arXiv subjects

J. Balog

Publications and source records attributed to J. Balog.

At least 19 recordsLinked to original sources

arXiv2026

Gravitational Memory: an approximate description

Plane gravitational waves play a role both in relativistic and in non-relativisitic physics, highlighted by two different mass parameters. The large-distance behaviour of a sandwich gravitational wave can be approximated by a continuous but not necessarily smooth profile, providing us with a simplified description of particle motion. Our model is consistent with the Carroll symmetry. Our strategy is illustrated by the Pöschl-Teller profile. The limitations of the sandwich approximation are discussed.

gr-qc↗

arXiv2025

Displacement memory for flyby

Zel'dovich and Polnarev, in their seminal paper [1] suggested that a gravitational wave generated by flyby would merely displace the particles. We confirm their prediction numerically by fine-tuning the wave profile proposed by Gibbons and Hawking [2], and then analytically for its approximation by a Pöschl-Teller potential. Higher-order derivative profiles proposed for gravitational collapse, etc [2] are shortly discussed.

gr-qc↗

arXiv2019

On the rotator Hamiltonian for the SU$(N)\times\,$SU$(N)$ sigma-model in the delta-regime

We investigate some properties of the standard rotator approximation of the SU$(N)\times\,$SU$(N)$ sigma-model in the delta-regime. In particular we show that the isospin susceptibility calculated in this framework agrees with that computed by chiral perturbation theory up to next-to-next to leading order in the limit $\ell=L_t/L\to\infty\,.$ The difference between the results involves terms vanishing like $1/\ell\,,$ plus terms vanishing exponentially with $\ell\,$. As we have previously shown for the O($n$) model, this deviation can be described by a correction to the rotator spectrum proportional to the square of the quadratic Casimir invariant. Here we confront this expectation with analytic nonperturbative results on the spectrum in 2 dimensions for $N=3\,.$

hep-th↗

arXiv2013

Short Distance Repulsion Among Baryons

We review recent investigations on the short distance behaviors of potentials among baryons, which are formulated through the Nambu-Bethe-Salpeter (NBS) wave function. After explaining the method to define the potentials, we analyze the short distance behavior of the NBS wave functions and the corresponding potentials by combining the operator product expansion and a renormalization group analysis in the perturbation theory of QCD. These analytic results are compared with numerical results obtained in lattice QCD simulations.

hep-lat↗

arXiv2012

Drastic Reduction of Cutoff Effects in 2-d Lattice O(N) Models

We investigate the cutoff effects in 2-d lattice O(N) models for a variety of lattice actions, and we identify a class of very simple actions for which the lattice artifacts are extremely small. One action agrees with the standard action, except that it constrains neighboring spins to a maximal relative angle delta. We fix delta by demanding that a particular value of the step scaling function agrees with its continuum result already on a rather coarse lattice. Remarkably, the cutoff effects of the entire step scaling function are then reduced to the per mille level. This also applies to the theta-vacuum effects of the step scaling function in the 2-d O(3) model. The cutoff effects of other physical observables including the renormalized coupling and the mass in the isotensor channel are also reduced drastically. Another choice, the mixed action, which combines the standard quadratic with an appropriately tuned large quartic term, also has extremely small cutoff effects. The size of cutoff effects is also investigated analytically in 1-d and at N = infinity in 2-d.

hep-lat↗

arXiv2008

Scaling function in AdS/CFT from the O(6) sigma model

Asymptotic behavior of the anomalous dimensions of Wilson operators with high spin and twist is governed in planar N=4 SYM theory by the scaling function which coincides at strong coupling with the energy density of a two-dimensional bosonic O(6) sigma model. We calculate this function by combining the two-loop correction to the energy density for the O(n) model with two-loop correction to the mass gap determined by the all-loop Bethe ansatz in N=4 SYM theory. The result is in agreement with the prediction coming from the thermodynamical limit of the quantum string Bethe ansatz equations, but disagrees with the two-loop stringy corrections to the folded spinning string solution.

hep-th↗

arXiv2007

Construction and clustering properties of the 2-d non-linear sigma-model form factors: O(3), O(4), large n examples

Multi-particle form factors of local operators in integrable models in two dimensions seem to have the property that they factorize when one subset of the particles in the external states are boosted by a large rapidity with respect to the others. This remarkable property, which goes under the name of form factor clustering, was first observed by Smirnov in the O(3) non-linear sigma-model and has subsequently found useful applications in integrable models without internal symmetry structure. In this paper we conjecture the nature of form factor clustering for the general O(n) sigma-model and make some tests in leading orders of the 1/n expansion and for the special cases n=3,4.

hep-th↗

arXiv2006

Does the XY Model have an integrable continuum limit?

