Universal anomalous dimensions at large spin and large twist

Kaviraj, Apratim; Sen, Kallol; Sinha, Aninda

doi:10.1007/jhep07(2015)026

Cited by 98 publications

(120 citation statements)

References 48 publications

(110 reference statements)

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“…The light cone limit of crossing equations has proved useful for studying the large spin asymptotics of the operator spectrum [57,58,[123][124][125][126][127][128][129][130]. Here we analyze the crossing equation (4.13) in the light cone limit.…”

Section: Appendix C: Light Cone Limitmentioning

confidence: 99%

The (2, 0) superconformal bootstrap

et al. 2016

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We develop the conformal bootstrap program for six-dimensional conformal field theories with (2, 0) supersymmetry, focusing on the universal four-point function of stress tensor multiplets. We review the solution of the superconformal Ward identities and describe the superconformal block decomposition of this correlator. We apply numerical bootstrap techniques to derive bounds on operator product expansion (OPE) coefficients and scaling dimensions from the constraints of crossing symmetry and unitarity. We also derive analytic results for the large spin spectrum using the light cone expansion of the crossing equation. Our principal result is strong evidence that the A 1 theory realizes the minimal allowed central charge (c ¼ 25) for any interacting (2, 0) theory. This implies that the full stress tensor four-point function of the A 1 theory is the unique unitary solution to the crossing symmetry equation at c ¼ 25. For this theory, we estimate the scaling dimensions of the lightest unprotected operators appearing in the stress tensor operator product expansion. We also find rigorous upper bounds for dimensions and OPE coefficients for a general interacting (2, 0) theory of central charge c. For large c, our bounds appear to be saturated by the holographic predictions obtained from eleven-dimensional supergravity.

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Section: Appendix C: Light Cone Limitmentioning

confidence: 99%

The (2, 0) superconformal bootstrap

et al. 2016

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“…, 1 around small v begins with a constant [54,60], we have τ = 2∆ φ + 2n in the spectrum. By matching the contribution of the l.h.s.…”

Section: Jhep06(2016)136mentioning

confidence: 93%

“…For more related works see [56][57][58]. While the authors have considered a special case for n = 0, the subsequent works [59,60] have extended this calculation for the n = 0 case. In these papers, it was shown that it is possible to obtain exact analytical expression for the anomalous dimension in terms of the twist (n) and also that an universal contribution of the anomalous dimension can be extracted in the limit when n 1 given by a generic form,…”

Section: Jhep06(2016)136mentioning

confidence: 99%

“…In this section we want to extract the leading n dependence of the coefficients of the anomalous dimensions for large n. In doing so we will follow [60]. γ i n can be written as, …”

Section: Jhep06(2016)136mentioning

confidence: 99%

“…Since y = m + τm 2 − 1, it can take any value. However, we can perform the summation only when y is integer or half integer using the techniques given in [60]. We can do the summation numerically for any y.…”

Section: Jhep06(2016)136mentioning

confidence: 99%

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More on analytic bootstrap for O(N) models

Dey

Kaviraj

Sen

2016

J. High Energ. Phys.

Self Cite

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This note is an extension of a recent work on the analytical bootstrapping of O(N ) models. An additonal feature of the O(N ) model is that the OPE contains trace and antisymmetric operators apart from the symmetric-traceless objects appearing in the OPE of the singlet sector. This in addition to the stress tensor (T µν ) and the φ i φ i scalar, we also have other minimal twist operators as the spin-1 current J µ and the symmetric-traceless scalar in the case of O(N ). We determine the effect of these additional objects on the anomalous dimensions of the corresponding trace, symmetric-traceless and antisymmetric operators in the large spin sector of the O(N ) model, in the limit when the spin is much larger than the twist. As an observation, we also verified that the leading order results for the large spin sector from the −expansion are an exact match with our n = 0 case. A plausible holographic setup for the special case when N = 2 is also mentioned which mimics the calculation in the CFT.

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Bootstrapping N = 2 $$ \mathcal{N}=2 $$ chiral correlators

Lemos

Liendo

2016

J. High Energ. Phys.

126

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We apply the numerical bootstrap program to chiral operators in fourdimensional N = 2 SCFTs. In the first part of this work we study four-point functions in which all fields have the same conformal dimension. We give special emphasis to bootstrapping a specific theory: the simplest Argyres-Douglas fixed point with no flavor symmetry. In the second part we generalize our setup and consider correlators of fields with unequal dimension. This is an example of a mixed correlator and allows us to probe new regions in the parameter space of N = 2 SCFTs. In particular, our results put constraints on relations in the Coulomb branch chiral ring and on the curvature of the Zamolodchikov metric.

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Universal anomalous dimensions at large spin and large twist

Cited by 98 publications

References 48 publications

The (2, 0) superconformal bootstrap

The (2, 0) superconformal bootstrap

More on analytic bootstrap for O(N) models

Bootstrapping N = 2 $$ \mathcal{N}=2 $$ chiral correlators

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