arXiv subjects
Publications and source records attributed to G. Takacs.
Multi-soliton form factors in sine-Gordon theory from the bootstrap are compared to finite volume matrix elements computed using the truncated conformal space approach. We find convincing agreement, and resolve most of the issues raised in a previous work.
Using the reduced WZNW formulation we analyse the classical $W$ orbit content of the space of classical solutions of the $A_2$ Toda theory. We define the quantized Toda field as a periodic primary field of the $W$ algebra satisfying the quantized equations of motion. We show that this local operator can be constructed consistently only in a Hilbert space consisting of the representations corresponding to the minimal models of the $W$ algebra.
The standard numerical approach to determining matrix elements of local operators and width of resonances uses the finite volume dependence of energy levels and matrix elements. Finite size corrections that decay exponentially in the volume are usually neglected or taken into account using perturbation expansion in effective field theory. Using two-dimensional sine-Gordon field theory as "toy model" it is shown that some exponential finite size effects could be much larger than previously thought, potentially spoiling the determination of matrix elements in frameworks such as lattice QCD. The particular class of finite size corrections considered here are mu-terms arising from bound state poles in the scattering amplitudes. In sine-Gordon model, these can be explicitly evaluated and shown to explain the observed discrepancies to high precision. It is argued that the effects observed are not special to the two-dimensional setting, but rather depend on general field theoretic features that are common with models relevant for particle physics. It is important to understand these finite size corrections as they present a potentially dangerous source of systematic errors for the determination of matrix elements and resonance widths.
We compare form factors in sine-Gordon theory, obtained via the bootstrap, to finite volume matrix elements computed using the truncated conformal space approach. For breather form factors, this is essentially a straightforward application of a previously developed formalism that describes the volume dependence of operator matrix elements up to corrections exponentially decaying with the volume. In the case of solitons, it is necessary to generalize the formalism to include effects of non-diagonal scattering. In some cases it is also necessary to take into account some of the exponential corrections (so-called mu-terms) to get agreement with the numerical data. For almost all matrix elements the comparison is a success, with the puzzling exception of some breather matrix elements that contain disconnected pieces. We also give a short discussion of the implications of the observed behaviour of mu-terms on the determination of operator matrix elements from finite volume data, as occurs e.g. in the context of lattice field theory.
A previously conjectured set of exact form factors of boundary exponential operators in the sinh-Gordon model is tested against numerical results from boundary truncated conformal space approach in boundary sine-Gordon theory, related by analytic continuation to sinh-Gordon model. We find that the numerical data strongly support the validity of the form factors themselves; however, we also report a discrepancy in the case of diagonal matrix elements, which remains unresolved for the time being.
We consider finite temperature correlation functions in massive integrable Quantum Field Theory. Using a regularization by putting the system in finite volume, we develop a novel approach (based on multi-dimensional residues) to the form factor expansion for thermal correlators. The first few terms are obtained explicitly in theories with diagonal scattering. We also discuss the validity of the LeClair-Mussardo proposal.
Using a regularization by putting the system in finite volume, we develop a novel approach to form factor perturbation theory for nonintegrable models described as perturbations of integrable ones. This permits to go beyond first order in form factor perturbation theory and in principle works to any order. The procedure is carried out in detail for double sine-Gordon theory, where the vacuum energy density and breather mass correction is evaluated at second order. The results agree with those obtained from the truncated conformal space approach. The regularization procedure can also be used to compute other spectral sums involving disconnected pieces of form factors such as those that occur e.g. in finite temperature correlators.
We analyze the evolution of the effective potential and the particle spectrum of two-parameter families of non-integrable quantum field theories. These theories are defined by deformations of conformal minimal models M_m by using the operators Phi_{1,3}, Phi_{1,2} and Phi_{2,1}. This study extends to all minimal models the analysis previously done for the classes of universality of the Ising, the Tricritical Ising and the RSOS models. We establish the symmetry and the duality properties of the various models also identifying the limiting theories that emerge when m goes to infinity.
A conjecture is presented for the thermal one-point function of boundary operators in integrable boundary quantum field theories in terms of form factors. It is expected to have applications in studying boundary critical phenomena and boundary flows, which are relevant in the context of condensed matter and string theory. The conjectured formula is verified by a low-temperature expansion developed using finite size techniques, which can also be used to evaluate higher point functions both in the bulk and on the boundary.
We describe the volume dependence of matrix elements of local boundary fields to all orders in inverse powers of the volume. Using the scaling boundary Lee-Yang model as testing ground, we compare the matrix elements extracted from boundary truncated conformal space approach to exact form factors obtained using the bootstrap method. We obtain solid confirmation for the boundary form factor bootstrap, which is different from all previously available tests in that it is a non-perturbative and direct comparison of exact form factors to multi-particle matrix elements of local operators, computed from the Hamiltonian formulation of the quantum field theory.
