M-theory. M-theory is a theory in physics that unifies all consistent versions of superstring theory.

The existence of such a theory was first conjectured by Edward Witten at the string theory conference at the University of Southern California in the summer of 1995. Witten's announcement initiated a flurry of research activity known as the second superstring revolution. Background[edit] Quantum gravity and strings[edit] Superstring theory. 'Superstring theory' is a shorthand for supersymmetric string theory because unlike bosonic string theory, it is the version of string theory that incorporates fermions and supersymmetry.

Since the second superstring revolution the five superstring theories are regarded as different limits of a single theory tentatively called M-theory, or simply string theory. Background[edit] The deepest problem in theoretical physics is harmonizing the theory of general relativity, which describes gravitation and applies to large-scale structures (stars, galaxies, super clusters), with quantum mechanics, which describes the other three fundamental forces acting on the atomic scale. Grand Unified Theory. A Grand Unified Theory (GUT) is a model in particle physics in which at high energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single interaction characterized by one larger gauge symmetry and thus one unified coupling constant.

During the grand unification epoch, the gauge force separated from the gravitational force. Models that do not unify all interactions using one simple Lie group as the gauge symmetry, but do so using semisimple groups, can exhibit similar properties and are sometimes referred to as Grand Unified Theories as well. Unifying gravity with the other three interactions would provide a theory of everything (TOE), rather than a GUT. Nevertheless, GUTs are often seen as an intermediate step towards a TOE. Supersymmetry. Supersymmetry differs notably from currently known symmetries in that it establishes a symmetry between classical and quantum physics, which up to now has not been observed in any other domain.

While any number of bosons can occupy the same quantum state, for fermions this is not possible because of the exclusion principle, which allows only one fermion in a given state. But when the occupation numbers become large, quantum physics approaches the classical limit. This means that while bosons also exist in classical physics, fermions do not. That makes it difficult to expect that bosons, if at all, possess the same quantum numbers as fermions.[4] There is only indirect evidence for the existence of supersymmetry, primarily in the form of evidence for gauge coupling unification.[5] However this refers only to electroweak and strong interactions and does not provide the ultimate unification of all interactions, since it leaves gravitation untouched.

Gauge theory. Lattice gauge theory. Basics[edit] In lattice gauge theory, the spacetime is Wick rotated into Euclidean space and discretized into a lattice with sites separated by distance and connected by links.

In the most commonly considered cases, such as lattice QCD, fermion fields are defined at lattice sites (which leads to fermion doubling), while the gauge fields are defined on the links. That is, an element U of the compact Lie group G is assigned to each link. Hence to simulate QCD, with Lie group SU(3), there is a 3×3 special unitary matrix defined on each link. Yang–Mills action[edit] The Yang–Mills action is written on the lattice using Wilson loops (named after Kenneth G. There are many possible lattice Yang-Mills actions, depending on which Wilson loops are used in the action.

Lattice field theory. Just as in all lattice models, numerical simulation gives access to field configurations that are not accessible to perturbation theory, such as solitons.

Likewise, non-trivial vacuum states can be discovered and probed. The method is particularly appealing for the quantization of a gauge theory. Most quantization methods keep Poincaré invariance manifest but sacrifice manifest gauge symmetry by requiring gauge fixing. Only after renormalization can gauge invariance be recovered. Lattice field theory differs from these in that it keeps manifest gauge invariance, but sacrifices manifest Poincaré invariance— recovering it only after renormalization. Effective field theory. The renormalization group[edit] Presently, effective field theories are discussed in the context of the renormalization group (RG) where the process of integrating out short distance degrees of freedom is made systematic.

Although this method is not sufficiently concrete to allow the actual construction of effective field theories, the gross understanding of their usefulness becomes clear through a RG analysis. Electroweak interaction. In particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction.

Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 100 GeV, they would merge into a single electroweak force. Thus if the universe is hot enough (approximately 1015 K, a temperature exceeded until shortly after the Big Bang) then the electromagnetic force and weak force merge into a combined electroweak force.

Quantum chromodynamics. Quantum field theory. For example, quantum electrodynamics (QED) has one electron field and one photon field; quantum chromodynamics (QCD) has one field for each type of quark; and, in condensed matter, there is an atomic displacement field that gives rise to phonon particles.

Edward Witten describes QFT as "by far" the most difficult theory in modern physics.[1] In QFT, quantum mechanical interactions between particles are described by interaction terms between the corresponding underlying fields. QFT interaction terms are similar in spirit to those between charges with electric and magnetic fields in Maxwell's equations. Standard Model.