Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Regularised Quantum Dimensions of the Singlet Vertex Operator Algebra
  and False Theta Functions   We study a family of non-C2-cofinite vertex operator algebras, called the
singlet vertex operator algebras, and connect several important concepts in the
theory of vertex operator algebras, quantum modular forms, and modular tensor
categories. More precisely, starting from explicit formulae for characters of
modules over the singlet vertex operator algebra, which can be expressed in
terms of false theta functions and their derivatives, we first deform these
characters by using a complex parameter {\epsilon}. We then apply modular
trans- formation properties of regularised partial theta functions to study
asymptotic behaviour of regularised characters of irreducible modules and
compute their regularised quantum dimensions. We also give a purely geometric
description of the regularisation parameter as a uniformisation parameter of
the fusion variety coming from atypical blocks. It turns out that the quantum
dimensions behave very differently depending on the sign of the real part of
{\epsilon}. The map from the space of characters equipped with the Verlinde
product to the space of regularised quantum dimensions turns out to be a
genuine ring isomorphism for positive real part of {\epsilon} while for
sufficiently negative real part of {\epsilon} its surjective image gives the
fusion ring of a rational vertex operator algebra. The category of modules of
this rational vertex operator algebra should be viewed as obtained through the
process of a semi-simplification procedure widely used in the theory of quantum
groups. Interestingly, the modular tensor category structure constants of this
vertex operator algebra, can be also detected from vector valued quantum
modular forms formed by distinguished atypical characters.

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The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat