Can AV slow down your PC?
That depends on which one you installed & how much physical RAM is available, and if you're a gamer it's even more critical if your AV is a resource hog.
Although Norton has reworked their AV to use less RAM, I found only a small improvement, in any case you have to pay a subscription to use Norton AV, something I refuse to do for that type of software whilst free alternatives exist.
I have found Comodo to be amongst the best for being light on system resources, I've been using it for 7 years and it's never let me down (even though I visit some "dodgy"websites occasionally).