On non-homogeneous tachyon condensation in closed string theory

Abstract

Lorentzian continuation of the Sine-Liouville model describes nonhomogeneous rolling closed string tachyon. Via T-duality, this relates to the gauged H 3 + Wess-Zumino-Witten model at subcritical level. This model is exactly solvable. We give a closed formula for the 3-point correlation functions for the model at level k within the range 0 < k < 2, which relates to the analogous quantity for k > 2 in a similar way as how the Harlow-Maltz-Witten 3-point function of timelike Liouville field theory relates to the analytic continuation of the Dorn-Otto-Zamolodchikov-Zamolodchikov structure constants: we find that the ratio between both 3-point functions can be written in terms of quotients of Jacobi's θ-functions, while their product exhibits remarkable cancellations and eventually factorizes. Our formula is consistent with previous proposals made in the literature.

2D quantum gravity partition function on the fluctuating sphere

“…By exponentiation, this implies that a sum of the form S(n) = n r=1 f (r) admits the extension S(−n) = − n−1 r=0 f (−r). This prescription has already been used in the context of non-rational CFTs [48,52] and its consistency can be checked by considering simple examples such as the geometric series n r=1 p r , the Faulhaber's numbers n r=1 r p and generalizations. This leads to expressions like +n r=−n γ(rb 2 ) = b −4n−2 γ(−n) which often appear in CFT calculations.…”

2D quantum gravity partition function on the fluctuating sphere

“…By exponentiation, this implies that a sum of the form S(n) = n r=1 f (r) admits the extension S(−n) = − n−1 r=0 f (−r). This prescription has already been used in the context of nonrational CFTs [50,54] and its consistency can be checked by considering simple examples such as the geometric series n r=1 p r , the Faulhaber's numbers n r=1 r p and generalizations. This leads to expressions like +n r=−n γ(rb 2 ) = b −4n−2 γ(−n) which often appear in CFT calculations.…”