# Symmetric-Gapped Surface States of Fractional Topological Insulators

## TL;DR

This paper constructs symmetric-gapped surface states for fractional topological insulators with specific electromagnetic and gauge properties, extending known states and confirming their anomaly consistency.

## Contribution

It introduces new symmetric-gapped surface states for fractional topological insulators with a $ heta$-angle of $rac{eta}{3}$ and a $ ext{Z}_3$ gauge field, generalizing existing states.

## Key findings

- Surface states exhibit correct time-reversal and charge conservation anomalies.
- States show extended periodicity compared to integer topological insulators.
- Construction applies to fractional topological insulators with specific electromagnetic parameters.

## Abstract

We construct the symmetric-gapped surface states of a fractional topological insulator with electromagnetic $\theta$-angle $\theta_{em} = \frac{\pi}{3}$ and a discrete $\mathbb{Z}_3$ gauge field. They are the proper generalizations of the T-pfaffian state and pfaffian/anti-semion state and feature an extended periodicity compared with their of "integer" topological band insulators counterparts. We demonstrate that the surface states have the correct anomalies associated with time-reversal symmetry and charge conservation.