The background field method and critical vector models

Goykhman, Mikhail; Rosenhaus, Vladimir; Smolkin, Michael

doi:10.1007/jhep02(2021)074

Cited by 12 publications

(18 citation statements)

References 61 publications

(137 reference statements)

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“…where µ is IR mass scale [32,33]. The second contribution to σ 2 σ 2 at the next-to-leading order in 1/N is due to insertions of two cubic σ vertices into the leading order diagram:…”

Section: σ 2 σmentioning

confidence: 99%

“…Such a calculation requires knowing the next-to-leading order corrections to the φφσ interaction vertex. We calculate this non-local effective vertex using the background field method [32]. In section 5.2 we calculate the σσσ three-point function at the leading order in 1/N expansion.…”

Section: Ope Coefficientsmentioning

confidence: 99%

“…In [32] it was proposed to use the background field method to calculate conformal triangles. Such a method can be applied for the purpose of determining the values of Z (0) φφσ , δZ φφσ in our case as well.…”

Section: Jhep09(2021)194mentioning

confidence: 99%

“…Such a method can be applied for the purpose of determining the values of Z (0) φφσ , δZ φφσ in our case as well. Following [32], we set the field σ to a non-dynamical background value σ ≡σ, and attach the full φ propagators to each term on both sides of (5.6). The resulting diagrammatic equation for the propagator φφ |σ in theσ background is given bȳ…”

Section: Jhep09(2021)194mentioning

confidence: 99%

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Long-range vector models at large N

Chai

Goykhman

Sinha

2021

J. High Energ. Phys.

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We calculate various CFT data for the O(N) vector model with the long-range interaction, working at the next-to-leading order in the 1/N expansion. Our results provide additional evidence for the existence of conformal symmetry at the long-range fixed point, as well as the continuity of the CFT data at the long-range to short-range crossover point s* of the exponent parameter s. We also develop the N > 1 generalization of the recently proposed IR duality between the long-range and the deformed short-range models, providing further evidence for its non-perturbative validity in the entire region d/2 < s < s*.

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“…where µ is IR mass scale [32,33]. The second contribution to σ 2 σ 2 at the next-to-leading order in 1/N is due to insertions of two cubic σ vertices into the leading order diagram:…”

Section: σ 2 σmentioning

confidence: 99%

Section: Ope Coefficientsmentioning

confidence: 99%

Section: Jhep09(2021)194mentioning

confidence: 99%

Section: Jhep09(2021)194mentioning

confidence: 99%

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Long-range vector models at large N

Chai

Goykhman

Sinha

2021

J. High Energ. Phys.

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“…perturbatively in 1/N there are no signs of pathologies, e.g., the scaling dimensions of various operators satisfy unitarity bounds [15], 2 the very presence of instability furnishes an obstacle to address the question of persistent symmetry breaking in the interacting φ 6 model.…”

Section: Jhep05(2021)192mentioning

confidence: 99%

The bi-conical vector model at 1/N

Chai

Rabinovici

Sinha

et al. 2021

J. High Energ. Phys.

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We study finite N aspects of the O(m) × O(N − m) vector model with quartic interactions in general 2 ≤ d ≤ 6 spacetime dimensions. This model has recently been shown [1, 2] to display the phenomenon of persistent symmetry breaking at a perturbative Wilson-Fisher-like fixed point in d = 4 − ϵ dimensions. The large rank limit of the biconical model displays a conformal manifold and a moduli space of vacua. We find a set of three double trace scalar operators that are respectively irrelevant, relevant and marginal deformations of the conformal manifold in general d. We calculate the anomalous dimensions of the single and multi-trace scalar operators to the first sub-leading order in the large rank expansion. The anomalous dimension of the marginal operator does not vanish in general, indicating that the conformal manifold is lifted at finite N . In the case of equal ranks we are able to derive explicitly the scaling dimensions of various operators as functions of only d.

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