Higgs phase
Encyclopedia
In theoretical physics
, it is often important to consider gauge theory
that admits many physical phenomena and "phases", connected by phase transition
s, in which the vacuum may be found.
Gauge symmetry may be broken by the Higgs mechanism
. In more general theories such as those relevant in string theory
, there are often many Higgs fields that transform in different representations of the gauge group.
If they transform in the adjoint representation
or a similar representation, the original gauge symmetry is typically broken to a product of U(1) factors. Because U(1) describes electromagnetism including the Coulomb field, the corresponding phase is called a Coulomb phase.
If the Higgs fields that induce the spontaneous symmetry breaking
transform in other representations, the Higgs mechanism often breaks the gauge group completely and no U(1) factors are left. In this case, the corresponding vacuum expectation value
s describe a Higgs phase.
Using the representation of a gauge theory in terms of a D-brane
, for example D4-brane combined with D0-branes, the Coulomb phase describes D0-branes that have left the D4-branes and carry their own independent U(1) symmetries. The Higgs phase describes D0-branes dissolved in the D4-branes as instanton
s.
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
, it is often important to consider gauge theory
Gauge theory
In physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...
that admits many physical phenomena and "phases", connected by phase transition
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
s, in which the vacuum may be found.
Gauge symmetry may be broken by the Higgs mechanism
Higgs mechanism
In particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire non-vanishing masses through absorption of Nambu-Goldstone bosons arising in spontaneous symmetry breaking....
. In more general theories such as those relevant 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...
, there are often many Higgs fields that transform in different representations of the gauge group.
If they transform in the adjoint representation
Adjoint representation
In mathematics, the adjoint representation of a Lie group G is the natural representation of G on its own Lie algebra...
or a similar representation, the original gauge symmetry is typically broken to a product of U(1) factors. Because U(1) describes electromagnetism including the Coulomb field, the corresponding phase is called a Coulomb phase.
If the Higgs fields that induce the spontaneous symmetry breaking
Spontaneous symmetry breaking
Spontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....
transform in other representations, the Higgs mechanism often breaks the gauge group completely and no U(1) factors are left. In this case, the corresponding vacuum expectation value
Vacuum expectation value
In quantum field theory the vacuum expectation value of an operator is its average, expected value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle...
s describe a Higgs phase.
Using the representation of a gauge theory in terms of a D-brane
D-brane
In string theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions, after which they are named. D-branes were discovered by Dai, Leigh and Polchinski, and independently by Hořava in 1989...
, for example D4-brane combined with D0-branes, the Coulomb phase describes D0-branes that have left the D4-branes and carry their own independent U(1) symmetries. The Higgs phase describes D0-branes dissolved in the D4-branes as instanton
Instanton
An instanton is a notion appearing in theoretical and mathematical physics. Mathematically, a Yang–Mills instanton is a self-dual or anti-self-dual connection in a principal bundle over a four-dimensional Riemannian manifold that plays the role of physical space-time in non-abelian gauge theory...
s.