Quantum corrections to broken N = 8 supergravity

TL;DR

This paper demonstrates that the one-loop effective potential in certain broken N=8 supergravity vacua is finite, calculable, and negative-definite, due to specific supertrace properties of the mass matrices.

Contribution

It provides the first detailed analysis showing the finiteness and calculability of quantum corrections in broken N=8 supergravity with flat vacua, highlighting supertrace cancellations.

Findings

Supertraces of mass matrices vanish for quadratic and quartic powers.

Str M^6 = 0, but Str M^8 > 0 in broad class of vacua.

One-loop effective potential is negative-definite.

Abstract

We show that the one-loop effective potential of spontaneously broken N=8 supergravity is calculable and finite at all classical four-dimensional Minkowski vacua without tachyons in the spectrum. The reason is that the supertraces of the quadratic and quartic mass matrices vanish along the classically flat directions: Str M^2 = Str M^4 =0. We also show that Str M^6 = 0 but Str M^8 > 0 in a broad class of vacua with broken supersymmetry on a flat background, which includes all those explicitly identified so far. We find analytical and numerical evidence that the corresponding one-loop effective potential is negative-definite.