The six-point families of exceptional representations of the conformal group

1984 ◽  
Vol 8 (3) ◽  
pp. 217-226 ◽  
Author(s):  
V. B. Petkova ◽  
G. M. Sotkov
Keyword(s):  
Conformal Group ◽  
Exceptional Representations

scholarly journals Fresh perspective on gauging the conformal group

2021 ◽  
Vol 103 (10) ◽  
Author(s):  
M. P. Hobson ◽  
A. N. Lasenby
Keyword(s):  
Conformal Group ◽  
Fresh Perspective

SU(2)k MODULAR-INVARIANT PARTITION FUNCTIONS FROM ORBIFOLDS

1991 ◽  
Vol 06 (26) ◽  
pp. 4763-4767 ◽  
Author(s):  
F. ARDALAN ◽  
H. ARFAEI ◽  
S. ROUHANI
Keyword(s):  
Conformal Group ◽  
Partition Functions ◽  
Discrete Subgroups ◽  
Modular Invariant ◽  
Orbifold Construction

We present a method which generates the modular-invariant partition functions of the ADE series of SU(2)k. Dividing the diagonal theory by discrete subgroups of the conformal group, we construct all the modular-invariant partition functions, thus proving that orbifold construction generates all the partition functions of SU(2)k.

scholarly journals Instability of complex CFTs with operators in the principal series

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Dario Benedetti
Keyword(s):  
Principal Series ◽  
Conformal Group ◽  
Point Of View ◽  
Field Theories ◽  
Operator Product ◽  
Quantum Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Primary Operator ◽  
Tensor Models

Abstract We prove the instability of d-dimensional conformal field theories (CFTs) having in the operator-product expansion of two fundamental fields a primary operator of scaling dimension h = $$ \frac{d}{2} $$ d 2 + i r, with non-vanishing r ∈ ℝ. From an AdS/CFT point of view, this corresponds to a well-known tachyonic instability, associated to a violation of the Breitenlohner-Freedman bound in AdSd+1; we derive it here directly for generic d-dimensional CFTs that can be obtained as limits of multiscalar quantum field theories, by applying the harmonic analysis for the Euclidean conformal group to perturbations of the conformal solution in the two-particle irreducible (2PI) effective action. Some explicit examples are discussed, such as melonic tensor models and the biscalar fishnet model.

Conformai Curvature Tensors

2011 ◽  
Author(s):  
Charles Fefferman ◽  
C. Robin Graham
Keyword(s):  
Normal Form ◽  
Curvature Tensor ◽  
Riemannian Metric ◽  
Conformal Group ◽  
Conformal Change ◽  
Conformal Curvature ◽  
Covariant Derivatives ◽  
Curvature Tensors ◽  
Derivatives Of

This chapter studies conformal curvature tensors of a pseudo-Riemannian metric g. These are defined in terms of the covariant derivatives of the curvature tensor of an ambient metric in normal form relative to g. Their transformation laws under conformal change are given in terms of the action of a subgroup of the conformal group O(p + 1, q + 1) on tensors. It is assumed throughout this chapter that n ≥ 3.

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