### Abstract

Abstract: Spacetime Virasoro and affine Lie algebras for strings propagating in AdS_{3} are known to all orders in α′. The central extension of such algebras is a string vertex, whose expectation value can depend on the number of long strings present in the background but should be otherwise state-independent. In hep-th/0106004, on the other hand, a state-dependent expectation value was found. Another puzzling feature of the theory is lack of cluster decomposition property in certain connected correlators. This note shows that both problems can be removed by defining the free energy of the spacetime boundary conformal field theory as the Legendre transform of the formula proposed in the literature. This corresponds to pass from a canonical ensemble, where the number of fundamental strings that create the background can fluctuate, to a microcanonical one, where it is fixed.

Original language | English (US) |
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Article number | 76 |

Journal | Journal of High Energy Physics |

Volume | 2015 |

Issue number | 5 |

DOIs | |

State | Published - May 22 2015 |

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### Keywords

- AdS-CFT Correspondence
- Conformal Field Models in String Theory

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

_{3}

*Journal of High Energy Physics*,

*2015*(5), [76]. https://doi.org/10.1007/JHEP05(2015)076