Localization of effective actions in Heterotic String Field Theory

TL;DR

This paper demonstrates how to compute the quartic effective potential in heterotic string field theory using algebraic relations, revealing localization phenomena and deriving the heterotic Yang-Mills potential without explicit vertex calculations.

Contribution

It introduces a method to compute quartic couplings in heterotic string field theory solely from $L_$ relations, avoiding explicit vertex expressions.

Findings

Quartic potentials localize at the boundary of moduli space.

The method applies to charged fields under $$-charge.

Heterotic Yang-Mills quartic potential is derived.

Abstract

We consider the algebraic couplings in the tree level effective action of the heterotic string. We show how these couplings can be computed from closed string field theory. When the light fields we are interested in are charged under an underlying ${\mathcal N}=2$ $R$-charge in the left-moving sector, their quartic effective potential localizes at the boundary of the worldsheet moduli space, in complete analogy to the previously studied open string case. In particular we are able to compute the quartic closed string field theory potential without resorting to any explicit expression for the 3- and the 4-strings vertices but only using the $L_\infty$ relations between them. As a non trivial example we show how the heterotic Yang-Mills quartic potential arises in this way.