Wall-crossing between stable and co-stable ADHM data

Ohkawa, Ryo

doi:10.1007/s11005-018-1071-2

Cited by 7 publications

(13 citation statements)

References 25 publications

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“…Nevertheless conjectural formula (B.5) states that corresponding equiavariant Euler characteristics are the same. In the conformal (or cohomology, or just q 1 , q 2 → 1) limit the corresponding statement was made in [3, Sec 4.1] (see also [17], [23]).…”

Section: (B2)mentioning

confidence: 70%

q-deformed Painlevéτfunction andq-deformed conformal blocks

Bershtein

Shchechkin

2017

J. Phys. A: Math. Theor.

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We propose q-deformation of the Gamayun-Iorgov-Lisovyy formula for Painlevé τ function. Namely we propose the formula for τ function for q-difference Painlevé equation corresponding to A(1)′ 7 surface (and A (1) 1 symmetry) in Sakai classification. In this formula τ function equals the series of q-Virasoro Whittaker conformal blocks (equivalently Nekrasov partition functions for pure SU (2) 5d theory). [arXiv:q-alg/9605002v2].

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Section: (B2)mentioning

confidence: 70%

q-deformed Painlevéτfunction andq-deformed conformal blocks

Bershtein

Shchechkin

2017

J. Phys. A: Math. Theor.

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“…Nonetheless the results of the JK residue calculation exactly match those of the Moyal products. Compared with instanton counting which also exhibits wall-crossing when the stability parameters are varied [23,24,25,20,26,27], for 't Hooft operators the physical meaning of the stability parameters (FI parameters) is simpler; they are the positions of the operators.…”

Section: Introductionmentioning

confidence: 99%

Wall-crossing and operator ordering for ’t Hooft operators in $$ \mathcal{N} $$ = 2 gauge theories

Hayashi¹,

Okuda²,

Yoshida³

2019

J. High Energ. Phys.

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We study half-BPS 't Hooft line operators in 4d N = 2 U (N ) gauge theories on S 1 ×R 3 with an Ω-deformation. The recently proposed brane construction of 't Hooft operators shows that non-perturbative contributions to their correlator are identified with the Witten indices of quiver supersymmetric quantum mechanics. For the products of minimal 't Hooft operators, a chamber in the space of Fayet-Iliopoulos parameters in the quantum mechanics corresponds to an ordering of the operators inserted along a line. These considerations lead us to conjecture that the Witten indices can be read off from the Moyal products of the expectation values of the minimal 't Hooft operators, and also that wall-crossing occurs in the quantum mechanics only when the ordering of the operators changes. We confirm the conjectures by explicitly computing the Witten indices for the products of two and three minimal 't Hooft operators in all possible chambers.2 In [18] the authors also observed the correspondence between the ordering and wall-crossing for the product of T and T . We complete their analysis by including the product of two minimal operators of the same type. We further investigate the products of three minimal operators of all types, which exhibit a richer structure.3 A primitive version of the conjectures and some evidence were presented by T.O. in the workshop "Representation Theory, Gauge Theory, and Integrable Systems" held at the Kavli IPMU in February, 2019. 5 The same symbol e i (or e a ) will denote an orthonormal basis of a Euclidean space other than R N . 6 To compare wtih [12,14] note the following. Λ cort in (2.3) is also the coroot lattice of SU (N ). The cocharacter lattice of SU (N ) is the sublattice { i z i = 0} of Λ cochar in (2.2). Defining z U (1) := (1/N ) i z i j e j and z SU (N ) := z − z U (1) for z = i z i e i , we have |v| ≤ |B| ⇔ |v SU (N ) | ≤ |B SU (N ) | for v ∈ B + Λ cort .7 Since the Langlands dual group of SU (N ) is SU (N )/Z N , 't Hooft operators corresponding to B = ±e i do not exist in an SU (N ) gauge theory.8 Section 5 discusses subtleties for N F odd.12 The D3-branes are assumed to be at generic positions in the (x 4 , x 5 )-space. 13 Due to the s-rule a single NS5-brane, with K D1-branes (1 ≤ K ≤ N ) attached and placed on the right of the stack of all the D3-and D7-branes, gives an 't Hooft operator with magnetic charge K i=1 e i , which seems to correspond to the K-th exterior power of the fundamental representation. Similarly an NS5-brane

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“…We do not include self-contained arguments in this paper, since many parts of the argument is similar as in the previous research [27] and [28]. Instead, we give outline here, and in the main body of the paper, we indicate proofs of corresponding statements in loc.…”

Section: Outline Of the Papermentioning

confidence: 99%

“…To analize wall-crossing formula, we introduce enhanced master spaces in terms of ADHM data. In our argument, vector spaces in [28] are replaced to Z 2 = Z/2Zgraded vector spaces. This change increase the dimension of spaces of stability parameters, which is similar to the situation in [27], and we have more complicated wall-and-chamber structure in R 2 than [28], where we have only two kinds of generic stability conditions.…”

Section: Outline Of the Papermentioning

confidence: 99%

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Functional equations of Nekrasov functions proposed by Ito-Maruyoshi-Okuda

Ohkawa

2018

Preprint

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We prove functional equations of Nekrasov partition functions for A 1 -singularity, suggested by Ito-Maruyoshi-Okuda [15]. Our proof is given by the computation similar to [28]. This is the method by Nakajima-Yoshioka [27] based on the theory of wall-crossing formula developed by Mochizuki [19]. 2000 Mathematics Subject Classification. 14D21 and 57R57. Key words and phrases. Nekrasov partition functions and Framed sheaves and Instantons.

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Wall-crossing between stable and co-stable ADHM data

Cited by 7 publications

References 25 publications

q-deformed Painlevéτfunction andq-deformed conformal blocks

q-deformed Painlevéτfunction andq-deformed conformal blocks

Wall-crossing and operator ordering for ’t Hooft operators in $$ \mathcal{N} $$ = 2 gauge theories

Functional equations of Nekrasov functions proposed by Ito-Maruyoshi-Okuda

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