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@article{Beccaria:2017:10.1007/JHEP05(2017)053,
author = {Beccaria, M and Tseytlin, AA},
doi = {10.1007/JHEP05(2017)053},
journal = {Journal of High Energy Physics},
title = {Partition function of free conformal fields in 3-plet representation},
url = {http://dx.doi.org/10.1007/JHEP05(2017)053},
volume = {2017},
year = {2017}
}

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TY  - JOUR
AB  - Simplest examples of AdS/CFT duality correspond to free CFTs in d dimensions with fields in vector or adjoint representation of an internal symmetry group dual in the large N limit to a theory of massless or massless plus massive higher spins in AdS d+1. One may also study generalizations when conformal fields belong to higher dimensional representations, i.e. carry more than two internal symmetry indices. Here we consider the case of the 3-fundamental (“3-plet”) representation. One motivation is a conjectured connection to multiple M5-brane theory: heuristic arguments suggest that it may be related to an (interacting) CFT of 6d (2,0) tensor multiplets in 3-plet representation of large N symmetry group that has an AdS7 dual. We compute the singlet partition function Z on S 1 × S d−1 for a free field in 3-plet representation of U(N) and analyse its novel large N behaviour. The large N limit of the low temperature expansion of Z which is convergent in the vector and adjoint cases here is only asymptotic, reflecting the much faster growth of the number of singlet operators with dimension, indicating a phase transition at very low temperature. Indeed, while the critical temperatures in the vector (T c ∼ N γ , γ > 0) and adjoint (T c ∼ 1) cases are finite, we find that in the 3-plet case T c ∼ (log N)−1, i.e. it approaches zero at large N. We discuss some details of large N solution for the eigenvalue distribution. Similar conclusions apply to higher p-plet representations of U(N) or O(N) and also to the free p-tensor theories invariant under [U(N)] p or [O(N)] p with p ≥ 3.
AU  - Beccaria,M
AU  - Tseytlin,AA
DO  - 10.1007/JHEP05(2017)053
PY  - 2017///
SN  - 1029-8479
TI  - Partition function of free conformal fields in 3-plet representation
T2  - Journal of High Energy Physics
UR  - http://dx.doi.org/10.1007/JHEP05(2017)053
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000401118200001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/65982
VL  - 2017
ER  -

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