Difference between local and dense layers in CNNs
I am quoting user2576346's comments under the question: 

As I understand, either it should be densely connected or be a convolutional layer ...

No this is not true. A more accurate way to phrase that statement would be that layers are either fully connected (dense) or locally connected.
A convolutional layer is an example of a locally connected layer. In general a locally connected layer is a layer in which each of its units is only connected to a local portion of the input. A convolutional layer is a special type of local layer which exhibits a spatial translation invariance as each convolutional feature detector is strided across the entire image in local receptive windows, e.g. of size 3x3 or 5x5 for example.
What is the difference between a "Local" layer and a "Dense" layer in a convolutional neural network?  I am trying to understand the CIFAR-10 code in TensorFlow, and I see it uses "Local" layers instead of regular dense layers. Is there any class in TF that supports implementing "Local" layers?