the SL(2, ℝ)/U(1) cigar geometry are described via a condensation of a Sine-Liouville operator that schematically can be written as W+ + W−, where W± describe a string with winding number ±1. This condensation leads to interesting effects in the cigar geometry that take place already at the classical level in string theory. Condensation of the analytically continued Sine-Liouville operator in the Lorentzian SL(2, ℝ)/U(1) black hole is problematic. Here, we propose that in the black hole case, the non-perturbative α′ corrections are described in terms of an operator that can be viewed as the analytic continuation of the fusion of W+ and W−. We show that this operator does not suffer from the same problem as the analytically continued Sine-Liouville operator and argue that it describes folded strings that fill the entire black hole and, in a sense, replace the black hole interior. We estimate the folded strings radiation, and show that they radiate at the Hawking temperature.
Highlights
It is well known that non-perturbative α corrections to the SL(2, R)/U(1) cigar geometry are described via a condensation of a Sine-Liouville operator that schematically can be written as W + + W −, where W ± describe a string with winding number ±1
This condensation leads to interesting effects in the cigar geometry that take place already at the classical level in string theory
We propose that in the black hole case, the non-perturbative α corrections are described in terms of an operator that can be viewed as the analytic continuation of the fusion of W + and W −
Summary
We argued that (1.3) has a precise meaning: F should be viewed as a bound state of W + and W − in the sense of (2.9) This is a strong claim: it implies that in correlation functions we can replace integrals over pairs of W + and W − with F ’s, e.g. that n λ2Wn j=1 n d2zjW +(zj) l=1. Whereas in the calculation based on on the r.h.s. implies that the integrals over zj on its l.h.s. must only receive contributions from regions where each of the W +’s approaches one of the W −’s (i.e. one of the zj is close to one of the wl), and the contribution from one such region is given by the r.h.s. of (3.1). Equation (1.1) implies that there is an attractive potential on the worldsheet, V ∼ k log |z − w|2, between W +(z) and W −(w); it is likely that this is part of the explanation for the formation of F
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