Conformal Embedding of Cluster Superlattices with Carbon

Abstract We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the W algebras defined using nilpotent orbit with partition [qm, 1s]. Gauging above AD matters, we can find VOAs for more general $$ \mathcal{N} $$ N = 2 SCFTs engineered from 6d (2, 0) theories. For example, the VOA for general (AN − 1, Ak − 1) theory is found as the coset of a collection of above W algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory.

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On local and integrated stress-tensor commutators

Journal of High Energy Physics ◽

10.1007/jhep07(2021)148 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Mert Besken ◽

Jan de Boer ◽

Grégoire Mathys

Keyword(s):

Stress Tensor ◽

Free Field ◽

Virasoro Algebra ◽

Light Sheet ◽

Operator Product ◽

Local Form ◽

Two Dimensional ◽

Conformal Embedding ◽

General Aspects ◽

The Right

Abstract We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE. We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor. We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincaré algebra, and the Virasoro algebra of two-dimensional CFT. We then consider commutators of light-ray operators built from the stress-tensor. Using simplifying features of the light sheet limit in four-dimensional CFT we provide a direct computation of the BMS algebra formed by a specific set of light-ray operators in theories with no light scalar conformal primaries. In four-dimensional CFT we define a new infinite set of light-ray operators constructed from the stress-tensor, which all have well-defined matrix elements. These are a direct generalization of the two-dimensional Virasoro light-ray operators that are obtained from a conformal embedding of Minkowski space in the Lorentzian cylinder. They obey Hermiticity conditions similar to their two-dimensional analogues, and also share the property that a semi-infinite subset annihilates the vacuum.

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Image Analysis by Conformal Embedding

Journal of Mathematical Imaging and Vision ◽

10.1007/s10851-011-0263-5 ◽

2011 ◽

Vol 40 (3) ◽

pp. 305-325 ◽

Cited By ~ 9

Author(s):

Oliver Fleischmann ◽

Lennart Wietzke ◽

Gerald Sommer

Keyword(s):

Image Analysis ◽

Conformal Embedding

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Anisotropic surface meshing with conformal embedding

Graphical Models ◽

10.1016/j.gmod.2014.03.011 ◽

2014 ◽

Vol 76 (5) ◽

pp. 468-483 ◽

Cited By ~ 11

Author(s):

Zichun Zhong ◽

Liang Shuai ◽

Miao Jin ◽

Xiaohu Guo

Keyword(s):

Anisotropic Surface ◽

Surface Meshing ◽

Conformal Embedding

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Conformal embedding and twisted theta functions at level one

Proceedings of the American Mathematical Society ◽

10.1090/proc/14695 ◽

2019 ◽

Vol 148 (1) ◽

pp. 9-22

Author(s):

Swarnava Mukhopadhyay ◽

Hacen Zelaci

Keyword(s):

Theta Functions ◽

Conformal Embedding

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An analogue of the Riemann mapping theorem for Lorentz metrics

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1985.0090 ◽

1985 ◽

Vol 401 (1820) ◽

pp. 117-130 ◽

Cited By ~ 9

Keyword(s):

Riemann Mapping ◽

Two Dimensional ◽

Standard Sphere ◽

Riemann Mapping Theorem ◽

Conformal Embedding ◽

Hyperbolic Operators ◽

Lorentz Metrics ◽

Dimension 2 ◽

Simply Connected ◽

Orientable Surfaces

The classical Riemann mapping theorem essentially says that a simply connected two-dimensional smooth Riemannian manifold is conformal to the standard sphere S 2 , the Euclidean plane E 2 , or the unit disk D 2 . The analogous problems in the Lorentz case are as follows. Let M be a simply connected two-dimensional smooth Lorentz manifold. Note that necessarily M is diffeomorphic to R 2 . (1) Does M admit a conformal embedding in E 1, 1 ,i.e. R 2 with cartesian coordinates { x, y } and the metric d x d y ? (2) What are the conformal types of such M’s ? In this paper these questions are partly answered in terms of an ‘ ideal boundary’ ∂ 0 M which is a conformal invariant of M. A geometric consequence is that among orientable surfaces only R 2 , R x S 1 and S 1 x S 1 admit complete Lorentz metrics of constant curvature. The results of this paper may be regarded as a part of a global study of space-times as well as of the second-order linear hyperbolic operators in dimension 2.

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