Saturating unitarity bounds at U-duality symmetric points

TL;DR

This paper investigates the extremal values of the leading Wilson coefficient in string theory across various dimensions, revealing that the minimum occurs at maximally symmetric points and is negative for dimensions less than 8.

Contribution

It extends the analysis of Wilson coefficients to D=6, 7, and 8, identifying the global minima at symmetric points and exploring their sign and implications.

Findings

Global minima occur at maximally symmetric points.

Minimum Wilson coefficient is negative for D<8.

Supports the idea of string theory as a unique quantum gravity theory.

Abstract

It has recently been shown that the leading Wilson coefficient in type II string theory can take (almost) all values allowed by unitarity, crossing symmetry and maximal supersymmetry in D=10 and D=9 dimensions. This suggests that string theory might define the unique consistent quantum theory of gravity with maximal supersymmetry. We study the minima of the leading Wilson coefficient in D=6, 7 and 8 dimensions and find the global minimum at the point in moduli space with maximal symmetry. The minimum value turns out to always be negative for D<8.