Nonlocal quantum field theory without acausality and nonunitarity at quantum level: is SUSY the key?

TL;DR

This paper explores how supersymmetry can cancel acausal diagrams in nonlocal quantum field theories at the quantum level, potentially preserving unitarity and causality, with implications for string theory.

Contribution

It demonstrates that supersymmetry can cancel acausal diagrams in nonlocal quantum field theories at all orders, suggesting a possible resolution to longstanding issues.

Findings

Supersymmetry leads to exact cancellations of harmful diagrams in nonlocal models.

In super Yang-Mills models, additional acausal diagrams from D-terms are addressed.

Infinite superfields may be required for complete cancellation in generic gauge theories.

Abstract

The realization of a nonlocal quantum field theory without losing unitarity, gauge invariance and causality is investigated. It is commonly retained that such a formulation is possible at tree level, but at quantum level acausality reappears at one loop. We suggest the the problem of acausality is, in a broad sense, similar to the one about anomalies in quantum field theory. By virtue of this analogy, we suggest that acausal diagrams resulting from the fermionic sector and the bosonic one might cancel each other, with a suitable content of fields and suitable symmetries. As a simple example, we show how supersymmetry can alleviate this problem in a simple and elegant way, i.e., by leading to exact cancellations of harmful diagrams, to all orders of perturbation theory, in the case of a nonlocal Wess-Zumino model. On the other hand, the same is true for a super Yang-Mills model, but in this case, other important acausal diagrams are also originating from supersymmetric D-terms. As a consequence, we conjecture that, for a generic gauge theory, an infinite number of superfields are needed in order to obtain a complete cancellation between all diagrams. This framework is naturally occurring in string theory, where infinite Kaluza-Klein towers of higher-spin fields are generally predicted.