Relating the archetypes of logarithmic conformal field theory

Creutzig, Thomas; Ridout, David

doi:10.1016/j.nuclphysb.2013.04.007

Cited by 67 publications

(103 citation statements)

References 105 publications

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“…The fact that these dimensions depend on α -a continuous real variable -confirms that we are dealing with an irrational CFT [14]. Our observations are consistent with the 2D logarithmic CFT interpretation discussed above, since it is known that logarithmic CFTs typically have a continuously infinite number of primary operators [15].…”

Section: Confinedsupporting

confidence: 88%

4D−2Dequivalence for large-NYang-Mills theory

Başar

Cherman²,

McGady

2015

Phys. Rev. D

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General string-theoretic considerations suggest that four-dimensional large-N gauge theories should have dual descriptions in terms of two-dimensional conformal field theories. However, for non-supersymmetric confining theories such as pure Yang-Mills theory, a long-standing challenge has been to explicitly show that such dual descriptions actually exist. In this paper, we consider the large-N limit of four-dimensional pure Yang-Mills theory compactified on a three-sphere in the solvable limit where the sphere radius is small compared to the strong length scale, and demonstrate that the confined-phase spectrum of this gauge theory coincides with the spectrum of an irrational two-dimensional conformal field theory.Introduction. Confining gauge theories in the large-N limit are believed to have dual descriptions as weaklycoupled string theories [1]. Since string theories have 2D worldsheet conformal field theory (CFT) descriptions, it is expected that confining 4D gauge theories may have alternative descriptions based on 2D CFTs. However, for non-supersymmetric quantum field theories (QFTs) such as Yang-Mills (YM) theory, no concrete relation between large-N confining theories and 2D CFTs has ever been found.In this paper we tackle this problem by studying the large-N limit of 4D pure SU (N ) YM theory, formulated at temperature T = β −1 and compactified on a threesphere S 3 of radius R. One can thus view the theory as living on S

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Section: Confinedsupporting

confidence: 88%

4D−2Dequivalence for large-NYang-Mills theory

Başar

Cherman²,

McGady

2015

Phys. Rev. D

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“…While this is straightforward, determining character formulae for the atypical irreducible M(u, )modules is much more subtle. We shall first follow a procedure [55,70] in which each atypical irreducible is resolved in terms of atypical standard modules. The character of the former then follow from the Euler-Poincaré principle, if the resolution converges.…”

Section: Non-unitary Minimal Model Charactersmentioning

confidence: 99%

“…These characters may be analytically continued to meromorphic vector-valued Jacobi forms of weight 0 and index k [58]. The decomposition of these forms is rather subtle.. As we have seen, the resolution trick of [55,70] fails for k > 0 and so we need to find another way to solve this problem. In principle, one can answer this question with careful contour integrals as explained in [60].…”

Section: Atypical Characters Via Decomposing Meromorphic Jacobi Formsmentioning

confidence: 99%

Unitary and non-unitary N = 2 minimal models

Creutzig

Liu

Ridout

et al. 2019

J. High Energ. Phys.

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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...

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“…The B p -algebra for p = 2 and p = 3 are the βγ vertex operator algebra and the affine vertex operator algebra L −4/3 (sl 2 ) of sl 2 at level −4/3, respectively. These vertex operator algebras have been discussed at length in [A2,CR1,CR2,CR4,CRW,Ri,Ri2,Ri3,RW2]. We use the notation of [CRW].…”

Section: 51mentioning

confidence: 99%

Braided Tensor Categories Related to $${\mathcal {B}}_{p}$$ Vertex Algebras

Auger

Creutzig

Kanade

et al. 2020

Commun. Math. Phys.

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The B p -algebras are a family of vertex operator algebras parameterized by p ∈ Z ≥2 . They are important examples of logarithmic CFTs and appear as chiral algebras of type (A 1 , A 2p−3 ) Argyres-Douglas theories. The first member of this series, the B 2 -algebra, are the well-known symplectic bosons also often called the βγ vertex operator algebra.We study categories related to the B p vertex operator algebras using their conjectural relation to unrolled restricted quantum groups of sl 2 . These categories are braided, rigid and non semisimple tensor categories. We list their simple and projective objects, their tensor products and their Hopf links. The latter are succesfully compared to modular data of characters thus confirming a proposed Verlinde formula of David Ridout and the second author.

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Relating the archetypes of logarithmic conformal field theory

Cited by 67 publications

References 105 publications

4D−2Dequivalence for large-NYang-Mills theory

4D−2Dequivalence for large-NYang-Mills theory

Unitary and non-unitary N = 2 minimal models

Braided Tensor Categories Related to $${\mathcal {B}}_{p}$$ Vertex Algebras

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