In
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interac ...
, a heterotic string is a closed string (or loop) which is a hybrid ('heterotic') of a
superstring
Superstring theory is an theory of everything, attempt to explain all of the Elementary particle, particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetry, supersymmetric String (physics), st ...
and a
bosonic string. There are two kinds of heterotic string, the heterotic SO(32) and the heterotic E
8 × E
8, abbreviated to HO and HE. Heterotic string theory was first developed in 1985 by
David Gross,
Jeffrey Harvey,
Emil Martinec
Emil John Martinec (born 1958) is an American string theorist, a physics professor at the Enrico Fermi Institute at the University of Chicago, and director of the Kadanoff Center for Theoretical Physics. He was part of a group at Princeton Universi ...
, and
Ryan Rohm (the so-called "Princeton string quartet"), in one of the key papers that fueled the
first superstring revolution.
Overview
In
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interac ...
, the left-moving and the right-moving excitations are completely decoupled, and it is possible to construct a string theory whose left-moving (counter-clockwise) excitations are treated as a bosonic string propagating in ''D'' = 26 dimensions, while the right-moving (clockwise) excitations are treated as a superstring in ''D'' = 10 dimensions.
The mismatched 16 dimensions must be compactified on an even,
self-dual lattice (a
discrete subgroup of a linear space). There are two possible even self-dual lattices in 16 dimensions, and it leads to two types of the heterotic string. They differ by the
gauge group in 10 dimensions. One gauge group is
SO(32) (the HO string) while the other is
E8 × E8 (the HE string).
These two gauge groups also turned out to be the only two
anomaly
Anomaly may refer to:
Science
Natural
*Anomaly (natural sciences)
** Atmospheric anomaly
** Geophysical anomaly
Medical
* Congenital anomaly (birth defect), a disorder present at birth
** Physical anomaly, a deformation of an anatomical struct ...
-free gauge groups that can be coupled to the ''N'' = 1
supergravity
In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such as ...
in 10 dimensions. (Although not realized for quite some time, U(1)
496 and E
8 × U(1)
248 are anomalous.
)
Every heterotic string must be a
closed string, not an
open string; it is not possible to define any
boundary conditions that would relate the left-moving and the right-moving excitations because they have a different character.
String duality
String duality
String or strings may refer to:
* String (structure), a long flexible structure made from threads twisted together, which is used to tie, bind, or hang other objects
Arts, entertainment, and media Films
* ''Strings'' (1991 film), a Canadian ani ...
is a class of symmetries in physics that link different string theories. In the 1990s, it was realized that the strong coupling limit of the HO theory is
type I string theory
In theoretical physics, type I string theory is one of five consistent supersymmetric string theories in ten dimensions. It is the only one whose strings are unoriented (both orientations of a string are equivalent) and the only one which contains ...
— a theory that also contains
open strings
''Open Strings'' is an album by French jazz fusion artist Jean-Luc Ponty, released in 1971 on vinyl by the MPS label.
Track listing
All songs written by Jean-Luc Ponty, except where noted.
Side one
#"Flipping, Pt.1" – 4:40
#"Flipping, Pt.2 ...
; this relation is called
S-duality
In theoretical physics, S-duality (short for strong–weak duality, or Sen duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. S-duality is useful for doing calculations in theore ...
. The HO and HE theories are also related by
T-duality
In theoretical physics, T-duality (short for target-space duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. In the simplest example of this relationship, one of the theories desc ...
.
Because the various superstring theories were shown to be related by dualities, it was proposed that each type of string was a different limit of a single underlying theory called
M-theory
M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witte ...
.
References
{{DEFAULTSORT:Heterotic String
String theory
E8 (mathematics)