3d Superconformal Theories from Three-Manifolds

Dimofte, Tudor

doi:10.1007/978-3-319-18769-3_11

Cited by 35 publications

(46 citation statements)

References 138 publications

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“…Although these theories generically do not have Lagrangian descriptions in 3d one can exploit the 6d origin of the theory by using the 3d-3d correspondence relating the superconformal index of the theory to certain topological invariants of Σ 3 . See [32][33][34][35][36][37] and [38] for a review. Using large N results for these invariants derived in [39] we are able to establish the relation in (1.1) for this class of theories.…”

Section: Introductionmentioning

confidence: 99%

Universal spinning black holes and theories of class $$ \mathcal{R} $$

Bobev

Crichigno

2019

J. High Energ. Phys.

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We study a supersymmetric, rotating, electrically charged black hole in AdS 4 which is a solution of four-dimensional minimal gauged supergravity. Using holography we show that the free energy on S 3 and the superconformal index of the dual three-dimensional N = 2 SCFT, in the planar limit, are related in a simple universal way. This result applies to large classes of SCFTs constructed from branes in string and M-theory which we discuss in some detail. For theories of class R, which arise from N M5-branes wrapped on hyperbolic three-manifolds, we show that the superconformal index agrees with the black hole entropy in the large N limit. arXiv:1909.05873v2 [hep-th]

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Section: Introductionmentioning

confidence: 99%

Universal spinning black holes and theories of class $$ \mathcal{R} $$

Bobev

Crichigno

2019

J. High Energ. Phys.

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“…the integration measure (3.4) is reproduced by the current 15) which is essentially the product of two commuting q-Virasoro screening currents defined in (2.24). In fact…”

Section: Free Boson Realizationmentioning

confidence: 99%

“…In order to describe the theory on S 3 b we consider the modular double construction of Sect. 3, namely we define where is the Weyl 15 The orientation does not actually matter for the ABJ(M) theory.…”

Section: Abj(m) Theorymentioning

confidence: 99%

“…Thirdly, the W q,t modular double algebra might also be useful to study 4d supersymmetric gauge theories in all those situations where 3d theories appear as boundary conditions or interfaces [12,13,15,[152][153][154]. In particular, S-duality domain wall in 4d N = 2 theories of class S [155] are realized by 3d N = 2 U(N ) YM theories on S 3 b [156][157][158][159][160], and their partition functions are modular kernels of Liouville [161][162][163] or Toda theories [160].…”

Section: Summary Comments and Outlookmentioning

confidence: 99%

“…Chern-Simons theory and its refined [2][3][4] or supersymmetric extensions feature prominently in topological string theory [5][6][7], in the study of the low energy physics of string/M-theory through Hanany-Witten brane constructions [8] or the celebrated ABJ(M) model for the effective theory of M2 branes [9,10]. The application of field theory methods for studying 3d manifolds and knot theory has recently produced many new results and connections between the two fields, culminated in the discovery of the 3d-3d correspondence [11][12][13][14] (see also the review [15]) relating 3d N = 2 SCFTs arising from M5 branes compactified on a 3d manifold to complex Chern-Simons on the latter [16]. More generally, the embedding of 3d N = 2 Chern-Simons-Yang-Mills theories in string/M-theory has provided many insights into their physics, including 3d Seiberg-like dualities [17][18][19][20][21][22] and mirror symmetry [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

q-Virasoro Modular Double and 3d Partition Functions

Nedelin

Nieri

Zabzine

2017

Commun. Math. Phys.

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Abstract:We study partition functions of 3d N = 2 U(N ) gauge theories on compact manifolds which are S 1 fibrations over S 2 . We show that the partition functions are free field correlators of vertex operators and screening charges of the q-Virasoro modular double, which we define. The inclusion of supersymmetric Wilson loops in arbitrary representations allows us to show that the generating functions of Wilson loop vacuum expectation values satisfy two SL(2, Z)-related commuting sets of q-Virasoro constraints. We generalize our construction to 3d N = 2 unitary quiver gauge theories and as an example we give the free boson realization of the ABJ(M) model.

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Line Operators in Supersymmetric Gauge Theories and the 2d-4d Relation

Okuda

2015

New Dualities of Supersymmetric Gauge Theories

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Four-dimensional gauge theories with N = 2 supersymmetry admit half-BPS line operators. We review the exact localization methods for analyzing these operators. We also review the roles they play in the relation between four-and two-dimensional field theories, and explain how the two-dimensional CFT can be used to obtain the quantitative results for 4d line operators. This is a contribution to the special LMP volume on the 2d-4d relation, edited by J. Teschner.

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3d Superconformal Theories from Three-Manifolds

Cited by 35 publications

References 138 publications

Universal spinning black holes and theories of class $$ \mathcal{R} $$

Universal spinning black holes and theories of class $$ \mathcal{R} $$

q-Virasoro Modular Double and 3d Partition Functions

Line Operators in Supersymmetric Gauge Theories and the 2d-4d Relation

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