For a sufficiently small value of 'break'
No, AES is not 'broken'. This is a very clever attack, but it only makes it 5x better than brute force (which, for a correctly implemented encryption scheme would take billions of years of computer power). To quote from the abstract: "In this paper we present a novel technique of block cipher cryptanalysis with bicliques, which leads to the following results:
* The first key recovery attack on the full AES-128 with computational complexity 2^126.1.
* The first key recovery attack on the full AES-192 with computational complexity 2^189.7.
* The first key recovery attack on the full AES-256 with computational complexity 2^254.4.
* Attacks with lower complexity on the reduced-round versions of AES not considered before, including an attack on 8-round AES-128 with complexity 2^124.9."
As Bruce Schneier puts it: "there is no reason to scrap AES in favor of another algorithm, NST should increase the number of rounds of all three AES variants. At this point, I suggest AES-128 at 16 rounds, AES-192 at 20 rounds, and AES-256 at 28 rounds."