2d SCFTs from M2-branes

Hori, Kentaro; Park, Chan Y.; Tachikawa, Yuji

doi:10.1007/jhep11(2013)147

Cited by 19 publications

(46 citation statements)

References 39 publications

(79 reference statements)

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“…Besides an unimportant (−1) (dim g−dim t)/2 we have an additional sign α>0 (−1) α(k) . This is equal to the sign that was originally missed in S 2 localization calculations [9,26,41], pointed out by Hori and collaborators [56,57], and described in detail in [13]. It would be good to clarify the correct sign on RP 2 .…”

Section: Jhep12(2017)099supporting

confidence: 51%

Agt/ℤ2

Floch

Turiaci

2017

J. High Energ. Phys.

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We relate Liouville/Toda CFT correlators on Riemann surfaces with boundaries and cross-cap states to supersymmetric observables in four-dimensional N = 2 gauge theories. Our construction naturally involves four-dimensional theories with fields defined on different Z 2 quotients of the sphere (hemisphere and projective space) but nevertheless interacting with each other. The six-dimensional origin is a Z 2 quotient of the setup giving rise to the usual AGT correspondence. To test the correspondence, we work out the RP 4 partition function of four-dimensional N = 2 theories by combining a 3d lens space and a 4d hemisphere partition functions. The same technique reproduces known RP 2 partition functions in a form that lets us easily check two-dimensional Seiberg-like dualities on this nonorientable space. As a bonus we work out boundary and cross-cap wavefunctions in Toda CFT.

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Section: Jhep12(2017)099supporting

confidence: 51%

Agt/ℤ2

Floch

Turiaci

2017

J. High Energ. Phys.

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“…Fortunately it has been shown that 2d-4d correspondence is seen in the matching of RG flows of 2d and 4d coupling constants, coincidence of spectra of BPS states [32,3,4], and conformal dimensions at Argyres-Douglas critical points [33]. A general discussion concerning the decoupling limits when the 4d degrees of freedom do not influence the world sheet theory can be found in [34].…”

Section: Comments On 2d-4d Correspondence 51 Brane Picture and 2d-4dmentioning

confidence: 99%

Dynamics of non-Abelian strings in the theory interpolating from N=2 to N=1 supersymmetric QCD

2020

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We study the dynamics of non-Abelian vortex strings supported in N = 2 supersymmetric QCD with the U(N ) gauge group and N f = N quark flavors deformed by the mass µ of the adjoint matter. In the limit of large µ the bulk four-dimensional theory flows to N = 1 supersymmetric QCD. The dynamics of orientational zero modes of the non-Abelian string is described by the world sheet CP(N − 1) model. At µ = 0 this model has N = (2, 2) supersymmetry while at large µ it flows to the non-supersymmetric CP(N − 1) model. We solve the world sheet model in the large N approximation and find a rich phase structure with respect to the deformation parameter µ and quark mass differences. The phases include two strong coupling phases and two Higgs phases. In particular, the Higgs phase at small µ supports CP(N − 1) model kinks representing confined monopoles of the bulk QCD, while in the large-µ Higgs phase monopoles disappear.

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“…Each edge corresponds to a generator of the charge lattice, whose dimension is 2r + f = M , where f the rank of the flavor lattice, while r is the complex dimension of the Coulomb branch. 42 The theory has two types of surface defects: a "regular" defect parameterized by the region near the regular puncture (inside the chamber delimited by double-walls), and an "irregular" one corresponding to the region near the irregular puncture (outside the chamber delimited by double-walls). The irregular defect corresponds to the defect considered in [36,37]; its BPS spectrum can be studied by a straightforward extension of the techniques adopted in the present paper, and it is relevant for the connection with chiral algebras [87].…”

Section: Including Irregular Puncturesmentioning

confidence: 99%

“…The description of the BPS spectrum is in fact very similar to that of higher-genus surfaces studied above. 42 There are in addition M single (or "one-way") S-walls that emanate from branch points, but end up on the puncture at infinity. They are denoted by dashed lines.…”

Section: Including Irregular Puncturesmentioning

confidence: 99%

An infrared bootstrap of the Schur index with surface defects

Fluder

Longhi

2019

J. High Energ. Phys.

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The infrared formula relates the Schur index of a 4d N = 2 theory to its wallcrossing invariant, a.k.a. BPS monodromy. A further extension of this formula, proposed by Córdova, Gaiotto and Shao, includes contributions by various types of line and surface defects. We study BPS monodromies in the presence of vortex surface defects of arbitrary vorticity for general class S theories of type A 1 engineered by UV curves with at least one regular puncture. The trace of these defect BPS monodromies is shown to coincide with the action of certain q-difference operators acting on the trace of the (pure) 4d BPS monodromy. We use these operators to develop a "bootstrap" (of traces) of BPS monodromies, relying only on their infrared properties, thereby reproducing the very general ultraviolet characterization of the Schur index.A relation between Schur indices and BPS monodromies was conjectured in [23], following 6 See also [45], for some results of an IR formula for the lens index. 9 The "no-exotics" property asserts that BPS states have R = 0 in 4d N = 2 gauge theories [33,54,55]. 10 In practice, BPS spectra at arbitrary moduli can be rather involved, and by moving onto a "simple" sector of the theory, in which one can explicitly compute the protected spin character, the wall-crossing formulae allow to extract the BPS degeneracies in other sectors. the latter reference are precisely the "vortex defects" considered in [31] via the Higgsing procedure (see also Appendix A.3), and in the present paper via the IR formalism.

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2d SCFTs from M2-branes

Cited by 19 publications

References 39 publications

Agt/ℤ2

Agt/ℤ2

Dynamics of non-Abelian strings in the theory interpolating from N=2 to N=1 supersymmetric QCD

An infrared bootstrap of the Schur index with surface defects

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