3d N=4 Bootstrap and Mirror Symmetry

Chang, Chi‐Ming; Fluder, Martin; Lin, Ying-Hsuan; Shao, Shu-Heng; Wang, Yifan

doi:10.21468/scipostphys.10.4.097

“…the complex dimension of the Coulomb branch. There have been numerous efforts in classifying SCFTs with 8 Qs for a given low rank in various space-time dimensions [15][16][17][18][19][20][21][22][23][24][25]. For 3D N = 4 SCFTs, however, the rank is in general not a duality-invariant concept since the Coulomb and Higgs branches are exchanged under the 3D mirror symmetry [26].…”

Section: Jhep08(2021)158mentioning

confidence: 99%

Non-unitary TQFTs from 3D $$ \mathcal{N} $$ = 4 rank 0 SCFTs

Gang

¹

,

Kim

²

,

Lee

³

et al. 2021

J. High Energ. Phys.

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We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT±[$$ \mathcal{T} $$ T rank 0], to a (2+1)D interacting $$ \mathcal{N} $$ N = 4 superconformal field theory (SCFT) $$ \mathcal{T} $$ T rank 0 of rank 0, i.e. having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a non-trivial dictionary, we propose that F = maxα (− log|$$ {S}_{0\alpha}^{\left(+\right)} $$ S 0 α + |) = maxα (− log|$$ {S}_{0\alpha}^{\left(-\right)} $$ S 0 α − |), where F is the round three-sphere free energy of $$ \mathcal{T} $$ T rank 0 and $$ {S}_{0\alpha}^{\left(\pm \right)} $$ S 0 α ± is the first column in the modular S-matrix of TFT±. From the dictionary, we derive the lower bound on F, F ≥ − log $$ \left(\sqrt{\frac{5-\sqrt{5}}{10}}\right) $$ 5 − 5 10 ≃ 0.642965, which holds for any rank 0 SCFT. The bound is saturated by the minimal $$ \mathcal{N} $$ N = 4 SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples.

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“…71, where the N = 8 bound has a kink. 18 At other values of 16 c T , the N = 6 lower bound is significantly weaker than the N = 8 one, which suggests that it may be saturated by N = 6 SCFTs that do not have N = 8 SUSY. Indeed, in figure 1 (3.41), respectively, and we see that these values do lie outside the N = 8 region and come close to saturating the N = 6 bounds.…”

Section: Bounds On Short Ope Coefficients and The Extremal Functional Conjecturementioning

confidence: 97%

“…For instance, in N = 4 theories the stress tensor multiplet is only 1/4-BPS but still has a scalar superprimary. Similarly, while conserved current multiplets are half-BPS for N = 4 theories (and were studied using the numerical bootstrap in [18]), for N = 3 theories they are 1/3-BPS and for N = 2 theories are only 1/4-BPS. Many localization results exist which could be applied to these cases, including N = 4 results computed in [90].…”

Section: Jhep05(2021)083mentioning

confidence: 99%

The 3d $$ \mathcal{N} $$ = 6 bootstrap: from higher spins to strings to membranes

Binder

¹

,

Chester

²

,

Jerdee

³

et al. 2021

J. High Energ. Phys.

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We study the space of 3d $$ \mathcal{N} $$ N = 6 SCFTs by combining numerical bootstrap techniques with exact results derived using supersymmetric localization. First we derive the superconformal block decomposition of the four-point function of the stress tensor multiplet superconformal primary. We then use supersymmetric localization results for the $$ \mathcal{N} $$ N = 6 U(N)k × U(N + M)−k Chern-Simons-matter theories to determine two protected OPE coefficients for many values of N, M, k. These two exact inputs are combined with the numerical bootstrap to compute precise rigorous islands for a wide range of N, k at M = 0, so that we can non-perturbatively interpolate between SCFTs with M-theory duals at small k and string theory duals at large k. We also present evidence that the localization results for the U(1)2M × U (1 + M)−2M theory, which has a vector-like large-M limit dual to higher spin theory, saturates the bootstrap bounds for certain protected CFT data. The extremal functional allows us to then conjecturally reconstruct low-lying CFT data for this theory.

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“…The construction has been later extended to Coulomb branch operators [25], complicated by the presence of monopole operators, and to more general manifolds [26]. A mini-bootstrap approach has been performed in this sector [27], leading to analytical bounds on flavor central charges and other OPE coefficients.…”

Section: Jhep06(2021)091mentioning

confidence: 99%

“…Another interesting perspective would be to apply conformal bootstrap techniques in this context. In the N = 4 case the OPE data in the relevant topological quantum mechanics can be obtained or constrained imposing the associativity and unitarity of the operator algebra [23,27]. This procedure is dubbed mini-bootstrap (or micro-bootstrap in fourdimensions [54]) because it concerns a closed subsystem of the full bootstrap equations.…”

Section: Jhep06(2021)091mentioning

confidence: 99%

The topological line of ABJ(M) theory

Gorini

¹

,

Guerrini

²

,

Penati

³

et al. 2021

J. High Energ. Phys.

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We construct the one-dimensional topological sector of $$ \mathcal{N} $$ N = 6 ABJ(M) theory and study its relation with the mass-deformed partition function on S3. Supersymmetric localization provides an exact representation of this partition function as a matrix integral, which interpolates between weak and strong coupling regimes. It has been proposed that correlation functions of dimension-one topological operators should be computed through suitable derivatives with respect to the masses, but a precise proof is still lacking. We present non-trivial evidence for this relation by computing the two-point function at two-loop, successfully matching the matrix model expansion at weak coupling and finite ranks. As a by-product we obtain the two-loop explicit expression for the central charge cT of ABJ(M) theory. Three- and four-point functions up to one-loop confirm the relation as well. Our result points towards the possibility to localize the one-dimensional topological sector of ABJ(M) and may also be useful in the bootstrap program for 3d SCFTs.

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3d N=4 Bootstrap and Mirror Symmetry

Cited by 17 publications

References 98 publications

Non-unitary TQFTs from 3D $$ \mathcal{N} $$ = 4 rank 0 SCFTs

Non-unitary TQFTs from 3D $$ \mathcal{N} $$ = 4 rank 0 SCFTs

The 3d $$ \mathcal{N} $$ = 6 bootstrap: from higher spins to strings to membranes

The topological line of ABJ(M) theory

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