The quantum field theory describing the massive O(2) nonlinear sigma-model is investigated through two non-perturbative constructions: The form factor bootstrap based on integrability and the lattice formulation as the XY model. The S-matrix, the spin and current two-point functions, as well as the 4-point coupling are computed and critically compared in both constructions. On the bootstrap side a new parafermionic super selection sector is found; in the lattice theory a recent prediction for the (logarithmic) decay of lattice artifacts is probed.

hep-lat↗

arXiv2006

Repairing Stevenson's step in the 4d Ising model

In a recent paper Stevenson claimed that analysis of the data on the wave function renormalization constant near the critical point of the 4d Ising model is not consistent with analytical expectations. Here we present data with improved statistics and show that the results are indeed consistent with conventional wisdom once one takes into account the uncertainty of lattice artifacts in the analytical computations.

hep-lat↗

arXiv2005

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

We propose TBA integral equations for 1-particle states in the O(n) non-linear sigma-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 Luscher's 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.

hep-th↗

arXiv2004

TBA equations for excited states in the O(3) and O(4) nonlinear $σ$-model

TBA integral equations are proposed for 1-particle states in the sausage- and SS-models and their $σ$-model limits. Combined with the ground state TBA equations the exact mass gap is computed in the O(3) and O(4) nonlinear $σ$-model and the results are compared to 3-loop perturbation theory and Monte Carlo data.

hep-th↗

arXiv2003

Comparison of analytic and numerical results in the XY-model

We study the two dimensional XY-model with high precision Monte Carlo techniques and investigate the continuum approach of the step-scaling function of its finite volume mass gap. The continuum extrapolated results are found consistent with analytic predictions for the finite volume energy spectrum based on the equivalence with sine-Gordon theory. To come to this conclusion it was essential to use an also predicted form of logarithmic decay of lattice artifacts for the extrapolation.

hep-lat↗

arXiv2003

TBA equations for excited states in the Sine-Gordon model

We propose TBA integral equations for multiparticle soliton (fermion) states in the Sine-Gordon (massive Thirring) model. This is based on T-system and Y-system equations, which follow from the Bethe Ansatz solution in the light-cone lattice formulation of the model. Even and odd charge sectors are treated on an equal footing, corresponding to periodic and twisted boundary conditions, respectively. The analytic properties of the Y-system functions are conjectured on the basis of the large volume solution of the system, which we find explicitly. A simple relation between the TBA Y-functions and the counting function variable of the alternative non-linear integral equation (Destri-deVega equation) description of the model is given.

hep-th↗

arXiv2003

Test of asymptotic freedom and scaling hypothesis in the 2d O(3) sigma model

The 7--particle form factors of the fundamental spin field of the O(3) nonlinear $σ$--model are constructed. We calculate the corresponding contribution to the spin--spin correlation function, and compare with predictions from the spectral density scaling hypothesis. The resulting approximation to the spin--spin correlation function agrees well with that computed in renormalized (asymptotically free) perturbation theory in the expected energy range. Further we observe simple lower and upper bounds for the sum of the absolute square of the form factors which may be of use for analytic estimates.

hep-th↗

arXiv2001

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.

hep-th↗

arXiv2000

The chiral WZNW phase space as a quasi-Poisson space

It is explained that the chiral WZNW phase space is a quasi-Poisson space with respect to the `canonical' Lie quasi-bialgebra which is the classical limit of Drinfeld's quasi-Hopf deformation of the universal enveloping algebra. This exemplifies the notion of quasi-Poisson-Lie symmetry introduced recently by Alekseev and Kosmann-Schwarzbach, and also permits us to generalize certain dynamical twists considered previously in this example.

hep-th↗

arXiv2000

A two-dimensional integrable axionic sigma-model and T-duality

An $S$-matrix is proposed for the two dimensional O(3) $σ$-model with a dynamical $θ$-term (axion model). Exploiting an Abelian T-duality transformation connecting the axion model to an integrable SU(2)$\times$U(1) symmetric principal $σ$-model, strong evidence is presented for the correctness of the proposed $S$-matrix by comparing the perturbatively calculated free energies with the ones based on the Thermodynamical Bethe Ansatz. This T-duality transformation also leads to a new Lax-pair for both models. The quantum non-integrability of the O(3) $σ$-model with a {\sl constant} $θ$-term, in contradistinction to the axion model, is illustrated by calculating the $2\to3$ particle production amplitude to lowest order in $θ$.

hep-th↗

arXiv2000

The Intrinsic Coupling in Integrable Quantum Field Theories

The intrinsic 4-point coupling, defined in terms of a truncated 4-point function at zero momentum, provides a well-established measure for the interaction strength of a QFT. We show that this coupling can be computed non-perturbatively and to high accuracy from the form factors of an (integrable) QFT. The technique is illustrated and tested with the Ising model, the XY-model and the O(3) nonlinear sigma-model. The results are compared to those from high precision lattice simulations.

hep-th↗