All order exact result for the anomalous dimension of the scalar primary in Chern-Simons vector models

Jain, Sachin; Malvimat, Vinay; Mehta, Abhishek; Prakash, Soam; Sudhir, Nidhi

doi:10.1103/physrevd.101.126017

Cited by 15 publications

(8 citation statements)

References 40 publications

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“…In the absence of a gauge field, the scaling dimensions of spin-s operators, (represented schematically, as φ∂ s φ), are not expected to not grow as log s when s → ∞, and instead approach a finite value as s → ∞, suggesting that the dual is not string-like. (This objection does not apply for the non-supersymmetric bi-fundamental Chern-Simons theories, where the Chern-Simons gauge field, although nondynamical, still gives rise to a log s dependence of anomalous dimensions of spin s operators for large s [85,17,86].) When M is finite and N is large, the theory is a large N vector model, so there are various computations possible in principle that may be worth exploring.…”

Section: Discussionmentioning

confidence: 99%

Bifundamental Multiscalar Fixed Points in $d=3-ε$

Kapoor¹,

Prakash²

2021

Preprint

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We study fixed points of scalar fields that transform in the bifundamental representation of O(N ) × O(M ) in 3 − dimensions, generalizing the classic tri-critical sextic vector model. In the limit where N is large but M is finite, we determine the complete beta function to order 1/N for arbitrary M . We find a rich collection of large N fixed points in d = 3, as well as fixed points in d = 3 − , that can be studied to all orders in the parameter ˆ = N . With the goal of defining a large-N non-supersymmetric CFT dominated by a web of planar diagrams, we also study fixed points in the "bifundamental" large N limit, in which M and N are both large, but the ratio M/N is held fixed. We find a unique infrared fixed point in d = 3 − , which we determine to order 2 . When M/N 1, we also find an ultraviolet fixed point in d = 3 and d = 3 − that merges with the infrared fixed point at ∼ O(M/N ).

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Section: Discussionmentioning

confidence: 99%

Bifundamental Multiscalar Fixed Points in $d=3-ε$

Kapoor¹,

Prakash²

2021

Preprint

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“….. The scalar primary, which we will denote by j0, has dimension 2 + O 1 N [6]. The spin 2 primary j 2 is exactly conserved.…”

Section: Jhep05(2021)097mentioning

confidence: 99%

Four point functions in CFT’s with slightly broken higher spin symmetry

Silva

2021

J. High Energ. Phys.

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We compute spinning four point functions in the quasi-fermionic three dimensional conformal field theory with slightly broken higher spin symmetry at finite t’Hooft coupling. More concretely, we obtain a formula for $$ \left\langle {j}_s{j}_{\tilde{0}}{j}_{\tilde{0}}{j}_{\tilde{0}}\right\rangle $$ j s j 0 ˜ j 0 ˜ j 0 ˜ , where js is a higher spin current and $$ {j}_{\tilde{0}} $$ j 0 ˜ is the scalar single trace operator. Our procedure consists in writing a plausible ansatz in Mellin space and using crossing, pseudo-conservation and Regge boundedness to fix all undetermined coefficients. Our method can potentially be generalised to compute all spinning four point functions in these theories.

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“…where the parentheses stand for symmetrisation. It was also shown in [8] that the dimensions of these operators are independent of λ (to leading order in 1/N [24,25]), and in the free fermionic theory, given by:…”

Section: Generalitiesmentioning

confidence: 99%