theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...

, it is often important to consider

gauge theory 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 groups) ...

that admits many physical phenomena and "phases", connected by

phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...

s, in which the vacuum may be found. Global symmetries in a gauge theory may be broken by the

Higgs mechanism In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other bein ...

. In more general theories such as those relevant 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 ...

, there are often many

Higgs field The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory. In the Stand ...

s that transform in different representations of 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 ...

. If they transform in the

adjoint representation In mathematics, the adjoint representation (or adjoint action) of a Lie group ''G'' is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if ''G'' is G ...

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 is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion or the ...

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 In quantum field theory the vacuum expectation value (also called condensate or simply VEV) of an operator is its average or expectation 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 In string theory, D-branes, short for ''Dirichlet membrane'', 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 Jin Dai, Leigh, and Polchi ...

, 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 An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a finite, non-zero action, either in quantum mechanics or in quantum field theory. Mo ...

References

Gauge theories {{quantum-stub