title: Infinite class of PT-symmetric theories from one timelike Liouville Lagrangian.
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=1/2(∇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 E_{m,n}∼(m+1/2)^{2}a^{2}/(16n^{2}).
authors.affiliation: Department of Physics, Washington University, St. Louis, Missouri 63130, USA and Department of Physics, King's College London, London WC2R 2LS, United Kingdom and Department of Mathematical Science, City University London, Northampton Square, London EC1V 0HB, United Kingdom.
authors.forename: Carl M
authors.initials: CM
authors.lastname: Bender
authors.affiliation: Department of Physics, Washington University, St. Louis, Missouri 63130, USA and Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom.
authors.forename: Daniel W
authors.initials: DW
authors.lastname: Hook
authors.affiliation: Department of Physics, King's College London, London WC2R 2LS, United Kingdom and Theory Division, CERN, CH-1211 Geneva 23, Switzerland.
authors.forename: Nick E
authors.initials: NE
authors.lastname: Mavromatos
authors.affiliation: Department of Physics, King's College London, London WC2R 2LS, United Kingdom.
authors.forename: Sarben
authors.initials: S
authors.lastname: Sarkar