Since we aim at drawing parallels between black holes and two-dimensional CFTs ( CFTs), it is useful
to describe some key properties of
CFTs. Background material can be found, e.g., in [120, 149, 234].
An important caveat to keep in mind is that there are only sparse results in gravity that can be
interpreted in terms of a
CFT. Only future research will tell if
CFTs are the right
theories to be considered (if a holographic correspondence can be precisely formulated at all) or if
generalized field theories with conformal invariance are needed. For progress in this direction,
see [130
, 169].
A CFT is defined as a local quantum field theory with local conformal invariance. In
two-dimensions, the local conformal group is an infinite-dimensional extension of the globally-defined
conformal group
on the plane or on the cylinder. It is generated by two sets of vector
fields
,
obeying the Lie bracket algebra
A CFT can be uniquely characterized by a list of (primary) operators
, the conformal
dimensions of these operators (their eigenvalue under
and
) and the operator product expansions
between all operators. Since we will only be concerned with universal properties of CFTs here, such detailed
data of individual CFTs will not be important for our considerations.
We will describe in the next short Sections 3.1, 3.2 and 3.3 some properties of CFTs that are conjectured to be relevant to the Kerr/CFT correspondence and its extensions: the Cardy formula, some properties of the discrete light-cone quantization (DLCQ) and some properties of symmetric product orbifold CFTs.
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Living Rev. Relativity 15, (2012), 11
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