Crosscap states and Boundary states in D=4,N=1,type-IIB Orientifold Theories

TL;DR

This paper constructs boundary and crosscap states in D=4, N=1 type-IIB Z_N orientifold theories, analyzing their properties and implications for amplitude factorization and tadpole divergences.

Contribution

It introduces explicit boundary and crosscap states in these orientifold models and studies their effects on amplitude factorization and tadpole cancellation.

Findings

Amplitudes do not factorize in Z_N (even N) models due to volume dependence.

Tadpole divergences persist in Z_4, Z_8, Z'_8, Z'_{12} models.

Z_3 and Z_7 models have factorized amplitudes allowing gauge group determination.

Abstract

We construct boundary state and crosscap state in D=4,N=1 type-IIB Z_N orientifold and investigate properties of amplitude. We find that the boundary state of a cylinder is different from the boundary state of a M\"{o}bius strip. Using these states, we find that amplitudes do not factorize in Z_N(N=even) orientifold. Tadpole divergence remain in Z_4, Z_8, Z'_8 and Z'_{12} model due to volume dependence of boundary and crosscap state. On the other hand the amplitude of Z_3 and Z_7 orientifolds factorize so that we obtain the gauge groups of the model by employing the massless tadpole cancellation condition.