Stability Problem in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">O</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">N</mml:mi><mml:mo>)</mml:mo></mml:math>Nonlinear Sigma Model

Derkachov, S. E.; Manashov, A. N.

doi:10.1103/physrevlett.79.1423

Cited by 24 publications

(29 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We For n = 0, 1, 2 this agrees with the known anomalous dimensions for the operators [56] and (φ i φ i ) 3 [57], see (3.94). We will see in the next section that for n > 2 our result (3.90) contains averaged values with contributions of multiple operators that are degenerate at lower orders in .…”

Section: Jhep12(2020)051supporting

confidence: 85%

Operator expansions, layer susceptibility and two-point functions in BCFT

Dey

Hansen

Shpot

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

We show that in boundary CFTs, there exists a one-to-one correspondence between the boundary operator expansion of the two-point correlation function and a power series expansion of the layer susceptibility. This general property allows the direct identification of the boundary spectrum and expansion coefficients from the layer susceptibility and opens a new way for efficient calculations of two-point correlators in BCFTs. To show how it works we derive an explicit expression for the correlation function 〈ϕiϕi〉 of the O(N) model at the extraordinary transition in 4 − ϵ dimensional semi-infinite space to order O(ϵ). The bulk operator product expansion of the two-point function gives access to the spectrum of the bulk CFT. In our example, we obtain the averaged anomalous dimensions of scalar composite operators of the O(N) model to order O(ϵ2). These agree with the known results both in ϵ and large-N expansions.

show abstract

Section: Jhep12(2020)051supporting

confidence: 85%

Operator expansions, layer susceptibility and two-point functions in BCFT

Dey

Hansen

Shpot

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…(For more details see Refs. [20,21,19].) Let us consider the 1-irreducible Green function Γ(p) that depends on the one momentum p only -the inverse propagator of φ field or the vertex function with one zero momentum.…”

Section: Preliminariesmentioning

confidence: 99%

“…At the straightforward generalization beyond the 1/N order (see Refs. [21,19]) the above method lost many its attractive features. In the present paper we shall take advantage of the other approach [22] which allow to derive the simple formula for the anomalous dimensions in the 1/N 2 order.…”

Section: Introductionmentioning

confidence: 99%

A simple scheme for the calculation of the anomalous dimensions of composite operators in the 1/N expansion

Derkachov¹,

Manashov²

1998

Nuclear Physics B

View full text Add to dashboard Cite

The simple method for the calculating of the anomalous dimensions of the composite operators up to 1/N 2 order is developed. We demonstrate the effectiveness of this approach by computing the critical exponents of the (⊗ Φ) s and ( Φ⊗(⊗ ∂) n Φ) operators in the 1/N 2 order in the nonlinear sigma model. The special simplifications due to the conformal invariance of the model are discussed.

show abstract

“…An interested reader can find detailed discussions in Refs. [24,27]. Thus at the order 1/n 2 one can neglect mixing and calculate only the diagonal matrix elements.…”

Section: Correction Exponents At 1/nmentioning

confidence: 99%