arXiv subjects

Roberto Tateo

Publications and source records attributed to Roberto Tateo.

At least 37 records · Page 2Linked to original sources

arXiv2021

$\text{T}\bar{\text{T}}$-deformed Nonlinear Schrödinger

The $\text{T}\bar{\text{T}}$-deformed classical Lagrangian of a 2D Lorentz invariant theory can be derived from the original one, perturbed only at first order by the bare $\text{T}\bar{\text{T}}$ composite field, through a field-dependent change of coordinates. Considering, as an example, the nonlinear Schrödinger (NLS) model with generic potential, we apply this idea to non-relativistic models. The form of the deformed Lagrangian contains a square-root and is similar but different from that for relativistic bosons. We study the deformed bright, grey and Peregrine's soliton solutions. Contrary to naive expectations, the $\text{T}\bar{\text{T}}$-perturbation of nonlinear Schrödinger NLS with quartic potential does not trivially emerge from a standard non-relativistic limit of the deformed sinh-Gordon field theory. The $c \rightarrow \infty$ outcome corresponds to a different type of irrelevant deformation. We derive the corresponding Poisson bracket structure, the equations of motion and discuss various interesting aspects of this alternative type of perturbation, including links with the recent literature.

hep-th↗

arXiv2021

Geometry of random potentials: Induction of 2D gravity in Quantum Hall plateau transitions

In the context of the Integer Quantum Hall plateau transitions, we formulate a specific map from random landscape potentials onto 2D discrete random surfaces. Critical points of the potential, namely maxima, minima and saddle points uniquely define a discrete surface $S$ and its dual $S^*$ made of quadrangular and $n-$gonal faces, respectively, thereby linking the geometry of the potential with the geometry of discrete surfaces. The map is parameter-dependent on the Fermi level. Edge states of Fermi lakes moving along equipotential contours between neighbour saddle points form a network of scatterings, which define the geometric basis, in the fermionic model, for the plateau transitions. The replacement probability characterizing the network model with geometric disorder recently proposed by Gruzberg, Klümper, Nuding and Sedrakyan, is physically interpreted within the current framework as a parameter connected with the Fermi level.

cond-mat.dis-nn↗

arXiv2020

Geometric aspects of the ODE/IM correspondence

This review describes a link between Lax operators, embedded surfaces and Thermodynamic Bethe Ansatz equations for integrable quantum field theories. This surprising connection between classical and quantum models is undoubtedly one of the most striking discoveries that emerged from the off-critical generalisation of the ODE/IM correspondence, which initially involved only conformal invariant quantum field theories. We will mainly focus of the KdV and sinh-Gordon models. However, various aspects of other interesting systems, such as affine Toda field theories and non-linear sigma models, will be mentioned. We also discuss the implications of these ideas in the AdS/CFT context, involving minimal surfaces and Wilson loops. This work is a follow-up of the ODE/IM review published more than ten years ago by JPA, before the discovery of its off-critical generalisation and the corresponding geometrical interpretation. (Partially based on lectures given at the Young Researchers Integrability School 2017, in Dublin.)

hep-th↗

arXiv2019

Conserved currents and $\text{T}\bar{\text{T}}_s$ irrelevant deformations of 2D integrable field theories

It has been recently discovered that the $\text{T}\bar{\text{T}}$ deformation is closely-related to Jackiw-Teitelboim gravity. At classical level, the introduction of this perturbation induces an interaction between the stress-energy tensor and space-time and the deformed EoMs can be mapped, through a field-dependent change of coordinates, onto the corresponding undeformed ones. The effect of this perturbation on the quantum spectrum is non-perturbatively described by an inhomogeneous Burgers equation. In this paper, we point out that there exist infinite families of models where the geometry couples instead to generic combinations of local conserved currents labelled by the Lorentz spin. In spirit, these generalisations are similar to the $\text{J}\bar{\text{T}}$ model as the resulting theories and the corresponding scattering phase factors are not Lorentz invariant. The link with the $\text{J}\bar{\text{T}}$ model is discussed in detail. While the classical setup described here is very general, we shall use the sine-Gordon model and its CFT limit as explanatory quantum examples. Most of the final equations and considerations are, however, of broader validity or easily generalisable to more complicated systems.

