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

Nonlinear integral equations are proposed for the description of the full finite size spectrum of the 2-dimensional O(3) nonlinear sigma-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.Comment: published version, two appendices adde

Bethe Ansatz és dinamikai R-mátrixok integrálható modellekben = Bethe Ansatz and Dynamical R-matrices in integrable models

Csoporttéren, ill. Riemann szimmetrikus téren mozgó részecske hamiltoni redukciójával előállítottunk különböző fontos Calogero-Sutherland típusú integrálható részecskemodelleket. Ilyen redukált rendszerként elsőként realizáltuk a három független csatolási állandóval rendelkező BC(n) Sutherland modelleket. Csoporttéren mozgó szabad részecskék redukciójaként állítottuk elő a relativisztikus Ruijsenaars-Schneider modell racionális változatát és megmutattuk, hogy ennek a hiperbólikus Sutherland modellekkel való dualitása természetes módon adódik a hamiltoni redukció módszerével. TBA integrálegyenleteket, ill. NLIE típusú integrálegyenleteket vezettünk le integrálható térelméleti modellek véges térfogati spektrumának meghatározására többek között szuper sine-Gordon modellekre és az O(n) nemlineáris szigma modellekre n=3,4 ill. általánosan páros n esetére. Ezt a technikát alkalmaztuk az AdS/CFT korrespondenciában szerepet játszó integrálható modell véges térfogati viselkedésének vizsgálatára és a korrespondencia segítségével 5-hurok pontosságú eredményeket sikerült megadnunk a (szuper) Yang-Mills elmélet bizonyos operátorainak anomális dimenziójára. | We represent Calogero-Sutherland type integrable particle systems by Hamiltonian reduction starting from simple motion of particles on group manifolds and Riemann symmetric spaces. The family of models represented by Hamiltonian reduction includes the BC(n) type Sutherland models with three independent coupling constants. The rational version of the relativistic Ruijsenaars-Schneider model is represented as reduction of the free motion on group manifolds and it is shown that the duality between this model and the hyperbolic version of the Sutherland model easily follows from the reduction procedure. We derive TBA integral equations and NLIE integral equations for the description of the finite size spectrum of integrable models, among others for the case of the super sine-Gordon model and for the O(n) nonlinear sigma model for n = 3, 4 and in general for even n. The same techniques are used also to describe the finite volume behaviour of the integrable model that occurs on the string side of the AdS/CFT correspondence. Using the correspondence 5-loop results are presented for the anomalous dimensions of some operators in (super) Yang-Mills theory

Resurgence in the O(4) sigma model

We analyze the free energy of the integrable two dimensional O(4) sigma model in a magnetic field. We use Volin's method to extract high number (2000) of perturbative coefficients with very high precision. The factorial growth of these coefficients are regulated by switching to the Borel transform, where we perform several asymptotic analysis. High precision data allowed to identify Stokes constants and alien derivatives with exact expressions. These reveal a nice resurgence structure which enables to formulate the first few terms of the ambiguity free trans-series. We check these results against the direct numerical solution of the exact integral equation and find complete agreement.Comment: 36 pages, 5 figure

Finite volume spectrum of N=1 superminimal models perturbed by Φ13\Phi_{13}

We describe an extension of the nonlinear integral equation (NLIE) tehnique to N=1 superminimal models perturbed by $\Phi_{13}$. Along the way, we also complete our previous studies of the finite volume spectrum of the N=1 supersymmetric sine-Gordon model by considering the attractive regime and more specifically, breather states

Virial expansion and TBA in O(N) sigma models

We study the free energy of the 1+1 dimensional O(N) nonlinear sigma-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.Comment: 14 pages, LaTe