Konishi Operator Research Articles

Five-loop Konishi from the mirror TBA

We use the Thermodynamic Bethe Ansatz equations for the AdS_5 \times S^5 mirror model to derive the five-loop anomalous dimension of the Konishi operator. We show numerically that the corresponding result perfectly agrees with the one recently obtained via the generalized Luscher formulae. This constitutes an important test of the AdS/CFT TBA system.

QUANTUM STRINGS IN AdS5 × S5 AND GAUGE–STRING DUALITY

We review some recent progress in understanding the spectrum of energies/dimensions of strings/operators in AdS5 × S5 – planar [Formula: see text] super Yang-Mills correspondence. We consider leading strong coupling corrections to the energy of lightest massive string modes in AdS5 × S5, which should be dual to members of the Konishi operator multiplet in the SYM theory. This determines the general structure of strong-coupling expansion of the anomalous dimension of the Konishi operator. We use 1-loop results for semiclassical string states to extract information about the leading coefficients in this expansion.

Quantum strings inAdS5×S5: strong-coupling corrections to dimension of Konishi operator

We consider leading strong coupling corrections to the energy of the lightest massive string modes in AdS_5 x S^5, which should be dual to members of the Konishi operator multiplet in N=4 SYM theory. This determines the general structure of the strong-coupling expansion of the anomalous dimension of the Konishi operator. We use 1-loop results for several semiclassical string states to extract information about the leading coefficients in this expansion. Our prediction is Delta= 2 lambda^{1/4} + b_0 + b_1 lambda^{-1/4} + b_3 lambda^{-3/4} +..., where b_0 and b_1 are rational while b_3 is transcendental containing zeta(3). Explicitly, we argue that b_0= Delta_0 - 4 (where Delta_0 is the canonical dimension of the corresponding gauge-theory operator in the Konishi multiplet) and b_1=1. Our conclusions are sensitive to few assumptions, implied by a correspondence with flat-space expressions, on how to translate semiclassical quantization results into predictions for the exact quantum string spectrum.

Five loop Konishi from AdS/CFT

We derive the perturbative five loop anomalous dimension of the Konishi operator in N = 4 SYM theory from the integrable string sigma model by evaluating finite size effects using Lüscher formulas adapted to multimagnon states at weak coupling. In addition, we derive the five loop wrapping contribution for the L = 2 single impurity state in the β deformed theory, which may be within reach of a direct perturbative computation. The Konishi expression exhibits two new features — a modification of Asymptotic Bethe Ansatz quantization and sensitiveness to an infinite set of coefficients of the BES/BHL dressing phase. The result satisfies nontrivial self-consistency conditions — simple transcendentality structure and cancellation of μ-term poles. It may be a testing ground for the proposed AdS/CFT TBA systems.

Wrapping at four loops in [formula omitted] SYM theory

In the papers [F. Fiamberti, A. Santambrogio, C. Sieg, and D. Zanon, Phys. Lett. B666 , 100–105 (2008); F. Fiamberti, A. Santambrogio, C. Sieg, and D. Zanon, Nucl. Phys. B805 , 231–266 (2008)] we have computed the anomalous dimension of the Konishi operator at four loops in N = 4 SYM theory in the planar limit. To compute this quantity for the first time, the wrapping interactions had to be included.

The four-loop anomalous dimension of the Konishi operator in % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBqj3BWbIqubWexLMBb50ujbqegm0B % 1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqr % Ffpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0F % irpepeKkFr0xfr-xfr-xb9adbaqaaeaacaGaaiaabeqaamaabaabaa % GcbaWefv3ySLgznfgDOfdarCqr1ngBPrginfgDObYtUvgaiuqacqWF % neVtaaa!44C0! $$ \mathcal{N} $$ = 4 Supersymmetric Yang-Mills theory

We present the result of a full direct component calculation for the planar four-loop anomalous dimension of the Konishi operator in \( \mathcal{N} \) = 4 Supersymmetric Yang-Mills theory. Our result confirms the results obtained from superfield and superstring computations, which take into account finite size corrections to the all-loop asymptotic Bethe ansatz for the integrable models describing the spectrum of the anomalous dimensions of the gaugeinvariant operators and the spectrum of the string states in the framework of the gauge/string duality.

Four-loop perturbative Konishi from strings and finite size effects for multiparticle states

We derive the perturbative four loop anomalous dimension of the Konishi operator in N = 4 SYM theory from the integrable string sigma model by evaluating the finite size effects using Lüscher formulas adapted to multimagnon states at weak coupling. We obtain these multiparticle generalizations of Lüscher formulas by studying certain exactly solvable relativistic integrable quantum field theories. The final result involves a summation of all bound states in the mirror theory and agrees with gauge theory perturbative computations.

Three‐loop test of the dilatation operator and integrability in 𝒩 = 4 SYM

AbstractWe report on a three‐loop calculation of the anomalous dimension of the Konishi operator and of the BMN operator of dimension three. Our results confirm the unique form of the 𝒩 = 4 SYM dilatation operator compatible with BMN scaling.

BMN operators and superconformal symmetry

Implications of N=4 superconformal symmetry on Berenstein–Maldacena–Nastase (BMN) operators with two charge defects are studied both at finite charge J and in the BMN limit. We find that all of these belong to a single long supermultiplet explaining a recently discovered degeneracy of anomalous dimensions on the sphere and torus. The lowest-dimensional component is an operator of naive dimension J+2 transforming in the [0, J,0] representation of SU(4). We thus find that the BMN operators are large J generalisations of the Konishi operator at J=0. We explicitly construct descendant operators by supersymmetry transformations and investigate their three-point functions using superconformal symmetry.

Anomalous currents in SCFT4

We analyse the critical behaviour of anomalous currents in N=1 four-dimensional supersymmetric gauge theories in the context of electric-magnetic duality. We show that the anomalous dimension of the Konishi superfield is related to the slope of the beta function at the critical point. We construct a duality map for the Konishi current in the minimal SQCD. As a byproduct we compute the slope of the beta function in the strong coupling regime. We note that the OPE of the stress tensor with itself does not close, but mixes with the Konishi operator. As a result in superconformal theories in four dimensions (SCFT$_4$) there are {\sl two} central charges; they allow us to count both the vector multiplet and the matter multiplet effective degrees of freedom. Some applications to N=4 SYM are discussed.