hep-th↗

arXiv2019

The $\textrm{T}\bar{\textrm{T}}$ perturbation and its geometric interpretation

Starting from the recently-discovered $\textrm{T}\bar{\textrm{T}}$-perturbed Lagrangians, we prove that the deformed solutions to the classical EoMs for bosonic field theories are equivalent to the unperturbed ones but for a specific field-dependent local change of coordinates. This surprising geometric outcome is fully consistent with the identification of $\textrm{T}\bar{\textrm{T}}$-deformed 2D quantum field theories as topological JT gravity coupled to generic matter fields. Although our conclusion is valid for generic interacting potentials, it first emerged from a detailed study of the sine-Gordon model and in particular from the fact that solitonic pseudo-spherical surfaces embedded in $\mathbb R^3$ are left invariant by the deformation. Analytic and numerical results concerning the perturbation of specific sine-Gordon soliton solutions are presented.

hep-th↗

arXiv2018

Generalised Born-Infeld models, Lax operators and the $\textrm{T} \bar{\textrm{T}}$ perturbation

Surprising links between the deformation of 2D quantum field theories induced by the composite $\textrm{T} \bar{\textrm{T}}$ operator, effective string models and the $AdS/$CFT correspondence, have recently emerged. The purpose of this article is to discuss various classical aspects related to the deformation of 2D interacting field theories. Special attention is given to the sin(h)-Gordon model, for which we were able to construct the $\textrm{T} \bar{\textrm{T}}$-deformed Lax pair. We consider the Lax pair formulation to be the first essential step toward a more satisfactory geometrical interpretation of this deformation within the integrable model framework. Furthermore, it is shown that the 4D Maxwell-Born-Infeld theory, possibly with the addition of a mass term or a derivative-independent potential, corresponds to a natural extension of the 2D examples. Finally, we briefly comment on 2D Yang-Mills theory and propose a modification of the heat kernel, for a generic surface with genus $p$ and $n$ boundaries, which fully accounts for the $\textrm{T} \bar{\textrm{T}}$ contribution.

hep-th↗

arXiv2018

Exploring the spectrum of planar $AdS_4/CFT_3$ at finite coupling

The Quantum Spectral Curve (QSC) equations for planar $\mathcal{N}=6$ super-conformal Chern-Simons (SCS) are solved numerically at finite values of the coupling constant for states in the $\mathfrak{sl}(2|1)$ sector. New weak coupling results for conformal dimensions of operators outside the $\mathfrak{sl}(2)$-like sector are obtained by adapting a recently proposed algorithm for the QSC perturbative solution. Besides being interesting in their own right, these perturbative results are necessary initial inputs for the numerical algorithm to converge on the correct solution. The non-perturbative numerical outcomes nicely interpolate between the weak coupling and the known semiclassical expansions, and novel strong coupling exact results are deduced from the numerics. Finally, the existence of contour crossing singularities in the TBA equations for the operator $\textbf{20}$ is ruled out by our analysis. The results of this paper are an important test of the QSC formalism for this model, open the way to new quantitative studies and provide further evidence in favour of the conjectured weak/strong coupling duality between $\mathcal{N}=6$ SCS and type IIA superstring theory on $AdS_4 \times CP^3$. Attached to the arXiv submission, a Mathematica implementation of the numerical method and ancillary files containing the numerical results are provided.

hep-th↗

arXiv2018

The full Quantum Spectral Curve for $AdS_4/CFT_3$

The spectrum of planar N=6 superconformal Chern-Simons theory, dual to type IIA superstring theory on $AdS_4 \times CP^3$, is accessible at finite coupling using integrability. Starting from the results of [arXiv:1403.1859], we study in depth the basic integrability structure underlying the spectral problem, the Quantum Spectral Curve. The new results presented in this paper open the way to the quantitative study of the spectrum for arbitrary operators at finite coupling. Besides, we show that the Quantum Spectral Curve is embedded into a novel kind of Q-system, which reflects the OSp(4|6) symmetry of the theory and leads to exact Bethe Ansatz equations. The discovery of this algebraic structure, more intricate than the one appearing in the $AdS_5/CFT_4$ case, could be a first step towards the extension of the method to $AdS_3/CFT_2$.

