Moduli Spaces of Supersymmetric Gauge Theories
In general quantum field theories, even if the classical potential energy is minimized over a large set of possible expectation values, generically once quantum corrections are included nearly all of these configurations cease to minimize the energy. The result is that the set of vacua of the quantum theory is generally much smaller than that of the classical theory. A notable exception occurs when the various vacua in question are related by a symmetry which guarantees that their energy levels remain exactly degenerate.
The situation is very different in supersymmetric quantum field theories. In general these possess large moduli spaces of vacua which are not related by any symmetry, for example the masses of the various excitations may differ at various points on the moduli space. The moduli spaces of supersymmetric gauge theories are in general easier to calculate than those of nonsupersymmetric theories because supersymmetry restricts the allowed geometries of the moduli space even when quantum corrections are included.
Read more about this topic: Moduli (physics)
Famous quotes containing the words spaces and/or theories:
“Surely, we are provided with senses as well fitted to penetrate the spaces of the real, the substantial, the eternal, as these outward are to penetrate the material universe. Veias, Menu, Zoroaster, Socrates, Christ, Shakespeare, Swedenborg,—these are some of our astronomers.”
—Henry David Thoreau (1817–1862)
“The wise man regulates his conduct by the theories both of religion and science. But he regards these theories not as statements of ultimate fact but as art-forms.”
—J.B.S. (John Burdon Sanderson)