Relationships are the art of the possible, much like politics or eating at a buffet. Some people will be capable of forgiving an unfaithful partner, some won't, and it will always depend on the particular circumstances. If you can't determine which type of person your significant other is, try this simple exercise:
Which of the following two statements is more likely to come out of their mouth?
1. Hey man, monogamy is just the by-product of a series of arbitrary, unnatural societal taboos that lionize the family unit to engender political stability.
2. I do.
If they're type 1, your infidelity could be the key that opens the door to a whole world of orgies, emotional awkwardness, and rampant venereal disease. If they're more of the second persuasion, prepare for some emotional awkwardness (but at least no junk rot). Also, if their favorite song is the Beatles' "Run For Your Life," they're automatically type 2.
Forgiveness is possible. Whether it's possible in your case is up to you and your partner to find out (or choose not to).
When making that decision, hopefully as a couple, important things to consider are whether the unfaithful person really wants the relationship to continue (when we cheat, it's rarely because we're happy at home), how likely it is to happen again, whether the wronged party feels trust can ever be rebuilt, and whether a series of humiliating physical challenges might be in order.
They usually are.