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Janos Balog

Publications and source records attributed to Janos Balog.

At least 19 recordsLinked to original sources
arXiv2024

Derivation of the GKP-Witten relation by symmetry without Lagrangian

We derive the GKP-Witten relation in terms of correlation functions by symmetry without referring to a Lagrangian or the large $N$ expansion. By constructing bulk operators from boundary operators in conformal field theory (CFT) by the conformal smearing, we first determine bulk-boundary 2-pt functions for an arbitrary spin using both conformal and bulk symmetries, then evaluate their small $z$ behaviors, where $z$ is the $(d+1)$-th coordinate in the bulk. Next, we explicitly determine small $z$ behaviors of bulk-boundary-boundary 3-pt functions also by the symmetries, while small $z$ behaviors of correlation functions among one bulk and $n$ boundary operators with $n\ge 3$ are fixed by the operator product expansion (OPE). Combining all results, we construct the GKP-Witten relation in terms of these correlation functions at all orders in an external source $J$. We compare our non-Lagrangian approach with the standard approach employing the bulk action. Our results indicate that the GKP-Witten relation holds not only for holographic CFTs but also for generic CFTs as long as certain conditions are satisfied.

hep-th↗
arXiv2022

The full analytic trans-series in integrable field theories

We analyze a family of generalized energy densities in integrable quantum field theories in the presence of an external field coupled to a conserved charge. By using the Wiener-Hopf technique to solve the linear thermodynamic Bethe ansatz equations we derive the full analytic trans-series for these observables in terms of a perturbatively defined basis. We show how to calculate these basis elements to high orders analytically and reveal their complete resurgence structure. We demonstrate that the physical value of the generalized energy densities is obtained by the median resummation of their ambiguity-free trans-series.

hep-th↗
arXiv2022

Running coupling and non-perturbative corrections for O$(N)$ free energy and for disk capacitor

We reconsider the complete solution of the linear TBA equation describing the energy density of finite density states in the $O(N)$ nonlinear sigma models by the Wiener-Hopf method. We keep all perturbative and non-perturbative contributions and introduce a running coupling in terms of which all asymptotic series appearing in the problem can be represented as pure power series without logs. We work out the first non-perturbative contribution in the $O(3)$ case and show that (presumably because of the instanton corrections) resurgence theory fails in this example. Using the relation of the $O(3)$ problem to the coaxial disks capacitor problem we work out the leading non-perturbative terms for the latter and show that (at least to this order) resurgence theory, in particular the median resummation prescription, gives the correct answer. We demonstrate this by comparing the Wiener-Hopf results to the high precision numerical solution of the original integral equation.

hep-th↗
arXiv2022

Special flow equation and GKP-Witten relation

We develop a framework for the reconstruction of the bulk theory dual to conformal field theory (CFT) without any assumption by means of a flow equation. To this end we investigate a minimal extension of the free flow equation and find that at a special parametrization the conformal transformation for a normalized smeared operator exactly becomes the isometry of anti-de Sitter space (AdS). By employing this special flow equation to O$(N)$ vector models, we explicitly show that the AdS geometry as well as the scalar field satisfying the GKP-Witten relation concurrently emerge in this framework.

hep-th↗
arXiv2021

Instanton effects vs resurgence in the $O(3)$ sigma model

We investigate the ground-state energy of the integrable two dimensional $O(3)$ sigma model in a magnetic field. By determining a large number of perturbative coefficients we explore the closest singularities of the corresponding Borel function. We then confront its median resummation to the high precision numerical solution of the exact integral equation and observe that the leading exponentially suppressed contribution is not related to the asymptotics of the perturbative coefficients. By analytically expanding the integral equation we calculate the leading non-perturbative contributions up to fourth order and find complete agreement. These anomalous terms could be attributed to instantons, while the asymptotics of the perturbative coefficients seems to be related to renormalons.

hep-th↗
arXiv2019

Non-relativistic Hybrid Geometry with Gravitational Gauge-Fixing Term

We search a gravitational system which allows a non-relativistic hybrid geometry interpolating the Schr\"odinger and Lifshitz spacetimes as a solution, as a continuation of the previous work employing a flow equation. As such a candidate an Einstein-Maxwell-Higgs system naturally arises and we verify that this system indeed supports the hybrid geometry with the help of a gauge-fixing term for diffeomorphism. As a result, this gravitational system may be interpreted as a holographic dual of a general non-relativistic system at the boundary.

hep-th↗
arXiv2019

Marchenko method with incomplete data and singular nucleon scattering

We apply the Marchenko method of quantum inverse scattering to study nucleon scattering problems. Assuming a $β/r^2$ type repulsive core and comparing our results to the Reid93 phenomenological potential we estimate the constant $β$, determining the singularity strength, in various spin/isospin channels. Instead of using Bargmann type S-matrices which allows only integer singularity strength, here we consider an analytical approach based on the incomplete data method, which is suitable for fractional singularity strengths as well.

nucl-th↗
arXiv2018

Neutron-proton scattering and singular potentials

We consider a Bargmann-type rational parametrization of the nucleon scattering phase shifts. Applying Marchenko's method of quantum inverse scattering we show that the scattering data suggest a singular repulsive core of the potential of the form $2/r^2$ and $6/r^2$ in natural units, for the ${}^3S_1$ and ${}^1S_0$ channels respectively. The simplest solution in the ${}^3S_1$ channel contains three parameters only but reproduces all features of the potential and bound state wave function within one percent error. We also consider the ${}^3S_1$-${}^3D_1$ coupled channel problem with the coupled channel Marchenko inversion method.

