超弦论习题测试答案Gt'Hooft.pdfVIP

SOLUTION OF THE STRING THEORY TEST Tuesday, June 22, 2004 Exercise 1 1. For an open superstring of type I, we have two sectors, called Ramond (R) and Neveu-Schwarz (NS). Summarize in your own words why we have exactly these two sectors. 2. Explain why the NS sector describes only bosonic solutions (string solutions that have integer spin) and the R sector only fermionic ones (solutions with spin integer+ 1). 2 3. In contrast with open strings, closed strings have four sectors: R-R, R-NS, NS- R and NS-NS. Explain why this is so, and explain which of these describe bosons and which describe fermions. 4. The GSO projection mechanism has two effects. Explain in your own words why this mechanism is needed to obtain consistent superstring theories. 5. Explain the main difference between type IIA and type IIB superstring theories. Solution There is of course some amount of freedom in answering the theoretical questions of this exercise. However, for each point the following facts should at least be mentioned. 1. Varying the action for µ , one gets the following boundary conditions: µ µ µ µ σ=π ( −δ − − +δ + ) = 0 , σ=0 which, for an open string, can be solved by imposing µ (τ, 0) = µ (τ, 0) (here + − we can choose the + sign due to some freedom in the definition of the sign of the wavefunctions) and µ (τ, π) = ± µ (τ, π). Anti-periodicity is allowed