The F-theorem in the melonic limit

Benedetti, Dario; Gurău, Razvan; Harribey, Sabine; Lettera, Davide

doi:10.1007/jhep02(2022)147

Cited by 11 publications

(4 citation statements)

References 80 publications

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“…This is a particular realization of the general result by Gubser and Klebanov [57] on large-N flows driven by a double-trace operator (in this case, the (ϕ 2 ) 2 interaction). There are many other ways to see the same result, for example by means of the conformal partial wave representation of the four-point function [46], or diagrammatically, as we will see below.…”

Section: Jhep02(2024)078mentioning

confidence: 95%

“…, thus matching the minus sign in (1.4). Notice also that despite such minus sign, the GFFT action is positive definite, as best understood in momentum space: this is because the position space representation of the fractional Laplacian is singular and needs a subtraction, which is not written explicitly in (1.4) (see footnote 18 of [46]).…”

Section: Generalized Free Field Theorymentioning

confidence: 99%

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Finite-size versus finite-temperature effects in the critical long-range O(N) model

Benedetti,

Gurau,

Harribey

et al. 2024

J. High Energ. Phys.

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In this paper we consider classical and quantum versions of the critical long-range O(N) model, for which we study finite-size and finite-temperature effects, respectively, at large N. First, we consider the classical (isotropic) model, which is conformally invariant at criticality, and we introduce one compact spatial direction. We show that the finite size dynamically induces an effective mass and we compute the one-point functions for bilinear primary operators with arbitrary spin and twist. Second, we study the quantum model, mapped to a Euclidean anisotropic field theory, local in Euclidean time and long-range in space, which we dub fractional Lifshitz field theory. We show that this model admits a fixed point at zero temperature, where it displays anisotropic Lifshitz scaling, and show that at finite temperature a thermal mass is induced. We then compute the one-point functions for an infinite family of bilinear scaling operators.In both the classical and quantum model, we find that, as previously noted for the short-range O(N) model in [1], the large-N two-point function contains information about the one-point functions, not only of the bilinear operators, but also of operators that appear in the operator product expansion of two fundamental fields only at subleading order in 1/N, namely powers of the Hubbard-Stratonovich intermediate field.

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Section: Jhep02(2024)078mentioning

confidence: 95%

Section: Generalized Free Field Theorymentioning

confidence: 99%

Finite-size versus finite-temperature effects in the critical long-range O(N) model

Benedetti,

Gurau,

Harribey

et al. 2024

J. High Energ. Phys.

Self Cite

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show abstract

“…This is not to be confused with the non-perturbative instability of the conformal solutions discussed in [87][88][89]. It is possible to circumvent this instability (and the non-unitarity) by considering the long-ranged version of the tensor model [90] which in particular satisfies the F -theorem [91] but no longer has a finite canonical stress energy tensor (as is the case for generalized free fields [92,93]).…”

Section: Scalar Quantum Field Theory and Localized Magnetic Defectsmentioning

confidence: 99%

Non-Perturbative Defects in Tensor Models from Melonic Trees

Popov,

Wang

2022

Preprint

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The Klebanov-Tarnopolsky tensor model is a quantum field theory for rank-three tensor scalar fields with certain quartic potential. The theory possesses an unusual large N limit known as the melonic limit that is strongly coupled yet solvable, producing at large distance a rare example of non-perturbative non-supersymmetric conformal field theory that admits analytic solutions. We study the dynamics of defects in the tensor model defined by localized magnetic field couplings on a p-dimensional subspace in the d-dimensional spacetime. While we work with general p and d, the physically interesting cases include line defects in d = 2, 3 and surface defects in d = 3. By identifying a novel large N limit that generalizes the melonic limit in the presence of defects, we prove that the defect one-point function of the scalar field only receives contributions from a subset of the Feynman diagrams in the shape of melonic trees. These diagrams can be resummed using a closed Schwinger-Dyson equation which enables us to determine non-perturbatively this defect one-point function. At large distance, the solutions we find describe nontrivial conformal defects and we discuss their defect renormalization group (RG) flows. In particular, for line defects, we solve the exact RG flow between the trivial and the conformal lines in d = 4 − ǫ. We also compute the exact line defect entropy and verify the g-theorem. Furthermore we analyze the defect twopoint function of the scalar field and its decomposition via the operator-product-expansion, providing explicit formulae for one-point functions of bilinear operators and the stress-energy tensor.

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“…This type of RG flows has been considered before in[3,4] 2. We show in general in appendix A that physical properties of the RG flow are independent of the choice of dimension of the field.…”

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confidence: 96%

Renormalization group flows between Gaussian fixed points

Diego

Percacci

2022

J. High Energ. Phys.

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A scalar theory can have many Gaussian (free) fixed points, corresponding to Lagrangians of the form ϕ□nϕ. We use the non-perturbative RG to study examples of flows between such fixed points. We show that the anomalous dimension changes continuously in such a way that at the endpoints the fields have the correct dimensions of the respective free theories. These models exhibit various pathologies, but are nonetheless interesting as examples of theories that are asymptotically free both in the infrared and in the ultraviolet. Furthermore, they illustrate the fact that a diverging coupling can actually correspond to a free theory.

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The F-theorem in the melonic limit

Cited by 11 publications

References 80 publications

Finite-size versus finite-temperature effects in the critical long-range O(N) model

Finite-size versus finite-temperature effects in the critical long-range O(N) model

Non-Perturbative Defects in Tensor Models from Melonic Trees

Renormalization group flows between Gaussian fixed points

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