Generalized Rogers Ramanujan Identities from AGT Correspondence

AGT correspondence and its generalizations attracted a great deal of attention recently. In particular it was suggested that $U(r)$ instantons on $R^4/Z_p$ describe the conformal blocks of the coset ${\cal A}(r,p)=U(1)\times sl(p)_r\times {sl(r)_p\times sl(r)_n\over sl(r)_{n+p}}$, where $n$ is a parameter. Our purpose here is to describe Generalized Rogers Ramanujan (GRR) identities for these cosets, which expresses the characters as certain $q$ series. We propose that such identities exist for the coset ${\cal A}(r,p)$ for all positive integers $n$ and all $r$ and $p$. We treat here the case of $n=1$ and $r=2$, finding GRR identities for all the characters.Comment: 11 page

Special geometry on the 101 dimesional moduli space of the quintic threefold

A new method for explicit computation of the CY moduli space metric was proposed by the authors recently. The method makes use of the connection of the moduli space with a certain Frobenius algebra. Here we clarify this approach and demonstrate its efficiency by computing the Special geometry of the 101-dimensional moduli space of the quintic threefold around the orbifold point.Comment: We made exposition more clear, in particular we explained how to generalize our idea

Special geometry on the moduli space for the two-moduli non-Fermat Calabi-Yau

We clarify the recently proposed method to compute a Special K\"ahler metric on a Calabi-Yau complex structures moduli space that uses the fact that the moduli space is a subspace of specific Frobenius manifold. We apply this method to computing the Special K\"ahler metric in a two-moduli non-Fermat model which has been unknown until now