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| Week 2 1) Using Q=\sigma ^-(W'(\phi)+i\pi), verify that the anticommutator of Q with Q^\dagger gives 2H=\pi ^2+(W')^2-\hbar W''\sigma _3 2) Using the above expression for Q, and the susy variations \delta \chi =[\epsilon ^*Q+\epsilon Q^\dagger, \chi], find the supervariations of \phi and \psi. 3) Using the superspace expressions for Q and Q^\dagger and the superfield \Phi given in lecture, compute \delta \Phi = [\epsilon ^*Q+\epsilon Q^\dagger, \Phi]. Note that \delta \Phi should be hermitian (self adjoint) using the conventions given in lecture. Using this \delta \Phi, determine the super variations of the superfield components \phi, \psi, and F. Note that these argee with those found in part 2 upon setting F=W'. To get the right signs, make sure that if you, say, compare the terms on both sides proportional to \theta, that \theta is all the way to the left of both compared quantities. Be careful with the minus signs, obtained every time a fermionic quantity (any \theta, \epsilon, or \psi) is pulled through another fermionic quantity. ps: there is a typo in the notes for the susy variation of F. As a check, note that the susy variation of F should be hermition, as F is. (Due Oct. 3) top |
| Week 3 PLEASE CLICK ON ASSIGNMENTS 3 ON PREVIOUS PAGE top |
| Week 4 PLEASE CLICK ON WEEK 4 ON PREVIOUS PAGE top |
| Week 5 Optional exercise given in lecture: do the theta integrals in the 2d action given in lecture in terms of superspace. Eliminate the field F. top |
| Week 6 PLEASE CLICK ON WEEK 6 top |
| Week 7 No Homework (time to catch up on those overdue assignments!) top |
| Week 8 PLEASE CLICK ON WEEK 8 top |
| Week 9 Find the scalar potential for the theory with superpotential W=\Phi _1+\Phi _1\Phi _2+\Phi _2\Phi _3 and canonical kinetic terms for the superfields \Phi _1, \Phi _2, \Phi _3. Is there a supersymmetric vacuum? What is Tr(-1)^F? (Due Nov. 21) top |
| Week 10 top |