## Infinitely many inequivalent field theories from one Lagrangian

Carl M. Bender, Daniel W. Hook, Nick E. Mavromatos, Sarben Sarkar

Logarithmic time-like 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 $$\phi$$. In Euclidean space the Lagrangian of such a theory, $$L=\frac{1}{2}(\nabla\phi)^2−ig\phi \exp(ia\phi)$$, 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 $$m$$th energy level in the $$n$$th sector is given by $$E_{m,n}∼(m+1/2)^2a^2/(16n^2)$$.

http://arxiv.org/abs/1408.2432
High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)