Anomaly induced effective actions in even dimensions and reliability of s-wave approximation

TL;DR

This paper compares 2d and 4d conformal anomaly induced effective actions for Majorana spinors, demonstrating that the s-wave approximation in 2d effectively captures the qualitative features of the 4d effective action without higher derivatives.

Contribution

It provides a detailed comparison between 2d s-wave and 4d anomaly induced effective actions for spinors, validating the s-wave approximation as a qualitative representation.

Findings

s-wave effective action qualitatively matches 4d effective action

s-wave approximation corresponds to no higher derivatives in 4d

Majorana spinor anomalies are consistent across dimensions

Abstract

The reduction of 4d matter-gravity theory to $S_2$, $H_2$ or $R_2$ leads to effective 2d dilatonic gravity with dilaton coupled matter. Spinors give the exceptional example of the theory which is conformally invariant in 4d as well as in 2d, after reduction. We find 4d and 2d conformal anomaly induced effective action (EA) for Majorana spinor. It is expected for some time that s-wave EA (i.e. the one for dilaton coupled 2d matter) is some (s-wave) approximation to 4d EA. We compare such 2d and 4d spinor EAs on the same gravitational background and argue that s-wave EA indeed qualitatively corresponds to no higher derivatives approximation for 4d EA.