Construction of Gaiotto states with fundamental multiplets through degenerate DAHA

Matsuo, Yutaka; Rim, Chaiho; Hong, Zhang

doi:10.1007/jhep09(2014)028

Cited by 31 publications

(43 citation statements)

References 46 publications

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“…Given the above interpretation of (4.7), we now conjecture that the rule (4.7) generally applies to the Liouville momentum α of any Liouville irregular state of integer rank n and the corresponding 4d mass parameter m. 33 This particularly implies that the O(Q) correction to β 1 in (4.4) is fixed by 9) and that to β 2 in (4.6) is fixed by…”

Section: Conjectural Dictionary Between 4d and 2d Parametersmentioning

confidence: 88%

Argyres-Douglas theories and Liouville irregular states

Nishinaka

Uetoko

2019

J. High Energ. Phys.

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We study irregular states of rank-two and three in Liouville theory, based on an ansatz proposed by D. Gaiotto and J. Teschner. Using these irregular states, we evaluate asymptotic expansions of irregular conformal blocks corresponding to the partition functions of (A 1 , A 3 ) and (A 1 , D 4 ) Argyres-Douglas theories for general Ω-background parameters. In the limit of vanishing Liouville charge, our result reproduces strong coupling expansions of the partition functions recently obtained via the Painlevé/gauge correspondence. This suggests that the irregular conformal block for one irregular singularity of rank 3 on sphere is also related to Painlevé II. We also find that our partition functions are invariant under the action of the Weyl group of flavor symmetries once four and two-dimensional parameters are correctly identified. We finally propose a generalization of this parameter identification to general irregular states of integer rank.

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Section: Conjectural Dictionary Between 4d and 2d Parametersmentioning

confidence: 88%

Argyres-Douglas theories and Liouville irregular states

Nishinaka

Uetoko

2019

J. High Energ. Phys.

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“…A few operators of order 0 and 1 are also shown, which appear in the defining relations in (2.1)-(2.4). For rank 1 case, one has the representation (same as the one in [15])…”

Section: Action Of Sh Generators On |T Mmentioning

confidence: 99%

“…After this consideration, the irregular conformal state of rank 1 in (4.3) is written in terms of the q-basis as appeared in [15]…”

Section: Colliding Limit and Irregular Statementioning

confidence: 99%

Nekrasov and Argyres–Douglas theories in spherical Hecke algebra representation

Rim

Hong

2017

Nuclear Physics B

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AGT conjecture connects Nekrasov instanton partition function of 4D quiver gauge theory with 2D Liouville conformal blocks. We re-investigate this connection using the central extension of spherical Hecke algebra in q-coordinate representation, q being the instanton expansion parameter. Based on AFLT basis together with interwiners we construct gauge conformal state and demonstrate its equivalence to the Liouville conformal state, with careful attention to the proper scaling behavior of the state. Using the colliding limit of regular states, we obtain the formal expression of irregular conformal states corresponding to Argyres-Douglas theory, which involves summation of functions over Young diagrams.1 the simultaneous eigenvector of two generators L 1 and L n in [8]. In addition, Virasoro irregular state of higher rank n (simultaneous eigenstate of L k with n ≤ k ≤ 2n) is suggested in [9], while some of the coefficients for the representation are not fixed.Colliding limit, a limiting procedure to obtain the irregular state from the regular state is clarified in [10]. The decoupling limit in [7] and also in the matrix model [11] is a special case of the colliding limit. The colliding limit turns out to be a very efficient tool to investigate the irregular state to find the correct representation of the irregular state of rank greater than 1. Indeed, the coefficients undetermined in [9] are fixed by irregular matrix model in [12] which obeys consistency conditions of Virasoro generators of lower positive modes L k with 0 ≤ k < n. The irregular matrix model analysis is extended to W-symmetry in [13].The irregular matrix model analysis, however, provides indirect information because the partition function of the matrix model is equivalent to the inner-product of two states. Direct process to find the irregular state is more desirable. For this goal, we resort to the representation of spherical double degenerate affine Hecke algebra (spherical DDAHA or SH for short). DDAHA is generated by z i and D i = z i ∇ i + j

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“…Notice that the momenta in the U(1) part are slightly different (by t 2 /q 2 ) for the positive and negative modes which matches the AGT prescription [41,[186][187][188]. The vertex operator (3.26), though it depends on the right combination of the oscillatorsα n is not the full Virasoro vertex operator (in particular, it does not have a smooth limit for t, q → 1).…”

Section: Jhep07(2016)103mentioning
confidence: 76%

“…Notice also that the Heisenberg vertex operator V Heis is not the required Carlsson-Okounkov vertex operator [189,190], i.e. the momenta are not shifted for the positive and negative modes (see also [186][187][188]). …”

Section: Jhep07(2016)103mentioning
confidence: 99%

Explicit examples of DIM constraints for network matrix models
Awata
¹
,
Kanno
²
,
Matsumoto
³

et al. 2016
J. High Energ. Phys.
97
0
118
0
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Dotsenko-Fateev and Chern-Simons matrix models, which describe Nekrasov functions for SYM theories in different dimensions, are all incorporated into network matrix models with the hidden Ding-Iohara-Miki (DIM) symmetry. This lifting is especially simple for what we call balanced networks. Then, the Ward identities (known under the names of Virasoro/W-constraints or loop equations or regularity condition for qq-characters) are also promoted to the DIM level, where they all become corollaries of a single identity.

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Construction of Gaiotto states with fundamental multiplets through degenerate DAHA

Cited by 31 publications

References 46 publications

Argyres-Douglas theories and Liouville irregular states

Argyres-Douglas theories and Liouville irregular states

Nekrasov and Argyres–Douglas theories in spherical Hecke algebra representation

Explicit examples of DIM constraints for network matrix models

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