# nLab tachyon

Contents

### Context

#### Fields and quanta

fields and particles in particle physics

and in the standard model of particle physics:

force field gauge bosons

scalar bosons

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks ($q$)
up-typeup quark ($u$)charm quark ($c$)top quark ($t$)
down-typedown quark ($d$)strange quark ($s$)bottom quark ($b$)
leptons
chargedelectronmuontauon
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion ($u d$)
ρ-meson ($u d$)
ω-meson ($u d$)
f1-meson
a1-meson
strange-mesons:
ϕ-meson ($s \bar s$),
kaon, K*-meson ($u s$, $d s$)
eta-meson ($u u + d d + s s$)

charmed heavy mesons:
D-meson ($u c$, $d c$, $s c$)
J/ψ-meson ($c \bar c$)
bottom heavy mesons:
B-meson ($q b$)
ϒ-meson ($b \bar b$)
baryonsnucleons:
proton $(u u d)$
neutron $(u d d)$

(also: antiparticles)

effective particles

hadrons (bound states of the above quarks)

solitons

in grand unified theory

minimally extended supersymmetric standard model

superpartners

bosinos:

dark matter candidates

Exotica

auxiliary fields

# Contents

## 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. This leads to the conjectured classification of D-brane charge in K-theory (see there).

(…)

## References

### General

The concept originates with

### 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.

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)

Last revised on December 22, 2020 at 13:16:56. See the history of this page for a list of all contributions to it.