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## Main Question or Discussion Point

Hello everybody,

I have three quite mathematical questions in modern QFT.

1) Why it's supposed that N=2 SUSY Yang-Mills probably cannot be put on a lattice?

2) What is the recent status of lattice approach to conformal quantum field theories?

This question is motivated by the following reason. There are some interesting mathematical structures (such as discrete holomorphicity and random walks) which arise in lattice approach to 2D statistical physics and help one to derive rigorous results (ctitical percolation, conformal invariance of scaling limit etc). Have these structures anything to say about 2D quantum CFT (Liouville theory for example).

3) E.Witten has shown in his work "Gauge theories and integrable lattice models" (1989) that calculation of expectation values of Wilson loops in 3D Chern-Simons theory with compact gauge group can be done with the help of partition functions of some integrable discrete statistical models. However, I've seen no explanation why these models need to be integrable (is they are at all). So what is known nowadays about the connection between 3D Chern-Simons theory and integrability in 2D? What is known about Chern-Simons theory with non-compact gauge group?

I would be gratefull for anybody who answer me.

I have three quite mathematical questions in modern QFT.

1) Why it's supposed that N=2 SUSY Yang-Mills probably cannot be put on a lattice?

2) What is the recent status of lattice approach to conformal quantum field theories?

This question is motivated by the following reason. There are some interesting mathematical structures (such as discrete holomorphicity and random walks) which arise in lattice approach to 2D statistical physics and help one to derive rigorous results (ctitical percolation, conformal invariance of scaling limit etc). Have these structures anything to say about 2D quantum CFT (Liouville theory for example).

3) E.Witten has shown in his work "Gauge theories and integrable lattice models" (1989) that calculation of expectation values of Wilson loops in 3D Chern-Simons theory with compact gauge group can be done with the help of partition functions of some integrable discrete statistical models. However, I've seen no explanation why these models need to be integrable (is they are at all). So what is known nowadays about the connection between 3D Chern-Simons theory and integrability in 2D? What is known about Chern-Simons theory with non-compact gauge group?

I would be gratefull for anybody who answer me.