hep-th↗

arXiv2016

$T \bar{T}$-deformed 2D Quantum Field Theories

It was noticed many years ago, in the framework of massless RG flows, that the irrelevant composite operator $T \bar{T}$, built with the components of the energy-momentum tensor, enjoys very special properties in 2D quantum field theories, and can be regarded as a peculiar kind of integrable perturbation. Novel interesting features of this operator have recently emerged from the study of effective string theory models.In this paper we study further properties of this distinguished perturbation. We discuss how it affects the energy levels and one-point functions of a general 2D QFT in finite volume through a surprising relation with a simple hydrodynamic equation. In the case of the perturbation of CFTs, adapting a result by Lüscher and Weisz we give a compact expression for the partition function on a finite-length cylinder and make a connection with the exact $g$-function method. We argue that, at the classical level, the deformation naturally maps the action of $N$ massless free bosons into the Nambu-Goto action in static gauge, in $N+2$ target space dimensions, and we briefly discuss a possible interpretation of this result in the context of effective string models.

hep-th↗

arXiv2015

12 loops and triple wrapping in ABJM theory from integrability

Adapting a method recently proposed by C. Marboe and D. Volin for ${\cal N}$=4 super-Yang-Mills, we develop an algorithm for a systematic weak coupling expansion of the spectrum of anomalous dimensions in the $sl(2)$-like sector of planar $\mathcal{N}$=6 super-Chern-Simons. The method relies on the Quantum Spectral Curve formulation of the problem and the expansion is written in terms of the interpolating function $h(λ)$, with coefficients expressible as combinations of Euler-Zagier sums with alternating signs. We present explicit results up to 12 loops (six nontrivial orders) for various twist L=1 and L=2 operators, corresponding to triple and double wrapping terms, respectively, which are beyond the reach of the Asymptotic Bethe Ansatz as well as Lüscher's corrections. The algorithm works for generic values of L and S and in principle can be used to compute arbitrary orders of the weak coupling expansion. For the simplest operator with L=1 and spin S=1, the Padé extrapolation of the 12-loop result nicely agrees with the available Thermodynamic Bethe Ansatz data in a relatively wide range of values of the coupling. A Mathematica notebook with a selection of results is attached.

hep-th↗

arXiv2015

A Riemann-Hilbert formulation for the finite temperature Hubbard model

Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are equivalent to a simple nonlinear Riemann-Hilbert problem for a finite number of unknown functions. The latter can be transformed into a set of three coupled nonlinear integral equations defined over a finite support, which can be easily solved numerically. We discuss the emergence of an exact Bethe Ansatz and the link between the TBA approach and the results by Jüttner, Klümper and Suzuki based on the Quantum Transfer Matrix method. We also comment on the analytic continuation mechanism leading to excited states and on the mirror equations describing the finite-size Hubbard model with twisted boundary conditions.

hep-th↗

arXiv2014

The Quantum Spectral Curve of the ABJM theory

Recently, it was shown that the spectrum of anomalous dimensions and other important observables in N = 4 SYM are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ-system or Quantum Spectral Curve. In this letter we present the Pμ-system for the spectrum of the ABJM theory. This may be an important step towards the exact determination of the interpolating function h(λ) characterising the integrability of the ABJM model. We also discuss a surprising symmetry between the Pμ-system equations for N = 4 SYM and ABJM.

hep-th↗

arXiv2014

Recent progress in the effective string theory description of LGTs

In presence of a static pair of sources, the spectrum of low-lying states of any confining gauge theory in D space-time dimensions is described, at large source separations, by an effective string theory. Recently two important advances improved our understanding of this effective theory. First, it was realized that the form of the effective action is strongly constrained by the requirement of the Lorentz invariance of the gauge theory, which is spontaneously broken by the formation of a long confining flux tube in the vacuum. This constraint is strong enough to fix uniquely the first few subleading terms of the action. Second, it has been realized that the first of these allowed terms - a quartic polynomial in the field derivatives - is exactly the composite field $T\bar{T}$, built with the chiral components, $T$ and $\bar{T}$, of the energy-momentum tensor of the 2d QFT describing the infrared limit of the effective string. This irrelevant perturbation is quantum integrable and yields, through the thermodynamic Bethe Ansatz (TBA), the energy levels of the string which exactly coincide with the Nambu-Goto spectrum. In this talk we first review the general implications of these two results and then, as a test of the power of these methods, use them to construct the first few boundary corrections to the effective string action.

