No we dont carry guns. Depending on the laws of the state that one is in, we are not even allowed to carry handcuffs. In NYS we are not allowed to even "arrest" people. Each store in the mall is responsible for its own security and if they have a shoplifter, we can only go there as protection for the tenants and customers of the store.
If the person leaves the store, we cannot even detain them. We can only follow them and write down information about them and take down the license plate if they leave in a car and give that info to the police when they arrive.
Technically, we are there just as a show of security for the customers, to look out for fire and safety hazards and assisst emergency services where possible.