nucl-th↗
arXiv2018

Holographic computation of quantum corrections to the bulk cosmological constant

We explore the program of the construction of the dual bulk theory in the flow equation approach. We compute the vacuum expectation value of the Einstein operator at the next to leading order in the 1/n expansion using a free O(n) vector model. We interpret the next to leading correction as the quantum correction to the cosmological constant of the AdS space. We finally comment on how to generalize this computation to matrix elements of the Einstein operator for excited states.

hep-th↗
arXiv2017

NLIE for the Sausage model

The sausage model, first proposed by Fateev, Onofri, and Zamolodchikov, is a deformation of the O(3) sigma model preserving integrability. The target space is deformed from the sphere to "sausage" shape by a deformation parameter ν. This model is defined by a factorizable S-matrix which is obtained by deforming that of the O(3) sigma model by a parameter λ. Clues for the deformed sigma model are provided by various UV and IR information through the thermodynamic Bethe ansatz (TBA) analysis based on the S-matrix. Application of TBA to the sausage model is, however, limited to the case of 1/λinteger where the coupled integral equations can be truncated to a finite number. In this paper, we propose a finite set of nonliear integral equations (NLIEs), which are applicable to generic value of λ. Our derivation is based on T-Q relations extracted from the truncated TBA equations. For consistency check, we compute next-leading order corrections of the vacuum energy and extract the S-matrix information in the IR limit. We also solved the NLIE both analytically and numerically in the UV limit to get the effective central charge and compared with that of the zero-mode dynamics to obtain exact relation between νand λ. This paper is a tribute to the memory of Prof. Petr Kulish.

hep-th↗
arXiv2016

Flow equation for the scalar model in the large $N$ expansion and its applications

We study the flow equation of the O($N$) $\varphi^4$ model in $d$ dimensions at the next-to-leading order (NLO) in the $1/N$ expansion. Using the Schwinger-Dyson equation, we derive 2-pt and 4-pt functions of flowed fields. As the first application of the NLO calculations, we study the running coupling defined from the connected 4-pt function of flowed fields in the $d+1$ dimensional theory. We show in particular that this running coupling has not only the UV fixed point but also an IR fixed point (Wilson-Fisher fixed point) in the 3 dimensional massless scalar theory. As the second application, we calculate the NLO correction to the induced metric in $d+1$ dimensions with $d=3$ in the massless limit. While the induced metric describes a 4-dimensional Euclidean Anti-de-Sitter (AdS) space at the leading order as shown in the previous paper, the NLO corrections make the space asymptotically AdS only in UV and IR limits. Remarkably, while the AdS radius does not receive a NLO correction in the UV limit, the AdS radius decreases at the NLO in the IR limit, which corresponds to the Wilson-Fisher fixed point in the original scalar model in 3 dimensions.

hep-th↗
arXiv2016

Effective potential for relativistic scattering

We consider quantum inverse scattering with singular potentials and calculate the Sine-Gordon model effective potential in the laboratory and centre-of-mass frames. The effective potentials are frame dependent but closely resemble the zero-momentum potential of the equivalent Ruijsenaars-Schneider model.

nucl-th↗
arXiv2016

Flow equation for the large $N$ scalar model and induced geometries

We study the proposal that a $d+1$ dimensional induced metric is constructed from a $d$ dimensional field theory using gradient flow. Applying the idea to the O($N$) $φ^4$ model and normalizing the flow field, we have shown in the large $N$ limit that the induced metric is finite and universal in the sense that it does not depend on the details of the flow equation and the original field theory except for the renormalized mass, which is the only relevant quantity in this limit. We have found that the induced metric describes Euclidean Anti-de-Sitter (AdS) space in both ultra-violet (UV) and infra-red (IR) limits of the flow direction, where the radius of the AdS is bigger in the IR than in the UV.

hep-th↗
arXiv2016

On the mass-coupling relation of multi-scale quantum integrable models

We determine exactly the mass-coupling relation for the simplest multi-scale quantum integrable model, the homogenous sine-Gordon model with two independent mass-scales. We first reformulate its perturbed coset CFT description in terms of the perturbation of a projected product of minimal models. This representation enables us to identify conserved tensor currents on the UV side. These UV operators are then mapped via form factor perturbation theory to operators on the IR side, which are characterized by their form factors. The relation between the UV and IR operators is given in terms of the sought-for mass-coupling relation. By generalizing the $Θ$ sum rule Ward identity we are able to derive differential equations for the mass-coupling relation, which we solve in terms of hypergeometric functions. We check these results against the data obtained by numerically solving the thermodynamic Bethe Ansatz equations, and find a complete agreement.

hep-th↗
arXiv2016

Effective potential from zero-momentum potential

We obtain the centre-of-mass frame effective potential from the zero-momentum potential in Ruijsenaars-Schneider type 1-dimensional relativistic mechanics using classical inverse scattering methods.

nucl-th↗
arXiv2015

Walking in the 3-dimensional large $N$ scalar model

The solvability of the three-dimensional O($N$) scalar field theory in the large $N$ limit makes it an ideal toy model exhibiting "walking" behavior, expected in some SU($N$) gauge theories with a large number of fermion flavors. We study the model using lattice regularization and show that when the ratio of the particle mass to an effective 4-point coupling (with dimension mass) is small, the beta function associated to the running 4-point coupling is "walking". We also study lattice artifacts and finite size effects, and find that while the former can be sizable at realistic correlation length, the latter are under control already at lattice sizes a few ($\sim$3) correlation lengths. We show the robustness of the walking phenomenon by showing that it can also be observed by studying physical observables such as the scattering phase shifts and the mass gap in finite volume.

hep-lat↗