Between 4.20pm and 4.40pm on Friday, January 3, the group deliberately set fire to the hedge at the back of a property in Abbots Way, causing significant damage to the bush.
The offenders, who were described as white boys, then ran off along a footpath towards Croyland Park.
Three of the group are believed to be aged 13 to 14 years old, of a slim build and with short dark hair. One was wearing a white coat and another boy had a blue coat.
The fourth offender was a slim, white man with short dark hair in his 20s. He was wearing a black coat and jeans.
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Anyone with information or who may have witnessed this incident is asked to call Northamptonshire Police on 101 quoting reference number 20000005242.