Partition function of free conformal fields in 3-plet representation
File(s)
Author(s)
Beccaria, M
Tseytlin, AA
Type
Journal Article
Abstract
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.
Date Issued
2017-05-10
Date Acceptance
2017-05-07
ISSN
1029-8479
Publisher
Springer Verlag (Germany)
Journal / Book Title
Journal of High Energy Physics
Volume
2017
Issue
5
Copyright Statement
© 2017 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0 - https://creativecommons.org/licenses/by/4.0/), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Sponsor
Commission of the European Communities
Science and Technology Facilities Council (STFC)
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000401118200001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
290456
ST/L00044X/1
Subjects
Science & Technology
Physical Sciences
Physics, Particles & Fields
Physics
AdS-CFT Correspondence
Conformal Field Theory
N GAUGE-THEORIES
STRING THEORY
HIGHER SPINS
P-BRANES
SUPERGRAVITY
TRANSITION
DIMENSIONS
GRAVITY
hep-th
01 Mathematical Sciences
02 Physical Sciences
Nuclear & Particles Physics
Publication Status
Published
Article Number
53
Date Publish Online
2017-05-10