On ’t Hooft defects, monopole bubbling and supersymmetric quantum mechanics

Brennan, T. Daniel; Dey, Anindya; Moore, Gregory W.

doi:10.1007/jhep09(2018)014

Cited by 34 publications

(90 citation statements)

References 66 publications

(194 reference statements)

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“…In Figure 1(a) we choose to put the four D7-branes between the two D3-branes. A crucial step [12] in specifying the precise 't Hooft operator and toward deriving the SQM is to terminate the semi-infinite D1-branes by NS5-branes. In this picture a product of 't Hooft operators is realized by a collection of D1-branes each of which ends on an NS5brane and a D3-brane.…”

Section: Sqms From Branesmentioning

confidence: 99%

“…From the brane setup, it is now possible to read off the desired SQM by following the procedure in Section 3.3 of [12]. This involves moving NS5-branes via Hanany-Witten transitions across D3-branes as well as reconnecting D1-branes.…”

Section: Sqms From Branesmentioning

confidence: 99%

“…Dependence on the ordering also appears in the Witten index of SQM. The brane construction of the product of minimal 't Hooft operators implies that the difference s a+1 −s a (in appropriate units) is nothing but an FI parameter ζ a for the SQM [12,13,14]: ζ a = s a+1 − s a (a = 1, . .…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Sqms From Branesmentioning

confidence: 99%

Section: Sqms From Branesmentioning

confidence: 99%

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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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“…By a standard argument the vev of a BPS loop is independent of its position along R. It takes the form of an index which counts framed BPS states [9], which are the BPS states of the theory in the presence of the line defect. Additional results for the N = 2 * theory were presented in [10].…”

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confidence: 99%

On monopole bubbling contributions to ’t Hooft loops

Assel

Sciarappa

2019

J. High Energ. Phys.

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Monopole bubbling contributions to supersymmetric 't Hooft loops in 4d N = 2 theories are computed by SQM indices. As recently argued, those indices are hard to compute due to the presence of Coulomb vacua that are not captured by standard localization techniques. We propose an algorithmic method to compute the full bubbling contributions that circumvent this issue, by considering SQM with more matter fields and isolating the bubbling terms as residues in flavor fugacities. The enlarged SQMs are read from brane configurations realizing the bubbling sector of a given 't Hooft loop. We apply our technique to loop operators in N = 2 conformal SQCD theories. In addition we embed this discussion in the larger setup of a 5d-4d system interacting along a line, associated to the brane systems previously discussed. The bubbling terms arise from residues of specific instanton sectors of 5d line operators in this context. arXiv:1903.00376v1 [hep-th] 1 Mar 2019 6 Comments and directions 44 A SQM matrix models 47

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“…For example this should relate the quantum parameter y to the square root of the canonical bundle over the Calabi-Yau, as in [32]. Furthermore it would be interesting to relate our construction with the more geometrical one of [31,6].…”

Section: Discussionmentioning

confidence: 99%

Quantum line defects and refined BPS spectra

Cirafici

2019

Lett Math Phys

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In this note we study refined BPS invariants associated with certain quantum line defects in quantum field theories of class S. Such defects can be specified via geometric engineering in the UV by assigning a path on a certain curve. In the IR they are described by framed BPS quivers. We study the associated BPS spectral problem, including the spin content. The relevant BPS invariants arise from the K-theoretic enumerative geometry of the moduli spaces of quiver representations, adapting a construction by Nekrasov and Okounkov. In particular refined framed BPS states are described via Euler characteristics of certain complexes of sheaves.

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On ’t Hooft defects, monopole bubbling and supersymmetric quantum mechanics

Cited by 34 publications

References 66 publications

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

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

On monopole bubbling contributions to ’t Hooft loops

Quantum line defects and refined BPS spectra

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