What if ϕ4 theory in 4 dimensions is non-trivial in the continuum?

Romatschke, Paul

doi:10.1016/j.physletb.2023.138270

Cited by 9 publications

(3 citation statements)

References 30 publications

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“…For a given value of µ, we can numerically calculate the value of ∆ from solving the saddle-point condition (57). With µ, ∆, we can then calculate n and E N .…”

Section: Lecture 2: Non-relativistic Neutronsmentioning

confidence: 99%

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Quantum Field Theory in Large-\(N\) Wonderland: Three Lectures

Romatschke

2024

Acta Phys. Pol. B

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In these lecture notes, I review how to use large-N techniques to solve quantum field theories in various dimensions. In particular, the case of N -dimensional quantum mechanics, non-relativistic cold and dense neutron matter, and scalar field theory in four dimensions are covered. A recurring theme is that large-N solutions are fully non-perturbative, and can be used to reliably access quantum field theory for parameter regions where weakcoupling expansions simply fail.

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“…For a given value of µ, we can numerically calculate the value of ∆ from solving the saddle-point condition (57). With µ, ∆, we can then calculate n and E N .…”

Section: Lecture 2: Non-relativistic Neutronsmentioning

confidence: 99%

“…Note that these proofs are limited to N ≤ 2 and positive bare coupling, so they do not apply to the O(N ) model in the large-N limit. Using analytic continuation of the path integral contour, it is possible (but numerically challenging) to study negative coupling field theory on the lattice [57].…”

Section: Guide To Further Readingmentioning

confidence: 99%

Quantum Field Theory in Large-\(N\) Wonderland: Three Lectures

Romatschke

2024

Acta Phys. Pol. B

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“…While the RG equations describe the flow of couplings as a function of scale, they naturally extend to complex couplings and do not themselves prescribe signs or reality properties. Examples of unconventional solutions include negative couplings in the far UV, related to PT symmetric (rather than Hermitean) quantum field theories [1,2], and trajectories where some couplings are purely imaginary [3][4][5][6], which nonetheless have been argued to yield quantum field theories with real-valued observables. In both cases, the theories appear to be asymptotically free, a property which conventionally is reserved for non-Abelian gauge theories in 4d.…”

Section: Introductionmentioning

confidence: 99%

Classifying large N limits of multiscalar theories by algebra

Flodgren,

Sundborg

2024

J. High Energ. Phys.

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We develop a new approach to RG flows and show that one-loop flows in multiscalar theories can be described by commutative but non-associative algebras. As an example related to D-brane field theories and tensor models, we study the algebra of a theory with M SU(N) adjoint scalars and its large N limits. The algebraic concepts of idempotents and Peirce numbers/Kowalevski exponents are used to characterise the RG flows. We classify and describe all large N limits of algebras of multiadjoint scalar models: the standard ‘t Hooft matrix theory limit, a ‘multi-matrix’ limit, each with one free parameter, and an intermediate case with extra symmetry and no free parameter of the algebra, but an emergent free parameter from a line of one-loop fixed points. The algebra identifies these limits without diagrammatic or combinatorial analysis.

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RG flows and fixed points of O(N)r models

Jepsen,

2024

J. High Energ. Phys.

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By means of ϵ and large N expansions, we study generalizations of the O(N) model where the fundamental fields are tensors of rank r rather than vectors, and where the global symmetry (up to additional discrete symmetries and quotients) is O(N)r, focusing on the cases r ≤ 5. Owing to the distinct ways of performing index contractions, these theories contain multiple quartic operators, which mix under the RG flow. At all large N fixed points, melonic operators are absent and the leading Feynman diagrams are bubble diagrams, so that all perturbative fixed points can be readily matched to full large N solutions obtained from Hubbard-Stratonovich transformations. The family of fixed points we uncover extend to arbitrary higher values of r, and as their number grows superexponentially with r, these theories offer a vast generalization of the critical O(N) model.We also study sextic O(N)r theories, whose large N limits are obscured by the fact that the dominant Feynman diagrams are not restricted to melonic or bubble diagrams. For these theories the large N dynamics differ qualitatively across different values of r, and we demonstrate that the RG flows possess a numerous and diverse set of perturbative fixed points beginning at rank four.

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What if ϕ4 theory in 4 dimensions is non-trivial in the continuum?

Cited by 9 publications

References 30 publications

Quantum Field Theory in Large-\(N\) Wonderland: Three Lectures

Quantum Field Theory in Large-\(N\) Wonderland: Three Lectures

Classifying large N limits of multiscalar theories by algebra

RG flows and fixed points of O(N)r models

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