A UV completion of scalar field theory in arbitrary even dimensions

TL;DR

This paper extends a UV-finite, unitary, and Lorentz invariant scalar field theory with modified propagators to arbitrary even dimensions, maintaining these properties across different interaction powers.

Contribution

It generalizes a previous 4D scalar field theory to arbitrary even dimensions, showing the theory remains UV-finite, unitary, and Lorentz invariant under specific propagator conditions.

Findings

The theory is UV-finite in arbitrary even dimensions.

The theory maintains unitarity and Lorentz invariance.

Propagator conditions depend only on space-time dimension, not on interaction power n.

Abstract

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.