ABCD of ’t Hooft operators

Hayashi, Hirotaka; Okuda, Takuya; Yoshida, Yutaka

doi:10.1007/jhep04(2021)241

Cited by 9 publications

(11 citation statements)

References 66 publications

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“…The low energy world volume theory on D3-branes suspended between NS5'-branes is 2d supersymmetric GLSM. This T-dual picture of the proposal in [28,26] suggests that the supersymmetric indices, i.e., elliptic genera for the world volume theories of D3-branes ended on NS5'-branes give the monopole bubbling effects Z mono .…”

Section: Brane Construction For T' Hooft Surface Operators and Monopo...mentioning

confidence: 80%

“…We concentrated on 5d N = 1 * U (N ) gauge theory and concretely studied the algebra of surface operators and monopole bubbling effects with small magnetic charges. For general 5d N = 1 gauge theories, monopole bubbling effects are described by elliptic genera of 2d N = (0, 4) GLSMs, which are obtained by the T-dual picture of the brane configuration studied in [26]. The gauge anomaly cancellation condition for 2d N = (0, 4) GLSMs give constraints on the matter contents of the five dimensional theory and also magnetic charge B.…”

Section: Discussionmentioning

confidence: 99%

“…It turned out that 't Hooft loops agree with Verlinde loop operators by including monopole bubbling effects. Moreover monopole bubbling effects are also necessary to reproduce the correct properties of operator product expansions (OPEs) of BPS 't Hooft loops [11,1,25,26]. In three dimensions, monopole bubbling effects for BPS monopole operators on R 3 were studied in [2,3].…”

Section: Monopole Surface Operators As Susy Indices Onmentioning

confidence: 99%

“…For BPS 't Hooft loops in 4d N = 2 U (N ) and SU (N ) gauge theories on S 1 × R 3 , monopole bubbling effects are given by Witten indices for supersymmetric quantum mechanics (SQM) arising from the low energy world volume theories on D1-branes [24,28,29] in the type IIB string theory. Monopole bubbling effects were also studied in [26] in terms of the type IIA string theory. By taking a T-dual of the brane configuration of [26] in the x 4 -direction, we obtain monopole bubbling effects Z mono for the surface operators on T 2 × R 3 which are given by elliptic genera for 2d gauged linear sigma models (GLSMs) living on T 2 .…”

Section: Monopole Bubbling Effects Via Branes and Elliptic Generamentioning

confidence: 99%

“…Monopole bubbling effects were also studied in [26] in terms of the type IIA string theory. By taking a T-dual of the brane configuration of [26] in the x 4 -direction, we obtain monopole bubbling effects Z mono for the surface operators on T 2 × R 3 which are given by elliptic genera for 2d gauged linear sigma models (GLSMs) living on T 2 .…”

Section: Monopole Bubbling Effects Via Branes and Elliptic Generamentioning

confidence: 99%

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't Hooft surface operators in five dimensions and elliptic Ruijsenaars operators

Yoshida

2021

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We introduce codimension three magnetically charged surface operators in fivedimensional (5d) N = 1 supersymmetric gauge on T 2 × R 3 . We evaluate the vacuum expectation values (vevs) of surface operators by supersymmetric localization techniques. Contributions of Monopole bubbling effects to the path integral are given by elliptic genera of world volume theories on D-branes. Our result gives an elliptic deformation of the SUSY localization formula [1] (resp. [2, 3]) of BPS 't Hooft loops (resp. bare monopole operators) in 4d N = 2 (resp. 3d N = 4) gauge theories. We define deformation quantizations of vevs of surface operators in terms of the Weyl-Wigner transform, where the Ω-background parameter play the role of the Planck constant. For 5d N = 1 * gauge theory, we find that the deformation quantization of the surface operators in the anti-symmetric representations agrees with the type A elliptic Ruijsenaars operators. The mutual commutativity of these difference operators is related to the commutativity of products of 't Hooft surface operators.

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Section: Brane Construction For T' Hooft Surface Operators and Monopo...mentioning

confidence: 80%

Section: Discussionmentioning

confidence: 99%

Section: Monopole Surface Operators As Susy Indices Onmentioning

confidence: 99%

Section: Monopole Bubbling Effects Via Branes and Elliptic Generamentioning

confidence: 99%

Section: Monopole Bubbling Effects Via Branes and Elliptic Generamentioning

confidence: 99%

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't Hooft surface operators in five dimensions and elliptic Ruijsenaars operators

Yoshida

2021

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$$ \mathcal{N} $$ = 2* Schur indices

Hatsuda

Okazaki

2023

J. High Energ. Phys.

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We find closed-form expressions for the Schur indices of 4d $$ \mathcal{N} $$ N = 2* super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas formulation. They can be written as a sum over the Young diagrams associated with spectral zeta functions of an ideal Fermi-gas system. These functions are expressed in terms of the twisted Weierstrass functions, generating functions for quasi-Jacobi forms. The indices lie in the polynomial ring generated by the Kronecker theta function and the Weierstrass functions which contains the polynomial ring of the quasi-Jacobi forms. The grand canonical ensemble allows for another simple exact form of the indices as infinite series. In addition, we find that the unflavored Schur indices and their limits can be expressed in terms of several generating functions for combinatorial objects, including sum of triangular numbers, generalized sums of divisors and overpartitions.

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Superspin chains solutions from 4D Chern-Simons theory

Boujakhrout,

Saidi,

Laamara

et al. 2024

J. High Energ. Phys.

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As a generalisation of the correspondence linking 2D integrable systems with 4D Chern-Simons (CS) gauge theory, superspin chains are realized by means of crossing electric and magnetic super line defects in the 4D CS with super gauge symmetry. The oscillator realization of Lax operators solving the RLL relations of integrability is obtained in the gauge theory by extending the notion of Levi decomposition to Lie superalgebras. Based on particular 3-gradings of Lie superalgebras, we obtain graded oscillator Lax matrices for superspin chains with internal symmetries given by A(m − 1 | n − 1), B(m | n), C(n) and D(m | n).

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ABCD of ’t Hooft operators

Cited by 9 publications

References 66 publications

't Hooft surface operators in five dimensions and elliptic Ruijsenaars operators

't Hooft surface operators in five dimensions and elliptic Ruijsenaars operators

$$ \mathcal{N} $$ = 2* Schur indices

Superspin chains solutions from 4D Chern-Simons theory

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