Boundary and interface CFTs from the conformal bootstrap

Gliozzi, F.; Liendo, Pedro; Meineri, Marco; Rago, Antonio

doi:10.1007/jhep05(2015)036

Cited by 171 publications

(260 citation statements)

References 98 publications

(198 reference statements)

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“…Indeed, this will be the reason that we can make progress in studying the conformal phase of (2, 0) SCFTs despite the absence of a conventional definition. Thus in broad terms this work will mirror many recent bootstrap studies [37][38][39]59,60,. We will not review the basic philosophy in any detail here.…”

Section: The Bootstrap Program For (2 0) Theoriesmentioning

confidence: 93%

The (2, 0) superconformal bootstrap

et al. 2016

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We develop the conformal bootstrap program for six-dimensional conformal field theories with (2, 0) supersymmetry, focusing on the universal four-point function of stress tensor multiplets. We review the solution of the superconformal Ward identities and describe the superconformal block decomposition of this correlator. We apply numerical bootstrap techniques to derive bounds on operator product expansion (OPE) coefficients and scaling dimensions from the constraints of crossing symmetry and unitarity. We also derive analytic results for the large spin spectrum using the light cone expansion of the crossing equation. Our principal result is strong evidence that the A 1 theory realizes the minimal allowed central charge (c ¼ 25) for any interacting (2, 0) theory. This implies that the full stress tensor four-point function of the A 1 theory is the unique unitary solution to the crossing symmetry equation at c ¼ 25. For this theory, we estimate the scaling dimensions of the lightest unprotected operators appearing in the stress tensor operator product expansion. We also find rigorous upper bounds for dimensions and OPE coefficients for a general interacting (2, 0) theory of central charge c. For large c, our bounds appear to be saturated by the holographic predictions obtained from eleven-dimensional supergravity.

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Section: The Bootstrap Program For (2 0) Theoriesmentioning

confidence: 93%

The (2, 0) superconformal bootstrap

et al. 2016

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“…This gives us a more straightforward opportunity to use the techniques in [21,22]. The explicit solution for hσσσσi along this line was found in [23], which focused on its special role in the nonunitary (severe truncation) bootstrap of [24][25][26]. 5 This solution exhibits Virasoro symmetry with a central charge given by…”

Section: ð1:3þmentioning

confidence: 96%

Unitary subsector of generalized minimal models

Behan

2018

Phys. Rev. D

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We revisit the line of nonunitary theories that interpolate between the Virasoro minimal models. Numerical bootstrap applications have brought about interest in the four-point function involving the scalar primary of lowest dimension. Using recent progress in harmonic analysis on the conformal group, we prove the conjecture that global conformal blocks in this correlator appear with positive coefficients. We also compute many such coefficients in the simplest mixed correlator system. Finally, we comment on the status of using global conformal blocks to isolate the truly unitary points on this line.

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“…Note that even when the external operators are identical, the coefficients of the conformal block expansion do not exhibit any positivity property. The numerical bootstrap program was applied to defect CFTs in [18,19] using the method of [20], and in [21,22] using the method of [23].…”

Section: Jhep01(2017)122mentioning

confidence: 99%

“…As in the non-supersymmetric case, see [18,21,57], the crossing equation for massless representations is solved by a finite number of blocks in both channels as…”

Section: Example: N = 4 Massless Representation P =mentioning

confidence: 99%

Bootstrap equations for N $$ \mathcal{N} $$ = 4 SYM with defects

Liendo

Meneghelli

2017

J. High Energ. Phys.

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174

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This paper focuses on the analysis of 4d N = 4 superconformal theories in the presence of a defect from the point of view of the conformal bootstrap. We will concentrate first on the case of codimension one, where the defect is a boundary that preserves half of the supersymmetry. After studying the constraints imposed by supersymmetry, we will obtain the Ward identities associated to two-point functions of 1 2 -BPS operators and write their solution as a superconformal block expansion. Due to a surprising connection between spacetime and R-symmetry conformal blocks, our results not only apply to 4d N = 4 superconformal theories with a boundary, but also to three more systems that have the same symmetry algebra: 4d N = 4 superconformal theories with a line defect, 3d N = 4 superconformal theories with no defect, and OSP(4 * |4) superconformal quantum mechanics. The superconformal algebra implies that all these systems possess a closed subsector of operators in which the bootstrap equations become polynomial constraints on the CFT data. We derive these truncated equations and initiate the study of their solutions.

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Boundary and interface CFTs from the conformal bootstrap

Cited by 171 publications

References 98 publications

The (2, 0) superconformal bootstrap

The (2, 0) superconformal bootstrap

Unitary subsector of generalized minimal models

Bootstrap equations for N $$ \mathcal{N} $$ = 4 SYM with defects

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