The Orbifolds of Permutation-Type as Physical String Systems at Multiples of $\mathbf{c=26}$ V. Cyclic Permutation Orbifolds

TL;DR

This paper studies permutation orbifolds of free bosonic strings at multiples of central charge 26, introducing twisted diagrams to confirm their spectra match ordinary strings and proposing forms for their one-loop amplitudes.

Contribution

It introduces twisted tree diagrams for permutation orbifolds and demonstrates their spectra are equivalent to standard strings, advancing understanding of their modular invariance.

Findings

Twisted sectors have spectra equivalent to ordinary c=26 strings.

Proposed forms for modular-invariant cosmological constants.

Addressed complexities in untwisted sector loop sewing.

Abstract

I consider the $\mathbb{Z}_\lambda,$ $\lambda$ prime free-bosonic permutation orbifolds as interacting physical string systems at $\hat{c} = 26\lambda $. As a first step, I introduce twisted tree diagrams which confirm at the interacting level that the physical spectrum of each twisted sector is equivalent to that of an ordinary $c=26$ closed string. The untwisted sectors are surprisingly more difficult to understand, and there are subtleties in the sewing of the loops, but I am able to propose provisional forms for the full modular-invariant cosmological constants and one-loop diagrams with insertions.