Approaching the conformal window ofO(n)×O(m)symmetric Landau-Ginzburg models using the conformal bootstrap

Abstract A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy certain consistency conditions that follow from associativity and the completeness of eigenmodes. We show that it is possible to obtain nontrivial bounds on the geometric data of closed Einstein manifolds by using semidefinite programming to study these consistency conditions, in analogy to the conformal bootstrap bounds on conformal field theories. These bootstrap bounds translate to constraints on the tree-level masses and cubic couplings of Kaluza-Klein modes in theories with compact extra dimensions. We show that in some cases the bounds are saturated by known manifolds.

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Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

Journal of High Energy Physics ◽

10.1007/jhep12(2020)019 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Yifei He ◽

Jesper Lykke Jacobsen ◽

Hubert Saleur

Keyword(s):

Potts Model ◽

Correlation Functions ◽

Liouville Theory ◽

Analytical Determination ◽

Conformal Weight ◽

Two Dimensional ◽

Conformal Blocks ◽

Conformal Bootstrap ◽

Point Correlation

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

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Fixing the conformal window in QCD

Physical Review D ◽

10.1103/physrevd.65.021701 ◽

2001 ◽

Vol 65 (2) ◽

Cited By ~ 8

Author(s):

G. Grunberg

Keyword(s):

Conformal Window

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Bootstrapping Coulomb and Higgs branch operators

Journal of High Energy Physics ◽

10.1007/jhep01(2021)175 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Aleix Gimenez-Grau ◽

Pedro Liendo

Keyword(s):

Recent Work ◽

Moment Map ◽

Mixed System ◽

Flavor Symmetry ◽

Coulomb Branch ◽

Conformal Bootstrap ◽

General Constraints ◽

Superconformal Theories ◽

The Moment

Abstract We apply the numerical conformal bootstrap to correlators of Coulomb and Higgs branch operators in 4d$$ \mathcal{N} $$ N = 2 superconformal theories. We start by revisiting previous results on single correlators of Coulomb branch operators. In particular, we present improved bounds on OPE coefficients for some selected Argyres-Douglas models, and compare them to recent work where the same cofficients were obtained in the limit of large r charge. There is solid agreement between all the approaches. The improved bounds can be used to extract an approximate spectrum of the Argyres-Douglas models, which can then be used as a guide in order to corner these theories to numerical islands in the space of conformal dimensions. When there is a flavor symmetry present, we complement the analysis by including mixed correlators of Coulomb branch operators and the moment map, a Higgs branch operator which sits in the same multiplet as the flavor current. After calculating the relevant superconformal blocks we apply the numerical machinery to the mixed system. We put general constraints on CFT data appearing in the new channels, with particular emphasis on the simplest Argyres-Douglas model with non-trivial flavor symmetry.

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