## Infinite Analysis Seminar Tokyo

Seminar information archive ～11/01｜Next seminar｜Future seminars 11/02～

Date, time & place | Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
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### 2016/10/27

15:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Non-unitary highest-weight modules over the $N=2$ superconformal algebra (JAPANESE)

**Ryou Sato**(Graduate School of Mathematical Scineces, The University of Tokyo)Non-unitary highest-weight modules over the $N=2$ superconformal algebra (JAPANESE)

[ Abstract ]

The $N=2$ superconformal algebra is a generalization of the Virasoro algebra having the super symmetry.

The character formulas associated with the unitary highest weight representations

are expressed in terms of the classical theta functions, and have the remarkable

modular invariance. Based on the method of the $W$-algebras,

Kac and Wakimoto, on the other hand, showed that the

characters for a certain class of non-unitary highest weight representations

can be written in terms of the mock theta functions associated with the affine ${sl}_{2|1}$.

Then they found a way to identify these formulas with

real analytic modular forms by using the correction terms given by Zwegers.

In this seminar, we explain a way to construct the above mentioned

non-unitary representations from the representations of the algebra affine ${sl}_{2}$,

based on the Kazama-Suzuki coset construction, namely not from the $W$-algebra method.

We also investigate the relations between the mock theta functions and the ordinary

theta functions, appearing in this method.

The $N=2$ superconformal algebra is a generalization of the Virasoro algebra having the super symmetry.

The character formulas associated with the unitary highest weight representations

are expressed in terms of the classical theta functions, and have the remarkable

modular invariance. Based on the method of the $W$-algebras,

Kac and Wakimoto, on the other hand, showed that the

characters for a certain class of non-unitary highest weight representations

can be written in terms of the mock theta functions associated with the affine ${sl}_{2|1}$.

Then they found a way to identify these formulas with

real analytic modular forms by using the correction terms given by Zwegers.

In this seminar, we explain a way to construct the above mentioned

non-unitary representations from the representations of the algebra affine ${sl}_{2}$,

based on the Kazama-Suzuki coset construction, namely not from the $W$-algebra method.

We also investigate the relations between the mock theta functions and the ordinary

theta functions, appearing in this method.