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Updated: Apr 19, 2026

Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
Infinite class of PT-symmetric theories from one timelike Liouville Lagrangian
Carl M Bender1, Daniel W Hook2, Nick E Mavromatos3
1Department 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.
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}).
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