physics, tachyon condensation is a process in which a tachyonic field—usually a scalar field—with a negative squared mass acquires a vacuum expectation valueand reaches the minimum of the potential energy. While the field is tachyonic (and unstable) near the original point—the local maximum of the potential—it gets a non-negative squared mass (and becomes stable) near the minimum.
The appearance of tachyons is a potentially lethal problem for any theory; examples of tachyonic fields amenable to condensation are all cases of
spontaneous symmetry breaking. In condensed matter physicsa notable example is Ferromagnetism; in particle physicsthe best known example is the Higgs mechanismin the standard modelthat breaks the electroweaksymmetry.
Although the notion of a tachyonic imaginary mass is troubling, what is really being quantized here is the
scalar field; even for tachyonic quantum fields, the field operators at spacelike separated points still commute (or anticommute), thus preserving causality. Therefore information still does not propagate faster than lightcite journal | first = Gerald | last = Feinberg | authorlink = Gerald Feinberg | title = Possibility of Faster-Than-Light Particles | journal = Physical Review | volume = 159 | year = 1967 | pages = 1089–1105 | doi = 10.1103/PhysRev.159.1089] . Also the "imaginary mass" really means that the system is unstable and that solutions will grow exponentially, but not superluminally (there is no violation of causality). Tachyon condensation drives the physical system to a stable state where no physical tachyons exist. The zero value field is at a local maximum rather than a local minimum of its potential energy, much like a ball at the top of a hill. A very small impulse (which will always happen due to quantum fluctuations) will lead the field to roll down with exponentially increasing amplitudes toward the local minimum. Once the tachyonic field reaches the minimum of the potential, its quanta are not tachyons any more but rather have a positive mass-squared, such as the Higgs boson.Michael E. Peskin and Daniel V. Schroeder (1995). "An Introduction to Quantum Field Theory", Perseus books publishing.]
Tachyon condensation in string theory
In the late 1990s, the Indian string theorist
Ashoke Senconjectured that the tachyons carried by open strings attached to D-branesin string theoryreflect the instability of the D-branes with respect to their complete annihilation. The total energy carried by these tachyons has been calculated in string field theory; it agrees with the total energy of the D-branes, and all other tests have confirmed Sen's conjecture as well. Tachyons therefore experienced a comeback in the early 2000s.
The character of
closed-string tachyon condensationis more subtle, though the first steps towards our understanding of their fate have been made by Adams, Polchinski, and Silverstein, in the case of twisted closed string tachyons, and by Hellerman and Swanson, in a wider array of cases. The fate of the closed string tachyon in the 26-dimensional bosonic string theoryremains unknown, though recent progress has revealed interesting new developments.
* [http://xstructure.inr.ac.ru/x-bin/theme2.py?arxiv=hep-th&level=2&index1=3877000 Tachyon condensation on arxiv.org]
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