Heterotic string
Encyclopedia
In physics
, a heterotic string is a peculiar mixture (or hybrid) of the bosonic string
and the superstring (the adjective heterotic comes from the Greek word heterosis
, hybrid vigour). In string theory
, the left-moving and the right-moving excitations almost do not interact with each other, and it is possible to construct a string theory whose left-moving (counter-clockwise) excitations "think" that they live on a bosonic string propagating in D = 26 dimensions, while the right-moving (clock-wise) excitations "think" that they belong to 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
-free gauge groups that can be coupled to the N = 1 supergravity
in 10 dimensions other than U(1)496 and E8 × U(1)248, which is suspected to lie in the swampland.
Heterotic string theory was first developed in 1985 by David Gross
, Jeffrey Harvey, Emil Martinec
, and Ryan Rohm (the so-called Princeton String Quartet), in one of the key papers that fueled the first superstring revolution. A year later in 1986, Strominger derived the Strominger's equations
which are the necessary and sufficient conditions for spacetime supersymmetry. In the 1990s, it was realized that the strong coupling limit of the HO theory is type I string theory — a theory that also contains open strings; this relation is called S-duality
. On the other hand, the strongly coupled limit of the HE theory is M-theory
compactified on a line interval (bounded by Horava-Witten domain walls, as explained by Petr Hořava
and Edward Witten
).
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.
A heterotic string is embedded in the membrane that creates harmonics on the string which translate into mass and energy through mechanisms discussed above.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, a heterotic string is a peculiar mixture (or hybrid) of the bosonic string
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...
and the superstring (the adjective heterotic comes from the Greek word heterosis
Heterosis
Heterosis, or hybrid vigor, or outbreeding enhancement, is the improved or increased function of any biological quality in a hybrid offspring. The adjective derived from heterosis is heterotic....
, hybrid vigour). 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...
, the left-moving and the right-moving excitations almost do not interact with each other, and it is possible to construct a string theory whose left-moving (counter-clockwise) excitations "think" that they live on a bosonic string propagating in D = 26 dimensions, while the right-moving (clock-wise) excitations "think" that they belong to 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
E8 (mathematics)
In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8...
(the HE string).
These two gauge groups also turned out to be the only two anomaly
Anomaly (physics)
In quantum physics an anomaly or quantum anomaly is the failure of a symmetry of a theory's classical action to be a symmetry of any regularization of the full quantum theory. In classical physics an anomaly is the failure of a symmetry to be restored in the limit in which the symmetry-breaking...
-free gauge groups that can be coupled to the N = 1 supergravity
Supergravity
In theoretical physics, supergravity is a field theory that combines the principles of supersymmetry and general relativity. Together, these imply that, in supergravity, the supersymmetry is a local symmetry...
in 10 dimensions other than U(1)496 and E8 × U(1)248, which is suspected to lie in the swampland.
Heterotic string theory was first developed in 1985 by David Gross
David Gross
David Jonathan Gross is an American particle 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. He is currently the director and holder of the Frederick W...
, Jeffrey Harvey, Emil Martinec
Emil Martinec
Emil John Martinec is an American theoretical physicist born in 1958. He graduated from Northwestern University in 1979 and obtained his Ph.D. from Cornell University in 1984. He spent the last two years of his graduate education at SLAC after his dissertation advisor, Michael Peskin, left...
, and Ryan Rohm (the so-called Princeton String Quartet), in one of the key papers that fueled the first superstring revolution. A year later in 1986, Strominger derived the Strominger's equations
Strominger's equations
In heterotic string theory, the Strominger's equations are the set of equations that are necessary and sufficient conditions for spacetime supersymmetry...
which are the necessary and sufficient conditions for spacetime supersymmetry. In the 1990s, it was realized that the strong coupling limit of the HO theory is type I string theory — a theory that also contains open strings; this relation is called S-duality
S-duality
In theoretical physics, S-duality is an equivalence of two quantum field theories or string theories. An S-duality transformation maps states and vacua with coupling constant g in one theory to states and vacua with coupling constant 1/g in the dual theory...
. On the other hand, the strongly coupled limit of the HE theory is M-theory
M-theory
In theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds that of superstring theories in 10 dimensions, proponents believe that the 11-dimensional theory unites all five string theories...
compactified on a line interval (bounded by Horava-Witten domain walls, as explained by Petr Hořava
Petr Horava
Petr Hořava is a Czech string theorist. He is currently a professor of physics at the University of California, Berkeley, where he frequently teaches courses on quantum field theory and string theory...
and Edward Witten
Edward Witten
Edward Witten is an American theoretical physicist with a focus on mathematical physics who is currently a professor of Mathematical Physics at the Institute for Advanced Study....
).
Every heterotic string must be a closed string, not an open string
String (physics)
A string is a hypothetical vibrating one-dimensional sub-atomic structure and one of the main objects of study in string theory, a branch of theoretical physics. There are different string theories, many of which are unified by M-theory. A string is an object with a one-dimensional spatial extent,...
; 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.
A heterotic string is embedded in the membrane that creates harmonics on the string which translate into mass and energy through mechanisms discussed above.