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 and a
bosonic string
Bosonic string theory is the original version of string theory, developed in the late 1960s and named after Satyendra Nath Bose. It is so called because it contains only bosons in the spectrum.
In the 1980s, supersymmetry was discovered in the co ...
. 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
David Jonathan Gross (; born February 19, 1941) is an American theoretical physicist and string theorist. Along with Frank Wilczek and David Politzer, he was awarded the 2004 Nobel Prize in Physics for their discovery of asymptotic freedom. Gr ...
,
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 Ryan Milton Rohm (born 22 December 1957, Gastonia, North Carolina) is an American string theorist. He is one of four physicists known as the Princeton string quartet, and is responsible for the development of heterotic string theory along with Davi ...
(the so-called "Princeton string quartet"), in one of the key papers that fueled the
first superstring revolution
The history of string theory spans several decades of intense research including two superstring revolutions. Through the combined efforts of many researchers, string theory has developed into a broad and varied subject with connections to quantu ...
.
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
In geometry and mathematical group theory, a unimodular lattice is an integral lattice of determinant 1 or −1. For a lattice in ''n''-dimensional Euclidean space, this is equivalent to requiring that the volume of any fundame ...
(a
discrete subgroup
In mathematics, a topological group ''G'' is called a discrete group if there is no limit point in it (i.e., for each element in ''G'', there is a neighborhood which only contains that element). Equivalently, the group ''G'' is discrete if and on ...
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 physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie group ...
in 10 dimensions. One gauge group is
SO(32)
In mathematics, the orthogonal group in dimension , denoted , is the Group (mathematics), group of isometry, distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by ...
(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-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
In physics, a string is a physical entity postulated in string theory and related subjects. Unlike elementary particles, which are zero-dimensional or point-like by definition, strings are one-dimensional extended entities. Researchers often h ...
, 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; 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 theoret ...
. 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 descr ...
.
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. Witten's ...
.
References
{{DEFAULTSORT:Heterotic String
String theory
E8 (mathematics)