Following a previous work (hep-th/0410248), where a scalar field theory with
a modified propagator and phi^4 interaction in 4 dimensions is constructed to
be UV-finite, unitary and Lorentz invariant, we discuss in this paper general
phi^n theory in arbitrary even space-time dimensions. We show that the theory
is still UV-finite, unitary and Lorentz invariant if the propagators are chosen
to meet certain simple conditions depending on the space-time dimension but
independent of n. We also comment that our model is reminiscent of string
theory in the way UV divergence is avoided.Comment: 18 page
The decoupling of zero-norm states leads to linear relations among 4-point functions in the high energy limit of string theory. Recently it was shown that the linear relations uniquely determine ratios among 4-point functions at the leading order. The purpose of this paper is to extend the validity of the same approach to the next-to-leading order and higher orders.
In previous works, we constructed UV-finite and unitary scalar field theories with an infinite spectrum of propagating modes for arbitrary polynomial interactions. In this paper, we introduce infinitely many massive vector fields into a U (1) gauge theory to construct a theory with UV-finiteness and unitarity.
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