A class of -algebras with infinitely generated classical limit

Boer, Jan de; Fehér, L.; Honecker, A.

doi:10.1016/0550-3213(94)90388-3

Cited by 26 publications

(8 citation statements)

References 29 publications

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“…32 For k = 2 which corresponds to the Ising CFT, the second Z 2 factor in (B.6) acts trivially and the faithful global symmetry is just Z k=2 . parafermion algebra generated by ψ n [86][87][88][89][90][91],…”

Section: B1 the Z K Parafermionsmentioning

confidence: 99%

Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond

Thorngren¹,

Wang²

2021

Preprint

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We study generalized symmetries of quantum field theories in 1+1D generated by topological defect lines with no inverse. This paper follows our companion paper on gapped phases and anomalies associated with these symmetries. In the present work we focus on identifying fusion category symmetries, using both specialized 1+1D methods such as the modular bootstrap and (rational) conformal field theory (CFT), as well as general methods based on gauging finite symmetries, that extend to all dimensions. We apply these methods to c = 1 CFTs and uncover a rich structure. We find that even those c = 1 CFTs with only finite group-like symmetries can have continuous fusion category symmetries, and prove a Noether theorem that relates such symmetries in general to non-local conserved currents. We also use these symmetries to derive new constraints on RG flows between 1+1D CFTs.

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Section: B1 the Z K Parafermionsmentioning

confidence: 99%

Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond

Thorngren¹,

Wang²

2021

Preprint

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“…3 = h 1 + h 2 19 Note that there exists also a configuration with x = h1 − h2 that does not seem to correspond to any simple realization. Similarly, we get one extra solution also at level two.…”

Section: Jhep05(2019)159mentioning

confidence: 99%

“…Originally, a linear version of the algebra was constructed as N → ∞ of W N algebras [14][15][16][17]. Later, it was gradually realized that there exists in fact a two-parametric family of non-linear algebras [18][19][20][21][22][23][24][25]. Recently, this algebra appeared in connection with equivariant cohomology of instanton moduli spaces [26][27][28][29] and its equivalence to Yangian of affine gl(1) was found [27,[29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

$$ \mathcal{W} $$ -algebra modules, free fields, and Gukov-Witten defects

Procházka¹,

Rapčák

2019

J. High Energ. Phys.

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We study the structure of modules of corner vertex operator algebras arrising at junctions of interfaces in N = 4 SYM. In most of the paper, we concentrate on truncations of W 1+∞ associated to the simplest trivalent junction. First, we generalize the Miura transformation for W N 1 to a general truncation Y N 1 ,N 2 ,N 3. Secondly, we propose a simple parametrization of their generic modules, generalizing the Yangian generating function of highest weight charges. Parameters of the generating function can be identified with exponents of vertex operators in the free field realization and parameters associated to Gukov-Witten defects in the gauge theory picture. Finally, we discuss some aspect of degenerate modules. In the last section, we sketch how to glue generic modules to produce modules of more complicated algebras. Many properties of vertex operator algebras and their modules have a simple gauge theoretical interpretation.

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“…The N = 2 case was studied in Ref. [12]. A set of classical currents for the stringy SU (2) coset can be obtained by acting on the Casimir invariant Tr(JJ) by derivatives.…”

Section: N =mentioning

confidence: 99%

Symmetry algebras of stringy cosets

Kumar

Sharma

2019

J. High Energ. Phys.

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We find the symmetry algebras of cosets which are generalizations of the minimalmodel cosets, of the specific form SU (N ) k ×SU (N ). We study this coset in its free field limit, with k, → ∞, where it reduces to a theory of free bosons. We show that, in this limit and at large N , the algebra W e ∞ [1] emerges as a sub-algebra of the coset algebra. The full coset algebra is a larger algebra than conventional W-algebras, with the number of generators rising exponentially with the spin, characteristic of a stringy growth of states. We compare the coset algebra to the symmetry algebra of the large N symmetric product orbifold CFT, which is known to have a stringy symmetry algebra labelled the 'higher spin square'. We propose that the higher spin square is a sub-algebra of the symmetry algebra of our stringy coset.

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A class of -algebras with infinitely generated classical limit

Cited by 26 publications

References 29 publications

Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond

Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond

$$ \mathcal{W} $$ -algebra modules, free fields, and Gukov-Witten defects

Symmetry algebras of stringy cosets

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