Cosets of affine vertex algebras inside larger structures

“…Recall that M(u, ) denotes the N = 2 minimal model of central charge c, given in (2.2). As is well known, see [16] for an early reference and Lemma 8.6 of [43] for a proof, this minimal model may be represented as the following coset (commutant):…”

mentioning

confidence: 99%

“…A different proof appears in [31], based on the coset-inspired categorical equivalences sketched in [28] but only recently proven in [32]. Another proof, based on invariant theory, has recently appeared in [43].…”

mentioning

confidence: 99%

Unitary and non-unitary N = 2 minimal models

Creutzig

Liu

Ridout

et al. 2019

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

A. The unitary N = 2 superconformal minimal models have a long history in string theory and mathematical physics, while their non-unitary (and logarithmic) cousins have recently attracted interest from mathematicians. Here, we give an efficient and uniform analysis of all these models as an application of a type of Schur-Weyl duality, as it pertains to the well-known Kazama-Suzuki coset construction. The results include straightforward classifications of the irreducible modules, branching rules, (super)characters and (Grothendieck) fusion rules.1. I 1.1. Background. N = 2 supersymmetry is ubiquitous in string theory where its first appearances even predate the conception of conformal field theory as a separate discipline, see [1] for example. Upon formalising conformal invariance, physicists quickly started exploring the properties of the N = 2 superconformal algebra [2-5] and its representations, especially the unitary ones [3,[6][7][8][9][10]. The discovery [11,12] of a coset construction for the corresponding minimal models led to many generalisations, now known as Kazama-Suzuki models, and important links to the geometry of string compactifications.On the representation-theoretic side, the unitary N = 2 superconformal minimal models were studied by mathematicians and physicists interested in their characters [13][14][15][16][17], modularity [18,19] and fusion rules [20,21]. Their non-unitary cousins unfortunately attracted relatively little attention, though a new construction as a minimal quantum hamiltonian reduction [22,23] realised an important link with mock modular forms [24][25][26][27]. Moreover, their Kazama-Suzuki coset relationship with the fractional-level sl(2) Wess-Zumino-Witten models was reformulated into a number of beautiful categorical equivalences [28][29][30][31][32][33][34].With these fractional-level models now well in hand [35][36][37][38][39][40][41][42], this relationship can be exploited in both directions.Our aim here is to use this knowledge to give a uniform and direct treatment of the N = 2 superconformal minimal models, both unitary and non-unitary, with the main results being a classification of irreducible modules, explicit branching rules and characters, and (Grothendieck) fusion rules. The point is that we have established an efficient procedure to extract representation theory from coset constructions: the N = 2 superconformal minimal models provide a beautiful and important illustration of these methods. 1.2. A Schur-Weyl duality for Heisenberg cosets. Over the last few years, in a joint effort with Shashank Kanade, Robert McRae and Andrew Linshaw, two of the authors have developed a working theory of coset vertex operator algebras [43-46]. This has been strongly influenced by physics ideas, but builds on the work of many mathematicians including Kac-Radul [47], Dong-Li-Mason [48], Huang-Lepowsky-Zhang [49] and Huang-Kirillov-Lepowsky [50]. The present paper is one of a series that applies this new technology to interesting examples. The picture is the following. We have...

show abstract

“…, 2n + 1 by Theorem 4.4. of [65]. The type of symmetry algebra of the coset at generic level is the same as the orbifold limit by the theory of [66,67]. The problem here is to obtain the map of parameters such that the central charge c and the level ℓ of su(M) currents coincide with each other.…”

Section: Degenerate Representationsmentioning

confidence: 99%

Rectangular W algebras and superalgebras and their representations

Creutzig

Hikida

2019

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

We study W-algebras obtained by quantum Hamiltonian reduction of sl(M n) associated to the sl(2) embedding of rectangular type. The algebra can be realized as the asymptotic symmetry of higher spin gravity with M × M matrix valued fields. In our previous work, we examined the basic properties of the W-algebra and claimed that the algebra can be realized as the symmetry of Grassmannianlike coset even with finite central charge based on a proposal of holography. In this paper, we extend the analysis in the following ways. Firstly, we compute the operator product expansions among low spin generators removing the restriction of n = 2. Secondly, we investigate the degenerate representations in several ways, and see the relations to the coset spectrum and the conical defect geometry of the higher spin gravity. For these analyses, we mainly set M = n = 2. Finally, we extend the previous analysis by introducing N = 2 supersymmetry. *

show abstract

Cosets of affine vertex algebras inside larger structures

Cited by 54 publications

References 55 publications

Higgs and Coulomb branches from vertex operator algebras

Higgs and Coulomb branches from vertex operator algebras

Unitary and non-unitary N = 2 minimal models

Rectangular W algebras and superalgebras and their representations

Contact Info

Product

Resources

About