Chiral algebras from Ω-deformation

Oh, Jihwan; Yagi, Junya

doi:10.1007/jhep08(2019)143

Cited by 47 publications

(76 citation statements)

References 34 publications

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“…A huge recent breakthrough upon this topic is the discovery of a systematic way to construct the chiral algebra from 4d N = 2 gauge theories via the Ω-deformation [39,40]. A similar construction was also provided in [25] by directly working on S 3 × S 1 background, where this background can locally be approximated by the Ω-background.…”

Section: Resultsmentioning

confidence: 99%

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Testing Macdonald index as a refined character of chiral algebra

Watanabe

Zhu

2020

J. High Energ. Phys.

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We test in (A n−1 , A m−1 ) Argyres-Douglas theories with gcd(n, m) = 1 the proposal of Song's in [1] that the Macdonald index gives a refined character of the dual chiral algebra. In particular, we extend the analysis to higher rank theories and Macdonald indices with surface operator, via the TQFT picture and Gaiotto-Rastelli-Razamat's Higgsing method. We establish the prescription for refined characters in higher rank minimal models from the dual (A n−1 , A m−1 ) theories in the large m limit, and then provide evidence for Song's proposal to hold (at least) in some simple modules (including the vacuum module) at finite m. We also discuss some observed mismatch in our approach.

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Section: Resultsmentioning

confidence: 99%

“…We can then evaluate for n = 2 (P λ , e 1 P µ ) = (ē 1 e 2 P λ , e 2 P µ ) = (e 1 P λ , e 2 P µ ), (A. 39) where we use the notationē 1 (x) = e 1 (x −1 ). Let us set λ = µ + 1, we obtain (P µ+1 , P µ+1 ) = (1 − q µ+1 )(1 − q µ t 2 ) (1 − q µ+1 t)(1 − q µ t) (P µ , P µ ), (A.…”

Section: Resultsmentioning

confidence: 99%

Testing Macdonald index as a refined character of chiral algebra

Watanabe

Zhu

2020

J. High Energ. Phys.

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“…And how should the SCFT/VOA correspondence be put in this picture? One possible direction is to look into the localization on the 4d backgrounds following the recent works [73][74][75][76][77].…”

Section: Discussionmentioning

confidence: 99%

Elliptic blowup equations for 6d SCFTs. Part II. Exceptional cases

Klemm

Sun

et al. 2019

J. High Energ. Phys.

108

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The building blocks of 6d (1, 0) SCFTs include certain rank one theories with gauge group G = SU (3), SO(8), F 4 , E 6,7,8 . In this paper, we propose a universal recursion formula for the elliptic genera of all such theories. This formula is solved from the elliptic blowup equations introduced in our previous paper. We explicitly compute the elliptic genera and refined BPS invariants, which recover all previous results from topological string theory, modular bootstrap, Hilbert series, 2d quiver gauge theories and 4d N = 2 superconformal H G theories. We also observe an intriguing relation between the k-string elliptic genus and the Schur indices of rank k H G SCFTs, as a generalization of Lockhart-Zotto's conjecture at the rank one cases. In a subsequent paper, we deal with all other non-Higgsable clusters with matters. arXiv:1905.00864v2 [hep-th] 12 May 2019 E Relation with modular ansatz 85 F Elliptic genera 89 G Refined BPS invariants 971 IntroductionSix is the highest dimension in which representation theory allows for interacting superconformal quantum theories [1]. Limits of non-perturbative string theory compactifications [2] and in particular the decoupling of gravity in F-theory compactifications to 6d provided the first examples [3,4] and lead recently to a complete classification of geometrically engineered 6d superconformal quantum field theories [5][6][7]. Such a classification in 6d is highly desirable, as it might lead by further compactifications, to an exhaustive classification of superconformal theories.The 6d geometry is the one of an -in general desingularised -elliptic fibration with a contractable configuration of desingularised elliptic surfaces fibred over a configuration of curves in the base. In the decoupling limit the volume outside of the configuration of elliptic surfaces is scaled to infinite size, leaving us with an, in general reducible, configuration of complex desingularised elliptic surfaces that can be contracted within a non-compact Calabi-Yau threefold. Because compact components can be contracted such geometries are sometimes called local Calabi-Yau spaces. We will call the above specific ones for short elliptic non-compact Calabi-Yau geometries X and describe them in more detail in section 2.1.The full topological string partition function on these elliptic non-compact CY geometries has received much attention as it contains important information about protected states of the 6d superconformal theories [3,8]. Solving the topological string partition function on compact Calabi-Yau manifolds is currently an open problem. On non-compact Calabi-Yau spaces with an U (1) R isometry a refined topological string partition function Z(t, 1 , 2 ), which depends on the Kähler parameters t and two Ω background parameters 1 , 2 is defined as generating function of refined stable pair invariants. 1 The refinement of the stable pair invariants [9,10] and the relation to the refined BPS invariants N β j l ,jr ∈ N was given in [11,12]. Here β ∈ H 2 (X, Z) is the degree and the half integer...

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“…A topological twist along with Ω-deformation enables us to study a particular protected sub-sector of a given supersymmetric field theory [11][12][13][14], which is localized not only in the field configuration space but also in the spacetime. Interesting dynamics usually disappear along the way, but as a payoff, we can make a more rigorous statement on the operator algebra.…”

Section: Introduction and Conclusionmentioning

confidence: 99%