Supermultiplet
Encyclopedia
In theoretical physics
, a supermultiplet is formally a group representation
of a supersymmetry
algebra. It consists of a collection of particles, called superpartner
s, corresponding to operators in a quantum field theory
which in superspace
are represented by superfield
s.
Superfields were introduced by Abdus Salam
and J. A. Strathdee in their 1974 article Supergauge Transformations. Operations on superfields and a partial classification were presented a few months later by Sergio Ferrara
, Julius Wess
and Bruno Zumino
in Supergauge Multiplets and Superfields.
The most commonly used supermultiplets are vector multiplets, linear multiplets, chiral multiplets
(in 4d N=1 supersymmetry for example), hypermultiplets (in 4d N=2 supersymmetry for example), tensor multiplets and gravity multiplets. The highest component of a vector multiplet is a gauge boson
, the highest component of a chiral or hypermultiplet is a spinor
, the highest component of a gravity multiplet is a graviton
. The names are defined so as to be invariant under dimensional reduction
, although the organization of the fields as representations of the Lorentz group
changes.
Especially in theories with extended supersymmetry, supermultiplets can be divided to short supermultiplets and long supermultiplets, essentially according to the dimensionality. The short supermultiplets coincide with the BPS state
s.
A scalar is never the highest component of a superfield, whether it appears in a superfield at all depends on the dimension of the spacetime. For example, in a 10-dimensional N=1 theory the vector multiplet contains only a vector and a Majorana-Weyl spinor, while its dimensional reduction on a d-dimensional torus
is a vector multiplet containing d real scalars. Similarly, in an 11-dimensional theory there is only one supermultiplet with a finite number of fields, the gravity multiplet, and it contains no scalars. However again its dimensional reduction on a d-torus to a maximal gravity multiplet does contain scalars.
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
, a supermultiplet is formally a group representation
Group representation
In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication...
of a supersymmetry
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
algebra. It consists of a collection of particles, called superpartner
Superpartner
In particle physics, a superpartner is a hypothetical elementary particle. Supersymmetry is one of the synergistic theories in current high-energy physics which predicts the existence of these "shadow" particles....
s, corresponding to operators in a quantum field theory
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...
which in superspace
Superspace
"Superspace" has had two meanings in physics. The word was first used by John Wheeler to describe the configuration space of general relativity; for example, this usage may be seen in his famous 1973 textbook Gravitation....
are represented by superfield
Superfield
In theoretical physics, one often analyzes theories with supersymmetry in which superfields play a very important role. In four dimensions, the simplest example - namely the minimal N=1 supersymmetry - may be written using a superspace with four extra fermionic coordinates...
s.
Superfields were introduced by Abdus Salam
Abdus Salam
Mohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk (Urdu: محمد عبد السلام, pronounced , (January 29, 1926– November 21, 1996) was a Pakistani theoretical physicist and Nobel laureate in Physics for his work on the electroweak unification of the...
and J. A. Strathdee in their 1974 article Supergauge Transformations. Operations on superfields and a partial classification were presented a few months later by Sergio Ferrara
Sergio Ferrara
Sergio Ferrara is an Italian physicist working on theoretical physics of elementary particles and mathematical physics. He is renowned for the discovery of theories introducing supersymmetry as a symmetry of elementary particles Sergio Ferrara (born 1945) is an Italian physicist working on...
, Julius Wess
Julius Wess
Julius Wess was an Austrian theoretical physicist noted as the co-inventor of the Wess–Zumino model and Wess–Zumino–Witten model in the field of supersymmetry...
and Bruno Zumino
Bruno Zumino
Bruno Zumino is an Italian theoretical physicist and emeritus faculty at the University of California, Berkeley. He got his bachelor degree from the University of Rome in 1945...
in Supergauge Multiplets and Superfields.
The most commonly used supermultiplets are vector multiplets, linear multiplets, chiral multiplets
Chiral superfield
In theoretical physics, one often analyzes theories with supersymmetry in which chiral superfields play an important role. In four dimensions, the minimal N=1 supersymmetry may be written using the notion of superspace...
(in 4d N=1 supersymmetry for example), hypermultiplets (in 4d N=2 supersymmetry for example), tensor multiplets and gravity multiplets. The highest component of a vector multiplet is a gauge boson
Gauge boson
In particle physics, gauge bosons are bosonic particles that act as carriers of the fundamental forces of nature. More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons, usually as virtual particles.-...
, the highest component of a chiral or hypermultiplet is a spinor
Spinor
In mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the space of spinors cannot be built up in a unique and natural way from spatial vectors...
, the highest component of a gravity multiplet is a graviton
Graviton
In physics, the graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton must be massless and must have a spin of 2...
. The names are defined so as to be invariant under dimensional reduction
Dimensional reduction
In physics, a theory in D spacetime dimensions can be redefined in a lower number of dimensions d, by taking all the fields to be independent of the location in the extra D − d dimensions....
, although the organization of the fields as representations of the Lorentz group
Lorentz group
In physics , the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical setting for all physical phenomena...
changes.
Especially in theories with extended supersymmetry, supermultiplets can be divided to short supermultiplets and long supermultiplets, essentially according to the dimensionality. The short supermultiplets coincide with the BPS state
BPS state
In theoretical physics, BPS states are massive representations of an extended supersymmetry algebra with mass equal to the supersymmetry central charge Z. Quantum mechanically, if the supersymmetry does not get broken, the mass is exactly equal to the modulus of Z...
s.
A scalar is never the highest component of a superfield, whether it appears in a superfield at all depends on the dimension of the spacetime. For example, in a 10-dimensional N=1 theory the vector multiplet contains only a vector and a Majorana-Weyl spinor, while its dimensional reduction on a d-dimensional torus
Torus
In geometry, a torus is a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with the circle...
is a vector multiplet containing d real scalars. Similarly, in an 11-dimensional theory there is only one supermultiplet with a finite number of fields, the gravity multiplet, and it contains no scalars. However again its dimensional reduction on a d-torus to a maximal gravity multiplet does contain scalars.