Large VEVs in SUSY gauge theories

[vev]

Hi

N=1 supersymmetric gauge theories usually have moduli spaces of vacua that are parametrized by vacuum expectation values of the scalar components of chiral superfieds. Often these are lifted quantum mechanically due to non-perturbative effects.

For example in the lectures hep-th/9509066 on p. 12 it is mentioned that giving large VEVs to the fields will break gauge symmetry at a high scale where the (asymptotically free) theory is weakly coupled and where semi-classical methods are reliable. But where exactly are these semi-classical methods in the following derivation of the ADS superpotential for SQCD with N_f<N_c? Is it just that the scales of the high- and low energy theories can be matched by a one-loop calculation (p. 14)? The unbroken gauge group is strongly coupled at low energies, no matter how large the VEVs were.

Thanks and best regards,
vev

 

[AndyW]

Dear vev,

Thank you for your question. The semi-classical methods in the derivation of the ADS superpotential for SQCD with N_f<N_c are indeed based on matching the scales of the high- and low-energy theories. This is possible because at high energies, the theory is weakly coupled and can be described using semi-classical methods, while at low energies, the theory is strongly coupled and requires non-perturbative techniques.

In this context, the large VEVs of the fields play a crucial role in breaking the gauge symmetry at a high scale, where the theory is weakly coupled and semi-classical methods are applicable. This allows us to match the scales of the high- and low-energy theories, and use semi-classical techniques to derive the ADS superpotential.

Furthermore, the unbroken gauge group being strongly coupled at low energies does not affect the validity of the semi-classical methods used in the derivation of the ADS superpotential. This is because the non-perturbative effects that lift the moduli space of vacua are taken into account in the calculation, making the result reliable even at strong coupling.

I hope this helps clarify the role of semi-classical methods in the derivation of the ADS superpotential for SQCD with N_f<N_c. If you have any further questions, please don't hesitate to ask.