# Limits of N=2 superconformal minimal models

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After conformal eld theory(CFT) became a popular topic to study in the 1980s, many different kinds of models were built to solve problems in physics; in particular minimal models as basic models. If the models contain two super-symmetry, we call them N = 2 superconformal minimal models. After that the minimal models without supersymmetry and N = 1 superconformal minimal models were studied. Until recently, the N = 2 superconformal conformal field theory(SCFT) minimal models were not studied. In this thesis we applied the character of N = 2 supersymmetry. From the expressions of the highest weight h and U(1) current, we obtained the relation between them. Based on this we got the spectrum of N = 2 conformal minimal models. Starting from correlation functions in CFT and considering N = 2 supersymmetry we calculated the two point function and the three point function for N = 2 SCFT minimal models. Because of N = 2 SCFT, we have a different form for two point function and three point function than that were obtained with N = 1 SCFT minimal models and CFT minimal models. By taking the limits, we got the explicit expression for three point function. In the calculation, 3j-Wigner symbols were used and BranesG function was involved in the integration. Because of the approximation we used in the calculation of spectrum, what we calculated before was all about A-type branes in string theory(with m coming from the representations of the chiral algebra is nonzero), but there are also B-type branes(with m equals zero). We then use the Cardy boundary conditions to calculate the one point function for A-type and B-type boundary states. The Cardy boundary condition for B-type branes is similar to the condition for A-type branes only with a dierent factor because the A-type boundary condition is in the closed string channel while the B-type boundary condition is in the open string channel. Using the normalization factor which we get from two and three point functions and applying the dierent Cardy boundary conditions for A-type and B-type boundary states, we calculate the one point function for both A-type and B-type branes. Instead of keeping the boundary labels xed, we x the U(1) current when take the limit, defining another class of boundary conditions we have the one point function in terms of U(1) current q. Similarly, we also calculated two point function for B-type branes.

**Nyckelord: **Superconformal field theory, minimal models, spectrum, two point function, three point function, one point function, Cardy boundary condition