Casimir effect in the planar setting is described using the boundary state formalism, for general partially reflecting boundaries. It is expressed in terms of the low-energy degrees of freedom, which provides a large distance expansion valid for general interacting field theories provided there is a non-vanishing mass gap. The expansion is written in terms of the scattering amplitudes, and needs no ultraviolet renormalization. We also discuss the case when the quantum field has a nontrivial vacuum configuration.
Using the recently introduced boundary form factor bootstrap equations, the form factors of boundary exponential operators in the sinh-Gordon model are constructed. The ultraviolet scaling dimension and the normalization of these operators are checked against previously known results. The construction presented in this paper can be applied to determine form factors of relevant primary boundary operators in general integrable boundary quantum field theories.
We describe the volume dependence of matrix elements of local fields to all orders in inverse powers of the volume (i.e. only neglecting contributions that decay exponentially with volume). Using the scaling Lee-Yang model and the Ising model in a magnetic field as testing ground, we compare them to matrix elements extracted in finite volume using truncated conformal space approach to exact form factors obtained using the bootstrap method. We obtain solid confirmation for the form factor bootstrap, which is different from all previously available tests in that it is a non-perturbative and direct comparison of exact form factors to multi-particle matrix elements of local operators, computed from the Hamiltonian formulation of the quantum field theory. We also demonstrate that combining form factor bootstrap and truncated conformal space is an effective method for evaluating finite volume form factors in integrable field theories over the whole range in volume.
Continuing the investigation started in a previous work, we consider form factors of integrable quantum field theories in finite volume, extending our investigation to matrix elements with disconnected pieces. Numerical verification of our results is provided by truncated conformal space approach. Such matrix elements are important in computing finite temperature correlation functions, and we give a new method for generating a low temperature expansion, which we test for the one-point function up to third order.
Using the recently introduced boundary form factor bootstrap equations, we map the complete space of their solutions for the boundary version of the scaling Lee-Yang model and sinh-Gordon theory. We show that the complete space of solutions, graded by the ultraviolet behaviour of the form factors can be brought into correspondence with the spectrum of local boundary operators expected from boundary conformal field theory, which is a major evidence for the correctness of the boundary form factor bootstrap framework.
We consider quantum field theories with boundary on a codimension one hyperplane. Using 1+1 dimensional examples, we clarify the relation between three parameters characterising one-point functions, finite size corrections to the ground state energy and the singularity structure of scattering amplitudes, respectively. We then develop the formalism of boundary states in general D+1 spacetime dimensions and relate the cluster expansion of the boundary state to the correlation functions using reduction formulae. This allows us to derive the cluster expansion in terms of the boundary scattering amplitudes, and to give a derivation of the conjectured relations between the parameters in 1+1 dimensions, and their generalization to D+1 dimensions. We use these results to express the large volume asymptotics of the Casimir effect in terms of the one-point functions or alternatively the singularity structure of the one-particle reflection factor, and for the case of vanishing one-particle couplings we give a complete proof of our previous result for the leading behaviour.
Boundary form factor axioms are derived for the matrix elements of local boundary operators in integrable 1+1 dimensional boundary quantum field theories using the analyticity properties of correlators via the boundary reduction formula. Minimal solutions are determined for the integrable boundary perturbations of the free boson, free fermion (Ising), Lee-Yang and sinh-Gordon models and the two point functions calculated from them are checked against the exact solutions in the free cases and against the conformal data in the ultraviolet limit for the Lee-Yang model. In the case of the free boson/fermion the dimension of the solution space of the boundary form factor equation is shown to match the number of independent local operators. We obtain excellent agreement which proves not only the correctness of the solutions but also confirms the form factor axioms.
We develop methods to extract resonance widths from finite volume spectra of 1+1 dimensional quantum field theories. Our two methods are based on Luscher's description of finite size corrections, and are dubbed the Breit-Wigner and the improved "mini-Hamiltonian" method, respectively. We establish a consistent framework for the finite volume description of sufficiently narrow resonances that takes into account the finite size corrections and mass shifts properly. Using predictions from form factor perturbation theory, we test the two methods against finite size data from truncated conformal space approach, and find excellent agreement which confirms both the theoretical framework and the numerical validity of the methods. Although our investigation is carried out in 1+1 dimensions, the extension to physical (3+1) space-time dimensions appears straightforward, given sufficiently accurate finite volume spectra.