How are these related?
There is only one dimensional constant in string theory, and that is the inverse string tension with units of area. Sometimes is therefore replaced by a length . The string tension is mostly defined as the fraction
Tension is energy or work per unit length. In natural units and , and hence has dimension of length/energy or length/mass. Since has the dimension of action, i.e. momentum times length, it follows that in natural units mass =1/length, and so has the unit of area.
The slope of a Regge trajectory in
Regge theory is the derivative of spin or angular momentum with respect to mass-squared, i.e.
Since angular momentum is moment of momentum , i.e. length times mass with , is dimensionless in natural units, and has units of or area like the inverse string tension.
3. A Fourier coefficient of a spacetime coordinate.
A function S on the space of fields given (formally) by the integral of the Lagrangian density over spacetime, whose stationary points are the solutions of the equations of motion.
Refers to the ADE classification (An,Dn, E6, E7, E8) of simply laced
Dynkin diagrams, and to several related classifications of Lie algebras, singularities and so on.
ADHM
Initials of Atiyah, Drinfeld, Hitchin, and Manin, as in the
ADHM construction of instantons.
ADM
Initials of Arnowitt, Deser, and Misner, as in
ADM energy, a way of defining the global energy in an asymptotically flat spacetime, or
ADM decomposition of a metric, or
ADM formalism.
AdS
Anti-de Sitter, as in
anti-de Sitter space, a Lorentzian analogue of hyperbolic space
A hypothetical scalar particle whose mass arises from a coupling rather than from a mass term in the Lagrangian, used to resolve the
strong CP problem.
B
b
1. One of the two conformal ghost fields b, c used in the BRST quantization of the bosonic string.
1. Not invariant under the parity symmetry. The word comes from the Greek χειρ meaning "hand"; the terms "left-handed" and "right-handed" are often used to describe chiral objects.
The critical dimension is the spacetime dimension in which a string or superstring theory is consistent; usually 26 for string theories and 10 for superstring theories.
Short for Dirichlet (mem)brane, a submanifold (of dimension p+1) on which the ends of strings are constrained to lie, so that the strings satisfy Dirichlet boundary conditions.
D-string
A D1-brane
DBI
Short for Dirac–Born–Infeld, as in the
DBI action, an action based on the
Born–Infeld action, a modification of the Maxwell action of electrodynamics.
Short for Dirichlet (mem)brane, a submanifold (of dimension p+1) on which the ends of strings are constrained to lie, so that the strings satisfy Dirichlet boundary conditions.
2. Short for
dimensional reduction, a way of constructing theories from simpler theories in higher dimensions, sometimes by making fields invariant under some spacelike translations.
dS
de Sitter, as in
de Sitter space, a Lorentzian analogue of a sphere
A symmetric tensor T (also called the stress-energy tensor) describing the variation of the action under changes in the metric, whose components give the local energy, momentum and stress densities. In flat spacetimes it can also be given by combining the Noether currents of the translation symmetries.
The exceptional Lie algebra of rank 2 and dimension 14, or a
G2 manifold with G2 holonomy.
gaugino
A spin 1/2 supersymmetric partner of a gauge boson.
gh
Abbreviation for ghost; for example, Sgh is the ghost action.
ghost
A vector of negative norm.
GKO
Short for Goddard–Kent–Olive. The GKO construction, also called the
coset construction, is a way of constructing unitary discrete series representations of the Virasoro algebra.
Named after the Greek word
heterosis, meaning hybrid vigour. A hybrid of bosonic string theory and superstring theory, introduced by David Gross, Jeffrey Harvey, Emil Martinec, and Ryan Rohm in 1985.
A partly conjectural relation between a type IIA superstring theory compactified on a Calabi–Yau manifold and a type IIB superstring theory compactified on a different "mirror" Calabi–Yau manifold.
An 11-dimensional theory introduced in the second string theory revolution to unify the 5 known superstring theories. The letter M has been said to stand for membrane, matrix, magic, mystery, monster, and so on.
A theorem stating that some hermitian form is positive semidefinite, in other words has no ghosts (negative norm vectors). The name is a word-play on
no-go theorem.
A p+1 dimensional membrane, where p is a non-negative integer. The dimension of membranes is often given by their space dimension, which is 1 less than their full spacetime dimension.
2.
Regge trajectory: the squared mass of a hadronic resonance is roughly linear in the spin, with the constant of proportionality called the Regge slope.
A
string duality relating theories on a large spacetime to theories on a small spacetime. In particular it exchanges type IIA and IIB superstring theory.
A type of superstring or the corresponding low-energy supergravity theory. The Roman numeral I or II refers to the number of d=10 supersymmetries, and types IIA or IIB are distinguished by whether the supersymmetries of left and right movers have opposite or identical chiralities.
