Green–Schwarz mechanism
String theory |
---|
Fundamental objects |
Perturbative theory |
Non-perturbative results |
Phenomenology |
Mathematics |
|
The Green–Schwarz mechanism (sometimes called the Green–Schwarz anomaly cancellation mechanism) is the main discovery that started the
Discovery
In 1984,
gauge group of type I string theory must be 496
and then demonstrated this to be so.
In the original calculation,
one-loop diagram, but in reality, both of these diagrams arise as one-loop diagrams in superstring theory
in which the anomaly cancellation is more transparent.
As recounted in The Theory of Everything".
Details
Anomalies in quantum theory arise from one-loop diagrams, with a chiral fermion in the loop and gauge fields,
SUSY
D = 10 gauge theory is the hexagon which has a particular linear combination of the two-form gauge field strength and Ricci tensor, , for the external lines.
Green and Schwarz realized that one can add a so-called
Chern–Simons
term to the classical action,
having the form , where the integral is over the 10 dimensions, is the rank-two Kalb–Ramond field, and is
a gauge invariant combination of (with space-time indices not contracted), which is precisely one of the factors appearing in the hexagon anomaly.
If the variation of under the transformations of gauge field for and under general coordinate transformations is appropriately specified, then
the Green–Schwarz term , when combined with a trilinear vertex through exchange of a gauge boson, has precisely the right variation to cancel the hexagon anomaly.
References
- .
- ^ Clifford V. Johnson, D-branes, Cambridge University Press, 2003, section 7.1.4.
- .