Descent Relations and Oscillator Level Truncation Method

TL;DR

This paper revisits the oscillator level truncation method in bosonic String Field Theory, analyzing descent relations and proposing two calculation schemes that yield consistent vertex structures but different normalization factors.

Contribution

It introduces two new schemes for calculating descent relations in SFT, improving understanding of normalization factors in oscillator level truncation.

Findings

Both schemes produce correct vertex structures.

Different normalization factors Z_3 are obtained.

The methods enhance the accuracy of SFT calculations.

Abstract

We reexamine the oscillator level truncation method in the bosonic String Field Theory (SFT) by calculation the descent relation <V_3|V_1>=Z_3<V_2|. For the ghost sector we use the fermionic vertices in the standard oscillator basis. We propose two new schemes for calculations. In the first one we assume that the insertion satisfies the overlap equation for the vertices and in the second one we use the direct calculations. In both schemes we get the correct structures of the exponent and pre-exponent of the vertex <V_2|, but we find out different normalization factors Z_3.