Leading exponential finite size corrections for non-diagonal form factors

Abstract We derive the leading exponential finite volume corrections in two dimensional integrable models for non-diagonal form factors in diagonally scattering theories. These formulas are expressed in terms of the infinite volume form factors and scattering matrices. If the particles are bound states then the leading exponential finite-size corrections (μ-terms) are related to virtual processes in which the particles disintegrate into their constituents. For non-bound state particles the leading exponential finite-size corrections (F-terms) come from virtual particles traveling around the finite world. In these F-terms a specifically regulated infinite volume form factor is integrated for the momenta of the virtual particles. The F-term is also present for bound states and the μ-term can be obtained by taking an appropriate residue of the F-term integral. We check our results numerically in the Lee-Yang and sinh-Gordon models based on newly developed Hamiltonian truncations.</jats:p

NLIE of Dirichlet sine-Gordon Model for Boundary Bound States

We investigate boundary bound states of sine-Gordon model on the finite-size strip with Dirichlet boundary conditions. For the purpose we derive the nonlinear integral equation (NLIE) for the boundary excited states from the Bethe ansatz equation of the inhomogeneous XXZ spin 1/2 chain with boundary imaginary roots discovered by Saleur and Skorik. Taking a large volume (IR) limit we calculate boundary energies, boundary reflection factors and boundary Luscher corrections and compare with the excited boundary states of the Dirichlet sine-Gordon model first considered by Dorey and Mattsson. We also consider the short distance limit and relate the IR scattering data with that of the UV conformal field theory.Comment: LaTeX, 21 pages with 10 eps figure

Truncated Hilbert space approach to the 2d ϕ 4 theory

We apply the massive analogue of the truncated conformal space approach to study the two dimensional φ4 theory in finite volume. We focus on the broken phase and determine the finite size spectrum of the model numerically. We interpret the results in terms of the Bethe- Yang spectrum, from which we extract the infinite volume masses and scattering matrices for various couplings. We compare these results against semiclassical analysis and perturbation theory. We also analyze the critical point of the model and confirm that it is in the Ising universality class

Six and seven loop Konishi from Luscher corrections

In the present paper we derive six and seven loop formulas for the anomalous dimension of the Konishi operator in N=4 SYM from string theory using the technique of Luscher corrections. We derive analytically the integrand using the worldsheet S-matrix and evaluate the resulting integral and infinite sum using a combination of high precision numerical integration and asymptotic expansion. We use this high precision numerical result to fit the integer coefficients of zeta values in the final analytical answer. The presented six and seven loop results can be used as a cross-check with FiNLIE on the string theory side, or with direct gauge theory computations. The seven loop level is the theoretical limit of this Luscher approach as at eight loops double-wrapping corrections will appear.Comment: 18 pages, typos correcte

Form factors in the presence of integrable defects

Form factor axioms are derived in two dimensional integrable defect theories for matrix elements of operators localized both in the bulk and on the defect. The form factors of bulk operators are expressed in terms of the bulk form factors and the transmission factor. The structure of the form factors of defect operators is established in general, and explicitly calculated in particular, for the free boson and for some operator of the Lee-Yang model. Fusion method is also presented to generate boundary form factor solutions for a fused boundary from the known unfused ones.Comment: 21 pages, 13 eps figure

Kétdimenziós kvantumtérelméletek nemperturbativ vizsgálata = Nonperturbative investigations of 2 dimensional quantum field theories

Kutatómunkánk legfontosabb eredményei I. Az integrálhatóság kiaknázásával sikerült számos, a planáris limeszen túlmenő effektust kiszámolnunk a tiz dimenziós typeIIB hurelmélet és a négy dimenziós N=4 szuperszimmetrikus Yang Mills elmélet ekvivalenciáját állitó AdS/CFT dualitás igazolására. E megfontolásokat kiterjesztettük a nyilt húrokat leiró peremes esetre is. II. Az elsők között tanulmányoztuk az integrálható peremes elméletek fromfaktorait (lokális operátorok sokrészecske mátrixelemei). Nagyon gondosan kianalizáltuk a formfaktorok véges térfogatbeli viselkedését mind a bulk mind a peremes esetekben. E vizsgálatok elvezettek a rezonanciák, valamint néhány fizikailag érdekes véges hőmérsékletű mennyiség (korrelátorok, várható értékek stb.) újfajta leirásához. III. A Casimir effektust sikerült egy peremes jelenségként leirni, és ezt a nézőpontot használva leirni a peremállapotokat. IV. Az integrálhatóságot és a TCSA-t kombinálva sikeresen leirtunk néhány, érdekes konform térelméleteket összekötő, peremes renormcsoport folyamot. V. Kiterjesztettük az NLIE-t és a TBA-t néhány érdekes peremes probléma tárgyalására (peremes sinh-Gordon modell, peremes kötött állapotok a Dirichlet sine-Gordon modellben). | The highlights of our research activity are I. In the AdS/CFT duality -which states the equivalence between a ten dimensional typeIIB string and N=4 supersymmetric Yang Mills in four dimensions - we computed several effects beyond the planar limit by exploiting integrability. We also extended these considerations to the boundary case. II. We were among the first ones to study form factors (multi-particle matrix elements of local operators) in integrable boundary theories. We investigated thoroughly the finite volume effects on form factors both in the bulk and in the boundary setting. These studies lead to a new description of resonances and some physically interesting finite temperature quantities (correlators, expectation values of boundary operators etc.). III. We described the Casimir effect as a boundary phenomena thus giving a new angle on the effect and used this viewpoint to deal with the boundary states. IV. By combining integrability and TCSA we described several boundary renormalization group flows connecting various conformal field theories. V. We extended the use of NLIE and TBA to some interesting boundary problems like the boundary sinh-Gordon model or the boundary bound states of the Dirichlet sine-Gordon model