A Note on Noncommutative String theory and its low energy limit

TL;DR

This paper examines the relationship between noncommutative string theory and its low-energy gauge theory limit, confirming the amplitude correspondence and absence of corrections due to massive modes in the low-energy limit.

Contribution

It demonstrates the precise connection between noncommutative string amplitudes and gauge theory amplitudes as ' approaches zero, including coupling relations and amplitude factors.

Findings

String amplitudes reduce to gauge theory amplitudes in the '  0 limit.

Coupling constants are related as g_{YM} = G_0  rac{1}{'}^{1/2}.

No corrections to gauge action from massive modes in the low-energy limit.

Abstract

The noncommutative string theory is described by embedding open string theory in a constant second rank antisymmetric $B_{\mu\nu}$ field and the noncommutative gauge theory is defined by a deformed $\star$ product. As a check, study of various scattering amplitudes in both noncommutative string and noncommutative gauge theory confirm that in the $\alpha^{'}\to 0$ limit, the noncommutative string theoretic amplitude goes over to the noncommutative gauge theoretic amplitude, and the couplings are related as $g_{YM}=G_0\sqrt{\frac{1}{2\alpha^{'}}}$. Furthermore we show that in this limit there will not be any correction to the gauge theoretic action because of absence of massive modes. We get sin/cos factors in the scattering amplitudes depending on the odd/even number of external photons.