General instanton counting and 5d SCFT

Hwang, Chiung; Kim, Joon-Ho; Kim, Seok; Park, Jaemo

doi:10.48550/arxiv.1406.6793

Cited by 81 publications

(292 citation statements)

References 20 publications

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“…The symmetry enhancement of the models mentioned above has been successfully confirmed by these methods, and even more diverse models are being explored, see e.g. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 86%

Instanton operators and symmetry enhancement in 5D supersymmetric gauge theories

Tachikawa

2015

Progress of Theoretical and Experimental Physics

147

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Supersymmetric gauge theories in five dimensions often exhibit less symmetry than the ultraviolet fixed points from which they flow. The fixed points might have larger flavor symmetry or they might even be secretly six-dimensional theories on S 1 . Here we provide a simple criterion when such symmetry enhancement in the ultraviolet should occur, by a direct study of the fermionic zero modes around one-instanton operators.S 1 , as originally found in the context of string duality [6,7].

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Section: Introductionmentioning

confidence: 86%

Instanton operators and symmetry enhancement in 5D supersymmetric gauge theories

Tachikawa

2015

Progress of Theoretical and Experimental Physics

147

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“…The Higgs branch at infinite coupling is therefore C 2 /Z N . 14 The generators of the Higgs branch at infinite coupling are I, S, I, singlets under SU (N ), and with U (1) I charge +1, 0 and − 1 respectively. For N > 2, the isometry group of C 2 /Z N is identified with U (1) I .…”

Section: Pure Super Yang-mills Theoriesmentioning

confidence: 99%

“…In particular, in the seminal work [1], it was pointed out that the UV fixed point of 5d N = 1 SU (2) gauge theory with N f ≤ 7 flavours exhibits E N f +1 flavour symmetry, which enhances from the global symmetry SO(2N f )×U (1) apparent in the Lagrangian at finite coupling. Since then a large class of five dimensional supersymmetric field theories have been constructed using webs of five-branes [5][6][7] and the enhancement of the global symmetry of these theories has been studied using various approaches, including superconformal indices [8][9][10][11][12][13][14][15][16][17][18][19], Nekrasov partition functions and (refined) topological string partition functions [20][21][22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Instanton operators and the Higgs branch at infinite coupling

Cremonesi

Ferlito

Hanany

et al. 2017

J. High Energ. Phys.

115

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The richness of 5d N = 1 theories with a UV fixed point at infinite coupling is due to the existence of local disorder operators known as instanton operators. By considering the Higgs branch of SU(2) gauge theories with N f ≤ 7 flavours at finite and infinite coupling, we write down the explicit chiral ring relations between instanton operators, the glueball superfield and mesons. Exciting phenomena appear at infinite coupling: the glueball superfield is no longer nilpotent and the classical chiral ring relations are quantum corrected by instanton operators bilinears. We also find expressions for the dressing of instanton operators of arbitrary charge. The same analysis is performed for USp(2k) with an antisymmetric hypermultiplet and pure SU(N ) gauge theories.

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“…The main result of this paper is the demonstration of the conjectures by the explicit computation of the Witten indices relevant for two and three minimal 't Hooft operators, in all possible FI-chambers. While the Moyal product is easy to calculate, the computation of the Witten indices requires the evaluation of the Jeffrey-Kirwan (JK) residues [19] of the poles in the one-loop determinants [20,21,22]; in some cases we encounter the socalled degenerate poles that are subtle to deal with. Nonetheless the results of the JK residue calculation exactly match those of the Moyal products.…”

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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General instanton counting and 5d SCFT

Cited by 81 publications

References 20 publications

Instanton operators and symmetry enhancement in 5D supersymmetric gauge theories

Instanton operators and symmetry enhancement in 5D supersymmetric gauge theories

Instanton operators and the Higgs branch at infinite coupling

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

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