28 research outputs found
Classifying three-character RCFTs with Wronskian index equalling 3 or 4
In the Mathur-Mukhi-Sen (MMS) classification scheme for rational conformal
field theories (RCFTs), a RCFT is identified by a pair of non-negative integers
, with being the number of characters and
the Wronskian index. The modular linear differential equation
(MLDE) that the characters of a RCFT solve are labelled similarly. All RCFTs
with a given solve the modular linear differential
equation (MLDE) labelled by the same . With the goal of
classifying and CFTs, we set-up and solve
those MLDEs, each of which is a three-parameter non-rigid MLDE, for
character-like solutions. In the former case, we obtain four infinite families
and a discrete set of solutions, all in the range . Amongst
these character-like solutions, we find pairs of them that
form coset-bilinear relations with meromorphic CFTs/characters of central
charges . There are six families of coset-bilinear
relations where both the RCFTs of the pair are drawn from the infinite families
of solutions. There are an additional coset-bilinear relations between
character-like solutions of the discrete set. The coset-bilinear relations
should help in identifying the CFTs. In the
case, we obtain nine character-like solutions each of which is a
character-like solution adjoined with a constant character.Comment: 64 pages, 20 table
New meromorphic CFTs from cosets
In recent years it has been understood that new rational CFTs can be discovered by applying the coset construction to meromorphic CFTs. Here we turn this approach around and show that the coset construction, together with the classification of meromorphic CFT with c β€ 24, can be used to predict the existence of new meromorphic CFTs with c β₯ 32 whose Kac-Moody algebras are non-simply-laced and/or at levels greater than 1. This implies they are non-lattice theories. Using three-character coset relations, we propose 34 infinite series of meromorphic theories with arbitrarily large central charge, as well as 46 theories at c = 32 and c = 40
Modular differential equations with movable poles and admissible RCFT characters
Studies of modular linear differential equations (MLDE) for the classification of rational CFT characters have been limited to the case where the coefficient functions (in monic form) have no poles, or poles at special points of moduli space. Here we initiate an exploration of the vast territory of MLDEs with two characters and any number of poles at arbitrary points of moduli space. We show how to parametrise the most general equation precisely and count its parameters. Eliminating logarithmic singularities at all the poles provides constraint equations for the accessory parameters. By taking suitable limits, we find recursion relations between solutions for different numbers of poles. The cases of one and two movable poles are examined in detail and compared with predictions based on quasi-characters to find complete agreement. We also comment on the limit of coincident poles. Finally we show that there exist genuine CFT corresponding to many of the newly-studied cases. We emphasise that the modular data is an output, rather than an input, of our approach
On the smoothness of multi-M2 brane horizons
We calculate the degree of horizon smoothness of multi- -brane solution
with branes along a common axis. We find that the metric is generically only
thrice continuously differentiable at any of the horizons. The four-form field
strength is found to be only twice continuously differentiable. We work with
Gaussian null-like co-ordinates which are obtained by solving geodesic
equations for multi- brane geometry. We also find different, exact
co-ordinate transformations which take the metric from isotropic co-ordinates
to co-ordinates in which metric is thrice differentiable at the horizon. Both
methods give the same result that the multi- brane metric is only thrice
continuously differentiable at the horizon.Comment: 24 pages, reference added, modified equation for non-singularity of
metri