Do convolutional neural networks also have recurrent connections? I asked my self this simple question while reading "Comment Abuse Classification with Deep Learning" by Chu and Jue. Indeed, they say at the end of the that 


  It is clear that RNNs, specifically LSTMs, and CNNs are state-of-the-art  architectures for sentiment analysis


To my mind CNNs were only neurons arranged so that they correspond to overlapping regions when paving the input field. It wasn't that recurrent at all.
You are right. I think you are just misinterpreting the part of the sentence ('specifically LSTMs'). LSTMs are an example of a popular type of RNN.
RNNs and CNNs are different architectures but they can be used together.

Here is another sentence with the same structure:


  It is clear than dogs, specifically corgis, and cats are very common in online memes.