hep-lat↗

arXiv2013

Exact results for the low energy AdS(4)XCP(3) string theory

We derive the Thermodynamic Bethe Ansatz equations for the relativistic sigma model describing the AdS(4)XCP(3) string II A theory at strong coupling (i.e. in the Alday-Maldacena decoupling limit). The corresponding Y-system involves an infinite number of Y functions and is of a new type, although it shares a peculiar feature with the Y-system for AdS(4)XCP(3). A truncation of the equations at level p and a further generalisation to generic rank N allow us an alternative description of the theory as the N=4, p= \infty representative in an infinite family of models corresponding to the conformal cosets CP(N-1)_p X U(1), perturbed by a relevant composite field ϕ(N,p) =ϕ_[CP(N-1)_p] X ϕ[U(1)] that couples the two independent conformal field theories. The calculation of the ultraviolet central charge confirms the conjecture by Basso and Rej and the conformal dimension of the perturbing operator, at every N and p, is obtained using the Y-system periodicity. The conformal dimension of ϕ[CP(N-1)_p] matches that of the field identified by Fendley while discussing integrability issues for the purely bosonic CP(N-1) sigma model.

hep-th↗

arXiv2013

Discontinuity relations for the AdS(4)/CFT(3) correspondence

We study in detail the analytic properties of the Thermodynamic Bethe Ansatz (TBA) equations for the anomalous dimensions of composite operators in the planar limit of the 3D N=6 superconformal Chern-Simons gauge theory and derive functional relations for the jump discontinuities across the branch cuts in the complex rapidity plane. These relations encode the analytic structure of the Y functions and are extremely similar to the ones obtained for the previously-studied AdS(5)/CFT(4) case. Together with the Y-system and more basic analyticity conditions, they are completely equivalent to the TBA equations. We expect these results to be useful to derive alternative nonlinear integral equations for the AdS(4)/CFT(3) spectrum.

hep-th↗

arXiv2013

Quantisation of the effective string with TBA

In presence of a static pair of sources, the spectrum of low-lying states of whatever confining gauge theory in D space-time dimensions is described, at large source separations, by an effective string theory. In the far infrared the latter flows, in the static gauge, to a two-dimensional massless free-field theory. It is known that the Lorentz invariance of the gauge theory fixes uniquely the first few subleading corrections of this free-field limit. We point out that the first allowed correction - a quartic polynomial in the field derivatives - is exactly the composite field $T\bar{T}$, built with the chiral components, $T$ and $\bar{T}$, of the energy-momentum tensor. This irrelevant perturbation is quantum integrable and yields, through the thermodynamic Bethe Ansatz (TBA),the energy levels of the string which exactly coincide with the Nambu-Goto spectrum. We obtain this way the results recently found by Dubovsky, Flauger and Gorbenko. This procedure easily generalizes to any two-dimensional CFT. It is known that the leading deviation of the Nambu-Goto spectrum comes from the boundary terms of the string action. We solve the TBA equations on an infinite strip, identify the relevant boundary parameter and verify that it modifies the string spectrum as expected.

hep-th↗

arXiv2012

The Bethe Ansatz and the Tzitzéica-Bullough-Dodd equation

The theory of classically integrable nonlinear wave equations, and the Bethe Ansatz systems describing massive quantum field theories defined on an infinite cylinder, are related by an important mathematical correspondence that still lacks a satisfactory physical interpretation. In this paper we shall describe this link for the case of the classical and quantum versions of the (Tzitzéica-)Bullough-Dodd model.

math-ph↗

arXiv2012

Quasi-exact solvability, resonances and trivial monodromy in ordinary differential equations

A correspondence between the sextic anharmonic oscillator and a pair of third-order ordinary differential equations is used to investigate the phenomenon of quasi-exact solvability for eigenvalue problems involving differential operators with order greater than two. In particular, links with Bender-Dunne polynomials and resonances between independent solutions are observed for certain second-order cases, and extended to the higher-order problems.

math-ph↗