Characters of the W 3 algebra

Iles, Nicholas J.; Watts, Gérard

doi:10.1007/jhep02(2014)009

Cited by 13 publications

(23 citation statements)

References 17 publications

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“…This has to do with the fact that one needs to simultaneously diagonalize vectors in V h,w with respect to L 0 and W 0 . See [40,41] for a recent development on this issue. Due to its computational difficulty, we will focus on the 'unrefined' character, which sets p = 1.…”

Section: Jhep12(2017)045mentioning

confidence: 99%

Modular constraints on conformal field theories with currents

Bae

Lee

Song

2017

J. High Energ. Phys.

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We study constraints coming from the modular invariance of the partition function of two-dimensional conformal field theories. We constrain the spectrum of CFTs in the presence of holomorphic and anti-holomorphic currents using the semi-definite programming. In particular, we find the bounds on the twist gap for the non-current primaries depend dramatically on the presence of holomorphic currents, showing numerous kinks and peaks. Various rational CFTs are realized at the numerical boundary of the twist gap, saturating the upper limits on the degeneracies. Such theories include Wess-Zumino-Witten models for the Deligne's exceptional series, the Monster CFT and the Baby Monster CFT. We also study modular constraints imposed by W-algebras of various type and observe that the bounds on the gap depend on the choice of W-algebra in the small central charge region.

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Section: Jhep12(2017)045mentioning

confidence: 99%

Modular constraints on conformal field theories with currents

Bae

Lee

Song

2017

J. High Energ. Phys.

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“…Our notation above corresponds to quantum numbers under the coset construction discussed in the appendix. These quantum numbers are in one-to-one correspondence with highest weight quantum numbers under the W 3 algebra as can be seen, for example, from Table 4.1 in [43].…”

Section: Basic Examplementioning

confidence: 68%

Anyonic Chains, Topological Defects, and Conformal Field Theory

Buican

Gromov

2017

Commun. Math. Phys.

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Abstract:Motivated by the three-dimensional topological field theory/two-dimensional conformal field theory (CFT) correspondence, we study a broad class of one-dimensional quantum mechanical models, known as anyonic chains, which can give rise to an enormously rich (and largely unexplored) space of two-dimensional critical theories in the thermodynamic limit. One remarkable feature of these systems is the appearance of non-local microscopic "topological symmetries" that descend to topological defects of the resulting CFTs. We derive various model-independent properties of these theories and of this topological symmetry/topological defect correspondence. For example, by studying precursors of certain twist and defect fields directly in the anyonic chains, we argue that (under mild assumptions) the two-dimensional CFTs correspond to particular modular invariants with respect to their maximal chiral algebras and that the topological defects descending from topological symmetries commute with these maximal chiral algebras. Using this map, we apply properties of defect Hilbert spaces to show how topological symmetries give a handle on the set of allowed relevant deformations of these theories. Throughout, we give a unified perspective that treats the constraints from discrete symmetries on the same footing as the constraints from topological ones.

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“…We studied two classes of W 3 -algebra representations in [1], Verma modules and minimal model representations. We found that traces over the minimal model representations with a single W 0 insertion satisfied differential equations and in section 3 here we show that these are modular, that is, they are covariant under modular transformations and this implies that the solutions (the traces) have particular modular properties.…”

Section: Jhep01(2016)089mentioning

confidence: 99%

“…In a previous paper [1], we found formulae for characters of the W 3 algebra with insertions of powers of the zero mode W 0 (see appendix B for the definition of the W 3 algebra). These characters with insertions have been of interest recently since they are involved in counting the states of black holes in (2+1)-dimensional AdS higher-spin gravity.…”

Section: Introductionmentioning

confidence: 99%

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Modular properties of characters of the W3 algebra

Iles

Watts

2016

J. High Energ. Phys.

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In a previous work, exact formulae and differential equations were found for traces of powers of the zero mode in the W 3 algebra. In this paper we investigate their modular properties, in particular we find the exact result for the modular transformations of traces of W n 0 for n = 1, 2, 3, solving exactly the problem studied approximately by Gaberdiel, Hartman and Jin. We also find modular differential equations satisfied by traces with a single W 0 inserted, and relate them to differential equations studied by Mathur et al. We find that, remarkably, these all seem to be related to weight 0 modular forms with expansions with non-negative integer coefficients.

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Characters of the W 3 algebra

Cited by 13 publications

References 17 publications

Modular constraints on conformal field theories with currents

Modular constraints on conformal field theories with currents

Anyonic Chains, Topological Defects, and Conformal Field Theory

Modular properties of characters of the W3 algebra

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