Tachyon condensation
Encyclopedia
In particle physics
, theoretical processes that eliminate or resolve particles or fields into better understood phenomena are called, by extension and metaphor with the macroscopic process, "condensation
". In particular, tachyon condensation is such a process that eliminates the tachyon
, which many physicists believe does not exist.
ic field
—usually a scalar field
—with a complex
mass acquires a vacuum expectation value
and 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 physics
a notable example is ferromagnetism
; in particle physics
the best known example is the Higgs mechanism
in the standard model
that breaks the electroweak symmetry.
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 light. 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
.
conjectured that the tachyons carried by open strings attached to D-branes in string theory
reflect 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 became an active area of interest in the early 2000s.
The character of closed-string tachyon condensation is 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 Simeon Hellerman and Ian Swanson, in a wider array of cases. The fate of the closed string tachyon in the 26-dimensional bosonic string theory
remains unknown, though recent progress has revealed interesting new developments.
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
, theoretical processes that eliminate or resolve particles or fields into better understood phenomena are called, by extension and metaphor with the macroscopic process, "condensation
Condensation
Condensation is the change of the physical state of matter from gaseous phase into liquid phase, and is the reverse of vaporization. When the transition happens from the gaseous phase into the solid phase directly, the change is called deposition....
". In particular, tachyon condensation is such a process that eliminates the tachyon
Tachyon
A tachyon is a hypothetical subatomic particle that always moves faster than light. In the language of special relativity, a tachyon would be a particle with space-like four-momentum and imaginary proper time. A tachyon would be constrained to the space-like portion of the energy-momentum graph...
, which many physicists believe does not exist.
Technical overview
Tachyon condensation is a process in which a tachyonTachyon
A tachyon is a hypothetical subatomic particle that always moves faster than light. In the language of special relativity, a tachyon would be a particle with space-like four-momentum and imaginary proper time. A tachyon would be constrained to the space-like portion of the energy-momentum graph...
ic field
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
—usually a scalar field
Scalar field theory
In theoretical physics, scalar field theory can refer to a classical or quantum theory of scalar fields. A field which is invariant under any Lorentz transformation is called a "scalar", in contrast to a vector or tensor field...
—with a complex
Complex number
A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
mass acquires a vacuum expectation value
Vacuum expectation value
In quantum field theory the vacuum expectation value of an operator is its average, expected value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle...
and 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
Spontaneous symmetry breaking
Spontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....
. In condensed matter physics
Condensed matter physics
Condensed matter physics deals with the physical properties of condensed phases of matter. These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system. The most familiar...
a notable example is ferromagnetism
Ferromagnetism
Ferromagnetism is the basic mechanism by which certain materials form permanent magnets, or are attracted to magnets. In physics, several different types of magnetism are distinguished...
; in particle physics
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
the best known example is the Higgs mechanism
Higgs mechanism
In particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire non-vanishing masses through absorption of Nambu-Goldstone bosons arising in spontaneous symmetry breaking....
in the standard model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
that breaks the electroweak symmetry.
Condensation evolution
Although the notion of a tachyonic imaginaryImaginary number
An imaginary number is any number whose square is a real number less than zero. When any real number is squared, the result is never negative, but the square of an imaginary number is always negative...
mass is troubling, what is really being quantized here is the scalar field
Scalar field
In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the...
; even for tachyonic quantum fields
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
, the field operators at spacelike
Minkowski space
In physics and mathematics, Minkowski space or Minkowski spacetime is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated...
separated points still commute (or anticommute)
Canonical commutation relation
In physics, the canonical commutation relation is the relation between canonical conjugate quantities , for example:[x,p_x] = i\hbar...
, thus preserving causality. Therefore information still does not propagate faster than light. 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
Exponential growth
Exponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value...
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
Higgs boson
The Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
.
Tachyon condensation in string theory
In the late 1990s, Ashoke SenAshoke Sen
Ashoke Sen , FRS, is an Indian theoretical physicist. He has made a number of major original contributions to the subject of string theory, including his landmark paper on strong-weak coupling duality or S-duality, which was influential in changing the course of research in the field...
conjectured that the tachyons carried by open strings attached to D-branes in string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
reflect 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
String field theory
String field theory is a formalism in string theory in which the dynamics of relativistic strings is reformulated in the language of quantum 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 became an active area of interest in the early 2000s.
The character of closed-string tachyon condensation is more subtle, though the first steps towards our understanding of their fate have been made by Adams, Polchinski
Joseph Polchinski
Joseph Polchinski is a physicist working on string theory. He graduated from Canyon del Oro High School in Tucson, Arizona in 1971, obtained his B.S. degree from Caltech in 1975, and his Ph.D. from the University of California, Berkeley in 1980 under the supervision of Stanley Mandelstam...
, and Silverstein
Eva Silverstein
Eva Silverstein is a string theorist. She is married to fellow string theorist Shamit Kachru. She and Kachru were both proteges of Edward Witten.She is best known for her work on tachyon condensation...
, in the case of twisted closed string tachyons, and by Simeon Hellerman and Ian Swanson, in a wider array of cases. The fate of the closed string tachyon in the 26-dimensional bosonic string theory
Bosonic string theory
Bosonic string theory is the original version of string theory, developed in the late 1960s.In the early 1970s, supersymmetry was discovered in the context of string theory, and a new version of string theory called superstring theory became the real focus...
remains unknown, though recent progress has revealed interesting new developments.