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In this paper we examine fermionic type characters (Universal Chiral Partition Functions) for general 2D conformal field theories with a bilinear form given by a matrix of the form K oplus K^{-1}. We provide various techniques for determining these K-matrices, and apply these to a variety of examples including (higher level) WZW and coset conformal field theories. Applications of our results to fractional quantum Hall systems and (level restricted) Kostka polynomials are discussed.
We extend the work of Hellerman (arxiv:0902.2790) to derive an upper bound on the conformal dimension $Delta_2$ of the next-to-lowest nontrival primary operator in unitary two-dimensional conformal field theories without chiral primary operators. The
We study the spectrum of Landau-Ginzburg theories in 1+1 dimensions using the truncated conformal space approach employing a compactified boson. We study these theories both in their broken and unbroken phases. We first demonstrate that we can reprod
The loss of criticality in the form of weak first-order transitions or the end of the conformal window in gauge theories can be described as the merging of two fixed points that move to complex values of the couplings. When the complex fixed points a
In this paper, we apply the K-theory scheme of classifying the topological insulators/superconductors to classify the topological classes of the massive multi-flavor fermions in anti-de Sitter (AdS) space. In the context of AdS/CFT correspondence, th
Supersymmetric theories with the same bosonic content but different fermions, aka emph{twins}, were thought to exist only for supergravity. Here we show that pairs of super conformal field theories, for example exotic $mathcal{N}=3$ and $mathcal{N}=1