Abstract
We use the Poincaré series method to compute gravity partition functions associated to SU(N)1 WZW models with arbitrarily large numbers of modular invariants. The result is an average over these invariants, with the weights being given by inverting a matrix whose size is of order the number of invariants. For the chosen models, this matrix takes a special form that allows us to invert it for arbitrary size and thereby explicitly calculate the weights of this average. For the identity seed we find that the weights are positive for all N, consistent with each model being dual to an ensemble average over CFT’s.
Highlights
JHEP08(2021)098 the AdS/CFT can be realised in a form where an average must be taken over boundary CFT’s [6, 7]
It is known that given a set of Kac-Moody characters, there are in general multiple modular invariants that can be made out of them, that correspond to different RCFT — all having the same central charge and Kac-Moody algebra [13,14,15,16,17,18,19,20]
A complex picture emerged wherein for many cases, the linear combinations of RCFT partition functions arise with non-negative coefficients, allowing us to interpret the result as a probabilistic average over a discrete ensemble of theories
Summary
To see what families lead to a given value of the total number of invariants, we start by writing the integer m defined in eq (2.4) in terms of its distinct prime factors:. We are interested in the case σ(m) ≡ σ0(m), which counts the number of divisors. This can be found by taking the r → 0 limit in the above expression. From eq (3.1) this means that the allowed prime decompositions are m = pq or p5. This corresponds to SU(N ) for N = pq, p5, 2pq2, 2p5 where p, q are arbitrary distinct primes that must be odd in the first two cases
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
