In modern theoretical physics, the word "tachyon" has evolved significantly from its original definition as a faster-than-light point particle. Today, in the context of Quantum Field Theory (QFT) and String Theory, "tachyon" almost exclusively refers to a tachyonic field—a field with an imaginary mass that signifies a fundamental instability in the vacuum state.
1. Tachyon Condensation and Symmetry Breaking
In quantum field theory, the mass squared ($m²$) of a field corresponds to the second derivative of its potential energy function at the local minimum (the vacuum state). For standard particles, $m²$ is positive, meaning the field sits in a stable "bowl" of potential energy. Any small perturbation will cause the field to oscillate around the minimum, creating the particles we observe.
A tachyonic field has a negative mass squared ($m² < 0$). This means the field is sitting at a local maximum of potential energy—like a ball balanced perfectly on the top of a hill. This state is mathematically possible but physically unstable.
Because of this instability, the field will spontaneously "roll down" the hill to find a true, stable minimum energy state. This process is called Tachyon Condensation. As the field settles into the new minimum, the original tachyonic instability vanishes, the field acquires a non-zero Vacuum Expectation Value (VEV), and the particles associated with the field acquire a real, positive mass.
The Higgs Mechanism
The most famous physical example of tachyon condensation is the Higgs field. In the extremely hot, early universe, the Higgs potential was symmetric, and the field effectively had a negative mass squared—it was tachyonic. As the universe cooled, the field rolled down to a stable minimum in a "Mexican hat" potential. This spontaneous symmetry breaking gave the W and Z bosons their mass, and the remaining excitations of the field are what we observe today as the Higgs boson (which has a positive, real mass).
2. The Tachyon Problem in Bosonic String Theory
String theory attempts to unify general relativity with quantum mechanics by replacing point particles with one-dimensional vibrating strings. The original formulation of this idea, developed in the late 1960s and 1970s, is known as Bosonic String Theory.
However, bosonic string theory suffered from a critical, fatal flaw: the lowest energy vibrational mode of the string (the ground state) yielded a particle with a negative mass squared. In other words, the vacuum of bosonic string theory contained a tachyon.
This indicated that the 26-dimensional spacetime of bosonic string theory was fundamentally unstable and would undergo tachyon condensation to decay into some lower-energy state. Theorist Ashoke Sen made groundbreaking contributions in the late 1990s by demonstrating that the condensation of the open string tachyon represents the decay of unstable D-branes into the closed string vacuum.
Ultimately, to fix the tachyon problem and successfully model fermions (matter particles), physicists introduced Supersymmetry. This led to Superstring Theory, which projects out the tachyonic ground state via the GSO projection, ensuring a stable vacuum.
3. Tachyonic Fields in Cosmology and Dark Energy
Tachyonic fields have also found profound applications in cosmology, specifically in models of cosmic inflation and dark energy.
Some inflationary models suggest that the rapid exponential expansion of the early universe was driven by a tachyon field rolling down its potential toward the minimum. Because the kinetic energy of the rolling tachyon field is bounded, it provides a natural mechanism for "slow-roll" inflation, where the universe expands smoothly before the field reaches the bottom of the potential and reheats the universe.
Similarly, in string cosmology, the rolling tachyon on a decaying D-brane has an equation of state that behaves remarkably like dark energy (or quintessence). As the tachyon field approaches its minimum, its pressure approaches the negative of its energy density ($p \to -\rho$), which is exactly the property required to drive the observed accelerating expansion of the universe.
Conclusion
When a modern theoretical physicist talks about tachyons, they are almost never referring to sci-fi spaceships traveling faster than light. They are discussing the deep mathematics of vacuum instabilities. Tachyon condensation is the universe's mechanism for spontaneously breaking symmetry and generating the complex, massive structures we observe from an initially unstable, massless void.