Supersymmetry tames the tachyon — and five consistent theories emerge
The original bosonic string was a beautiful idea with three fatal flaws. It only works in 26 dimensions. Its lowest vibration mode is a tachyon — a state with negative mass-squared, which means the vacuum itself is unstable, like a pencil balanced on its tip. And it contains no fermions at all: a world of forces with no matter to act on. The fix for all three came from the same idea — supersymmetry — and it left behind not one theory but five.
Supersymmetry (SUSY) is a symmetry that pairs every boson with a fermion whose spin differs by one half, and vice versa. The electron gets a selectron, the photon a photino, the graviton a gravitino. On the string, imposing this symmetry adds fermionic vibrations to the bosonic ones — solving the "no matter" problem in one stroke.
The electron (a matter fermion) is paired with the selectron, a spin-0 boson carrying the same charge.
Supersymmetry pairs every boson with a fermion of spin differing by 1/2, and vice versa. Cyan dots are fermions, violet dots are bosons; dashed pink circles are the hypothetical superpartners. On the string, this same pairing is what removes the tachyon and drops the critical dimension from 26 to 10.
Try it: Flip the SUSY toggle to overlay the superpartner spectrum, then step through the carousel. Notice the pattern: every partner sits exactly half a unit of spin away from its Standard Model particle.
Supersymmetry does more than add fermions. The consistent supersymmetric spectrum (via the GSO projection) simply deletes the tachyonic ground state: the lowest rung of the mass ladder now sits at exactly zero, not below it. The vacuum is stable. As a bonus, the anomaly-cancellation arithmetic changes and the critical dimension drops from 26 to 10.
The bosonic string's lowest state has negative mass-squared — a tachyon, signaling that the vacuum itself is unstable. Applying supersymmetry (the GSO projection) deletes the tachyon rung, adds spacetime fermions at every level, and lowers the critical dimension from 26 to 10. Units: open-string levels, alpha' M² = N − 1 (bosonic) vs N (superstring).
Try it: Click "Apply supersymmetry" and watch the superstring ladder assemble — with the pulsing red tachyon rung crossed out. The readout tracks the dimension count dropping from 26 to 10.
When physicists worked out every way to build a consistent superstring, exactly five survived. Type I: open and closed unoriented strings with gauge group SO(32). Type IIA: closed strings, non-chiral — mirror-symmetric physics. Type IIB: closed strings, chiral — left and right are genuinely different, like our universe. And two heterotic theories, with gauge groups SO(32) and E₈×E₈. Five candidate "theories of everything" was four too many — by the early 1990s this embarrassment of riches was string theory's most awkward open problem.
Try it: Click each vignette (or button) to read its fact card. Compare the arrows on the two Type II loops: IIA's point both ways around the string (non-chiral), IIB's all circulate the same way (chiral).
On a closed string, waves can circulate clockwise or counterclockwise — left-movers and right-movers — and the two families never mix. The heterotic theories exploit this with the boldest construction in string theory: use bosonic-string left-movers (which want 26 dimensions) alongside superstring right-movers (which want 10). The 16 leftover dimensions are curled onto a special internal lattice, and consistency allows exactly two choices — the lattices of SO(32) and E₈×E₈.
Try it: Watch the red and cyan waves pass through each other without interacting, then switch on the heterotic trick to see the left-movers become 26-dimensional and the 16 extra dimensions appear as a glowing lattice.