Affine.m—Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras

Nazarov, Anton

doi:10.1016/j.cpc.2012.06.014

Cited by 10 publications

(20 citation statements)

References 27 publications

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“…I.K. thanks Anton Nazarov for providing him an updated version of the mathematica package affine.m [20]. The branching function computations were performed on DESY's Theory Cluster and DESY's IT High Performance Cluster (IT-HPC).…”

Section: Acknowledgmentsmentioning

confidence: 99%

Chiral primaries in strange metals

2014

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It was suggested recently that the study of 1-dimensional QCD with fermions in the adjoint representation could lead to an interesting toy model for strange metals and their holographic formulation. In the high density regime, the infrared physics of this theory is described by a constrained free fermion theory with an emergent N = (2, 2) superconformal symmetry. In order to narrow the choice of potential holographic duals, we initiate a systematic search for chiral primaries in this model. We argue that the bosonic part of the superconformal algebra can be extended to a coset chiral algebra of the form W N = SO(2N 2 − 2) 1 /SU(N) 2N . In terms of this algebra the spectrum of the low energy theory decomposes into a finite number of sectors which are parametrized by special necklaces. We compute the corresponding characters and partition functions and determine the set of chiral primaries for N ≤ 5. †

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Section: Acknowledgmentsmentioning

confidence: 99%

Chiral primaries in strange metals

2014

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“…However, at the time we started the project no such implementation existed for the computer-algebra system Mathematica. (Meanwhile a package for computations in finite-dimensional and affine Lie algebras has been published [15] that has a similar intention as our software, as well as a package for the calculation of the 2-loop renormalization-group equations of supersymmetric models based on gauge groups incorporating many Lie algebra related computations [16]). Mathematica ® is a computer algebra software by Wolfram Research, Inc. which is widely used especially among particle physicists.…”

Section: Introductionmentioning

confidence: 99%

LieART—A Mathematica application for Lie algebras and representation theory

Feger

Kephart²

2015

Computer Physics Communications

172

209

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We present the Mathematica application "LieART" (Lie Algebras and Representation Theory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. LieART can handle all classical and exceptional Lie algebras. It computes root systems of Lie algebras, weight systems and several other properties of irreducible representations. LieART's user interface has been created with a strong focus on usability and thus allows the input of irreducible representations via their dimensional name, while the output is in the textbook style used in most particle-physics publications. The unique Dynkin labels of irreducible representations are used internally and can also be used for input and output. LieART exploits the Weyl reflection group for most of the calculations, resulting in fast computations and a low memory consumption. Extensive tables of properties, tensor products and branching rules of irreducible representations are included in the appendix.

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“…They are both implemented using well-known methods (see refs. [25][26][27][28][29][30][31]), which are summarized here, for completeness.…”

Section: Basic Operations With Representationsmentioning

confidence: 99%

“…They are reviewed, for example, in ref. [25], and implemented in several computer packages with different purposes [26][27][28][29][30][31]. To remove integration by parts redundancy, an adaptation of the method in ref.…”

Section: Introductionmentioning

confidence: 99%

BasisGen: automatic generation of operator bases

Criado

2019

Eur. Phys. J. C

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BasisGen is a Python package for the automatic generation of bases of operators in effective field theories. It accepts any semisimple symmetry group and fields in any of its finite dimensional irreducible representations. It takes into account integration by parts redundancy and, optionally, the use of equations of motion. The implementation is based in well-known methods to generate and decompose representations using roots and weights, which allow for fast calculations, even with large numbers of fields and high-dimensional operators. BasisGen can also be used to do some representation-theoretic operations, such as finding the weight system of an irreducible representation from its highest weight or decomposing a tensor product of representations.

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Affine.m—Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras

Cited by 10 publications

References 27 publications

Chiral primaries in strange metals

Chiral primaries in strange metals

LieART—A Mathematica application for Lie algebras and representation theory

BasisGen: automatic generation of operator bases

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