## Abstract

Logarithmic timelike Liouville quantum field theory has a generalized PT invariance, where T is the time-reversal operator and P stands for an S-duality reflection of the Liouville field φ. In Euclidean space, the Lagrangian of such a theory L=12(∇φ)2-igφexp(iaφ) is analyzed using the techniques of PT-symmetric quantum theory. It is shown that L defines an infinite number of unitarily inequivalent sectors of the theory labeled by the integer n. In one-dimensional space (quantum mechanics), the energy spectrum is calculated in the semiclassical limit and the mth energy level in the nth sector is given by Em,n∼(m+1/2)2a2/(16n2).

Original language | English |
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Journal | Physical Review Letters |

Volume | 113 |

Issue number | 23 |

DOIs | |

Publication status | Published - 3 Dec 2014 |