nLab tachyon

Idea

In perturbation theory (in QFT) a tachyon is an excitation/particle with negative mass squared, hence technically with imaginary mass.

Since the masses of particles in perturbation theory give the second derivative of the background potential energy at the point about which the perturbation series is developed, a tachyon in the spectrum indicates that the perturbation theory is set up about an unstable vacuum.

The dynamics of a tachyon will hence make it form a condensate at an actual local potential energy minimum. Once there it is no longer a tachyon, but a genuine particle excitation (“tachyon decay”).

Examples

In bosonic string theory

The excitation of the open string in bosonic string theory famously contains a tachyon mode. By Sen's conjecture this indicates the instability of the space-filling D25-brane on which the ends of the open bosonic string propagate. Using string field theory to get a non-perturbative description of the situation one can follow the decay of the D25-brane to the “true” (stable) open bosonic string theory vacuum. (Where however analysis shows that this no longer contains open string excitations, so it is maybe better called a closed string vacuum.) See at Sen's conjecture for more.

The fate of the closed bosonic string tachyon is more subtle. But see the references below.

In superstring theory

Similarly, in superstring theory open string states between D-brane/anti D-brane pairs may be tachyonic, signallying the decay of these brane configurations: see Sen's conjecture in superstring theory. This leads to the conjectured classification of D-brane charge in K-theory (see there).

(…)

Related concepts

quantum probability theory – observables and states

• states

  • classical state

  • quantum state

    • space of states (in geometric quantization)

    • state on a star-algebra, quasi-state

    • qbit, Bell state

      dimer, tensor network state

    • quantum state preparation

    • probability amplitude, quantum fluctuation

    • pure state

      • wave function

      • bra-ket

      • Bell state

    • quantum superposition, quantum interference

    • quantum entanglement

    • quantum measurement

      wave function collapse

      Born rule

      deferred measurement principle

      quantum reader monad

      measurement problem

    • superselection sector

    • mixed state, density matrix

      entanglement entropy

      holographic entanglement entropy

    • coherent quantum state

  • ground state, excited state

  • quasi-free state

  • Fock space, second quantization

  • vacuum, vacuum state

    • Hadamard state

    • vacuum diagram

    • vacuum expectation value, vacuum amplitude, vacuum fluctuation

    • vacuum energy

    • vacuum polarization

    • interacting vacuum

    • thermal vacuum, KMS state

    • vacuum stability

      • false vacuum, tachyon, Coleman-De Luccia instanton

    • theta vacuum

    • perturbative string theory vacuum

      • non-geometric string theory vacuum

      • landscape of string theory vacua

  • entangled state

  • tensor network state

    • matrix product state

    • tree tensor network state

• observables

  • quantum observable, beable

  • algebra of observables, star-algebra

  • Bohr topos

  • quantum operator (in geometric quantization)

  • quantum operation, quantum effect, effect algebra

  • in quantum field theory

    • local observable

    • polynomial observable

      • linear observable

        • field observable

    • regular observable

    • microcausal observable

    • normal-ordered product, time-ordered products, retarded product

    • Wick algebra

    • scattering amplitude

    • interacting field algebra of observables, Bogoliubov's formula

• GNS construction

• theorems

  • order-theoretic structure in quantum mechanics

    • Gleason's theorem

    • Alfsen-Shultz theorem

    • Harding-Döring-Hamhalter theorem

    • Kochen-Specker theorem

    • Nuiten's lemma

  • Wigner's theorem

  • no-cloning theorem

  • Bell's theorem

• field (physics)

• inflaton field

References

General

The concept originates with

• Olexa‐Myron Bilaniuk, V. K. Deshpande, E. C. G. Sudarshan, “Meta” Relativity, American Journal of Physics 30, 718 (1962) (doi:10.1119/1.1941773)

• Olexa‐Myron Bilaniuk, E. C. George Sudarshan, Particles beyond the light barrier, Physics Today 22, 5, 43 (1969) (doi:10.1063/1.3035574)

See also

• Wikipedia, Tachyon

In string theory

In addition to the open string tachyon condensation discussed in the references at Sen's conjecture, there is also work on the closed string tachyon condensation in the following articles.

• A. Adams, Joseph Polchinski and Eva Silverstein, Don’t panic! Closed string tachyons in ALE space-times, JHEP 0110 (2001) 029 (arXiv:hep-th/0108075).

• R. Rabadan and Joan Simon, M theory lift of brane anti-brane systems and localized closed string tachyons, JHEP 0205 (2002) 045 (arXiv:hep-th/0203243).

• Ángel Uranga, Localized instabilities at conifolds, (arXiv:hep-th/0204079).

• Shin Nakamura, Closed-string Tachyon Condensation and the On-shell Effective Action of Open-string Tachyons, Prog.Theor.Phys. 106 (2001) 989-1016, (arXiv:hep-th/0105054)

The following articles specifically identify closed string tachyon condensation as the disappearing of dimensions of spacetime.

• Simeon Hellerman, X. Liu, Dynamical dimension change in supercritical string theory, JHEP0709:096 (2007)

  [hep-th/0409071]

• Simeon Hellerman, Ian Swanson, Dimension-changing exact solutions of string theory, JHEP0709:096 (2007) [arXiv:hep-th/0612051]

• Mikel Berasaluce-González, Miguel Montero, Ander Retolaza, Ángel Uranga, Discrete gauge symmetries from (closed string) tachyon condensation (arXiv:1305.6788)