Noncommutativity from the string perspective: modification of gravity at a mm without mm sized extra dimensions

TL;DR

This paper investigates how noncommutative field theories derived from string theory resolve IR pathologies, showing a flow to commutative physics at low energies with suppressed Lorentz violations and implications for gravity at large scales.

Contribution

It demonstrates the IR behavior of noncommutative theories from string theory, including the flow to commutative physics and effects on gravity at macroscopic distances.

Findings

IR singularities are controlled by string theory mechanisms.

The theory flows to commutative physics in the deep IR.

UV/IR mixing affects graviton behavior and gravity scale.

Abstract

We explore how the IR pathologies of noncommutative field theory are resolved when the theory is realized as open strings in background B-fields: essentially, since the IR singularities are induced by UV/IR mixing, string theory brings them under control in much the same way as it does the UV singularities. We show that at intermediate scales (where the Seiberg-Witten limit is a good approximation) the theory reproduces the noncommutative field theory with all the (un)usual features such as UV/IR mixing, but that outside this regime, in the deep infra-red, the theory flows continuously to the commutative theory and normal Wilsonian behaviour is restored. The resulting low energy physics resembles normal commutative physics, but with additional suppressed Lorentz violating operators. We also show that the phenomenon of UV/IR mixing occurs for the graviton as well, with the result that, in configurations where Planck's constant receives a significant one-loop correction (for example brane-induced gravity), the distance scale below which gravity becomes non-Newtonian can be much greater than any compact dimensions.