Weak Gravity Conjecture for Noncommutative Field Theory

TL;DR

This paper explores how the weak gravity conjecture applies to noncommutative field theories, deriving bounds on the noncommutative scale and comparing results with commutative theories, revealing connections at tree-level.

Contribution

It provides new bounds on noncommutative gauge theories and discusses their relation to commutative theories within the weak gravity conjecture framework.

Findings

Derived an upper bound on the noncommutative scale $g_{YM}M_p$ in 4D noncommutative U(1) gauge theory.

Showed that in certain limits, noncommutative results reduce to commutative counterparts.

Analyzed weak gravity bounds for scalar and gauge theories in various dimensions.

Abstract

We investigate the weak gravity bounds on the U(1) gauge theory and scalar field theories in various dimensional noncommutative space. Many results are obtained, such as the upper bound on the noncommutative scale $g_{YM}M_p$ for four dimensional noncommutative U(1) gauge theory. We also discuss the weak gravity bounds on their commutative counterparts. For example, our result on 4 dimensional noncommutative U(1) gauge theory reduces in certain limit to its commutative counterpart suggested by Arkani-Hamed et.al at least at tree-level.