Árpád Hegedűs

Five loop Konishi from AdS/CFT

Abstract 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 Luscher 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.

AdS5×S5 mirror TBA equations from Y-system and discontinuity relations

Using the recently proposed set of discontinuity relations we translate the AdS/CFT Y-system to TBA integral equations and quantization conditions for a large subset of excited states from the

Hybrid-NLIE for the AdS/CFT spectral problem

\mathfrak{s}\mathfrak{l}(2)

Exact finite size spectrum in super sine-Gordon model

sector oftheAdS5× S5 string σ-model. Our derivation provides an analytic proof of the fact that the exact Bethe equations reduce to the Beisert-Staudacher equations in the asymptotic limit. We also construct the corresponding T-system and show that in the language of T-functions the energy formula reduces to a single term which depends on a single T-function.

TBA equations for the mass gap in the O(2r) non-linear σ-models

A bstractHybrid-NLIE equations, an alternative finite NLIE description for the spectral problem of the super sigma model of AdS/CFT and its γ-deformations are derived by replacing the semi-infinite SU(2) and SU(4) parts of the AdS/CFT TBA equations by a few appropriately chosen complex NLIE variables, which are coupled among themselves and to the Y-functions associated to the remaining central nodes of the TBA diagram. The integral equations are written explicitly for the ground state of the γ-deformed system. We linearize these NLIE equations, analytically calculate the first correction to the asymptotic solution and find agreement with analogous results coming from the original TBA formalism. Our equations differ substantially from the recently published finite FiNLIE formulation of the spectral problem.

The finite size spectrum of the 2-dimensional O(3) nonlinear σ-model

Abstract We present the coupled nonlinear integral equations (NLIE) governing the finite size effects in N = 1 super sine-Gordon model for the vacuum as well as for the excited states. Their infrared limit correctly yields the scattering data of the super sine-Gordon S-matrix conjectured by Ahn [C. Ahn, Nucl. Phys. B 354 (1991) 57–84]. Ultraviolet analysis is in agreement with the expected conformal data of c = 3 / 2 CFT. Conformal perturbation theory further corroborates this result.

Virial expansion and TBA in O (N) sigma-models

Abstract We propose TBA integral equations for 1-particle states in the O ( n ) non-linear σ-model for even n. The equations are conjectured on the basis of the analytic properties of the large volume asymptotics of the problem, which is explicitly constructed starting from Luschers asymptotic formula. For small volumes the mass gap values computed numerically from the TBA equations agree very well with results of three-loop perturbation theory calculations, providing support for the validity of the proposed TBA system.

Strong coupling results in the AdS 5 /CF T 4 correspondence from the numerical solution of the quantum spectral curve

Abstract Nonlinear integral equations are proposed for the description of the full finite size spectrum of the 2-dimensional O ( 3 ) nonlinear σ -model in a periodic box. Numerical results for the energy eigenvalues are compared to the rotator spectrum and perturbation theory for small volumes and with the recently proposed generalized Luscher formulas at large volumes.

Quasi-local formulation of the mirror TBA

Abstract We study the free energy of the (1+1)-dimensional O ( N ) nonlinear σ -models for even N using the TBA equations proposed recently. We give explicit formulae for the constant solution of the TBA equations (Y-system) and calculate the first two virial coefficients. The free energy is also compared to the leading large N result.

Finite-size effects in the SS-model: Two component nonlinear integral equations

A bstractIn this paper, we solved numerically the Quantum Spectral Curve (QSC) equations corresponding to some twist-2 single trace operators with even spin from the sl(2) sector of AdS5/CFT4 correspondence. We describe all technical details of the numerical method which are necessary to implement it in C++ language.In the S = 2, 4, 6, 8 cases, our numerical results confirm the analytical results, known in the literature for the first 4 coefficients of the strong coupling expansion for the anomalous dimensions of twist-2 operators. In the case of the Konishi operator, due to the high precision of the numerical data we could give numerical predictions to the values of two further coefficients, as well.The strong coupling behaviour of the coefficients ca,n in the power series representation of the Pa-functions is also investigated. Based on our numerical data, in the regime, where the index of the coefficients is much smaller than λ1/4, we conjecture that the coefficients have polynomial index dependence at strong coupling. This allows one to propose a strong coupling series representation for the P-functions being valid far enough from the real short cut. In the paper the qualitative strong coupling behaviour of the P-functions at the branch points is also discussed.