nLab chiral ring

Idea

The cohomology groups of the twisting operator in topologically twisted N=2 D=4 super Yang-Mills theory form a ring. This is called the chiral ring of the theory.

For one of the possible twists this is the ordinary cohomology of a corresponding Kähler manifold. For the other it is a deformation thereof by instanton-correction, also called a quantum cohomology.

References

Lecture notes are in

• Edward Witten, Dynamical aspects of QFT, Lecture 14: $N=2$ SUSY Theories in Dimension Two, Part II: Chiral Rings and Twisted Theories, in Part IV of Quantum Fields and Strings.

Original articles include

• Freddy Cachazo, Michael Douglas, Nathan Seiberg, Edward Witten. Chiral Rings and Anomalies in Supersymmetric Gauge Theory, JHEP 0212:071,2002 (arXiv:hep-th/0211170)