How are these related?
There is only one dimensional constant in string theory, and that is the inverse string tension with units of area. Sometimes is therefore replaced by a length . The string tension is mostly defined as the fraction
Tension is energy or work per unit length. In natural units and , and hence has dimension of length/energy or length/mass. Since has the dimension of action, i.e. momentum times length, it follows that in natural units mass =1/length, and so has the unit of area.
The slope of a Regge trajectory in
Regge theory is the derivative of spin or angular momentum with respect to mass-squared, i.e.
Since angular momentum is moment of momentum , i.e. length times mass with , is dimensionless in natural units, and has units of or area like the inverse string tension.
3. A Fourier coefficient of a spacetime coordinate.
A function S on the space of fields given (formally) by the integral of the Lagrangian density over spacetime, whose stationary points are the solutions of the equations of motion.
Refers to the ADE classification (An,Dn, E6, E7, E8) of simply laced
Dynkin diagrams, and to several related classifications of Lie algebras, singularities and so on.
ADHM
Initials of Atiyah, Drinfeld, Hitchin, and Manin, as in the
ADHM construction of instantons.
ADM
Initials of Arnowitt, Deser, and Misner, as in
ADM energy, a way of defining the global energy in an asymptotically flat spacetime, or
ADM decomposition of a metric, or
ADM formalism.
AdS
Anti-de Sitter, as in
anti-de Sitter space, a Lorentzian analogue of hyperbolic space
A hypothetical scalar particle whose mass arises from a coupling rather than from a mass term in the Lagrangian, used to resolve the
strong CP problem.
B
b
1. One of the two conformal ghost fields b, c used in the BRST quantization of the bosonic string.
1. Not invariant under the parity symmetry. The word comes from the Greek χειρ meaning "hand"; the terms "left-handed" and "right-handed" are often used to describe chiral objects.
The critical dimension is the spacetime dimension in which a string or superstring theory is consistent; usually 26 for string theories and 10 for superstring theories.
Short for Dirichlet (mem)brane, a submanifold (of dimension p+1) on which the ends of strings are constrained to lie, so that the strings satisfy Dirichlet boundary conditions.
D-string
A D1-brane
DBI
Short for Dirac–Born–Infeld, as in the
DBI action, an action based on the
Born–Infeld action, a modification of the Maxwell action of electrodynamics.
Short for Dirichlet (mem)brane, a submanifold (of dimension p+1) on which the ends of strings are constrained to lie, so that the strings satisfy Dirichlet boundary conditions.
2. Short for
dimensional reduction, a way of constructing theories from simpler theories in higher dimensions, sometimes by making fields invariant under some spacelike translations.
dS
de Sitter, as in
de Sitter space, a Lorentzian analogue of a sphere
A symmetric tensor T (also called the stress-energy tensor) describing the variation of the action under changes in the metric, whose components give the local energy, momentum and stress densities. In flat spacetimes it can also be given by combining the Noether currents of the translation symmetries.
The exceptional Lie algebra of rank 2 and dimension 14, or a
G2 manifold with G2 holonomy.
gaugino
A spin 1/2 supersymmetric partner of a gauge boson.
gh
Abbreviation for ghost; for example, Sgh is the ghost action.
ghost
A vector of negative norm.
GKO
Short for Goddard–Kent–Olive. The GKO construction, also called the
coset construction, is a way of constructing unitary discrete series representations of the Virasoro algebra.
Named after the Greek word
heterosis, meaning hybrid vigour. A hybrid of bosonic string theory and superstring theory, introduced by David Gross, Jeffrey Harvey, Emil Martinec, and Ryan Rohm in 1985.
A partly conjectural relation between a type IIA superstring theory compactified on a Calabi–Yau manifold and a type IIB superstring theory compactified on a different "mirror" Calabi–Yau manifold.
An 11-dimensional theory introduced in the second string theory revolution to unify the 5 known superstring theories. The letter M has been said to stand for membrane, matrix, magic, mystery, monster, and so on.
A theorem stating that some hermitian form is positive semidefinite, in other words has no ghosts (negative norm vectors). The name is a word-play on
no-go theorem.
A p+1 dimensional membrane, where p is a non-negative integer. The dimension of membranes is often given by their space dimension, which is 1 less than their full spacetime dimension.
2.
Regge trajectory: the squared mass of a hadronic resonance is roughly linear in the spin, with the constant of proportionality called the Regge slope.
A
string duality relating theories on a large spacetime to theories on a small spacetime. In particular it exchanges type IIA and IIB superstring theory.
A type of superstring or the corresponding low-energy supergravity theory. The Roman numeral I or II refers to the number of d=10 supersymmetries, and types IIA or IIB are distinguished by whether the supersymmetries of left and right movers have opposite or identical chiralities.