Studies in N = 2 supersymmetric conformal field theory

Thesis/Dissertation · Wed Jan 01 04:00:00 EST 1992

OSTI ID:50555

Huitu, K L.P.

The two-dimensional conformal field theories are important as building blocks for the compactification of the string theories as well as models for the long distance behavior of two-dimensional statistical mechanical systems at the critical point. Through the study of conformal field theory new connections between physics and mathematics have been established. An outstanding problem in the context of conformal theories is the classification of all theories. An important tool in the classification is the modular invariance of the partition function. Modular invariance is one of the most stringent constraints in the theory. The partition function is built of the characters of representations of the theory. Another important restriction in a theory is the single-valuedness of the correlation functions. An attractive property for a theory is N = 1 supersymmetry in space-time. This is achieved by choosing a conformal theory with N = 2 supersymmetry. A wide class of N = 2 superconformal models were found by Kazama and Suzuki. The author shows how to calculate branching functions for coset models. As an example consider the parafermionic theories SU(2)/U(1) and the minimal N = 2 supersymmetric models. The author also derives the character for the SU(3)/SU(3)/SU(2) x U(1) coset model of Kazama and Suzuki and SU(3)/U(1){sup 2} parafermions. Furthermore, characters of a class of Kazama-Suzuki models, the N = 2 superconformal CP{sup n} models, are found by the so-called Feigin-Fuks method. These characters are in a manifestly supersymmetric form. Via the Feigien-Fuks method the author finds the correlation functions of bosioinized parafermionic models and explains how to use these results to obtain the correlation functions of N = 2 superconformal models. The modular properties of characters of the N = 2 CP{sup 3} models are examined.

• Research Organization: University of Southern California, Los Angeles, CA (United States)
• OSTI ID: 50555
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
COMPACTIFICATION
CONFORMAL GROUPS
FIELD THEORIES
PARTITION FUNCTIONS
STRING MODELS
SUPERSYMMETRY