# Axel Cortes CuberoProtocol Labs · CryptoEconLab

Axel Cortes Cubero

PhD

## About

29

Publications

1,076

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340

Citations

Introduction

Additional affiliations

September 2021 - present

October 2020 - September 2021

August 2019 - July 2020

Education

August 2009 - May 2014

August 2004 - July 2009

## Publications

Publications (29)

The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional E_7 E 7 Lie algebra. The high and low temperature phases of this model are related by duality. This duality guarantees that the leading and sub-leading magnetisation...

The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional $E_7$ Lie algebra. The high and low temperature phases of this model are related by duality. This duality guarantees that the leading and sub-leading magnetisation op...

Our review covers microscopic foundations of generalized hydrodynamics (GHD). As one generic approach we develop form factor expansions, for ground states and generalized Gibbs ensembles (GGE), and compare the so obtained results with predictions from GHD. One cornerstone of GHD is the GGE averaged microscopic currents. They can be obtained using f...

Within the generalized hydrodynamics (GHD) formalism for quantum integrable models, it is possible to compute simple expressions for a number of correlation functions at the Eulerian scale. Specializing to integrable relativistic field theories, we show the same correlators can be computed as a sum over form factors, the GHD regime corresponding to...

The generalized hydrodynamics (GHD) formalism has become an invaluable tool for the study of spatially inhomogeneous quantum quenches in (1+1)-dimensional integrable models. The main paradigm of the GHD is that at late times local observables can be computed as generalized Gibbs ensemble averages with space-time dependent chemical potentials. It is...

Within the generalized hydrodynamics (GHD) formalism for quantum integrable models, it is possible to compute simple expressions for a number of correlation functions at the Eulerian scale. Specializing to integrable relativistic field theories, we show the same correlators can be computed as a sum over form factors, the GHD regime corresponding to...

Motivated by recent works aimed at understanding the status of equilibration and the eigenstate thermalization hypothesis in theories with confinement, we return to the 't Hooft model, the large-$N_c$ limit of (1+1)-d quantum chromodynamics. This limit has been studied extensively since its inception in the mid-1970s, with various exact results bei...

A bstract
We study the form factors of local operators of integrable QFT’s between states with finite energy density. These states arise, for example, at finite temperature, or from a generalized Gibbs ensemble. We generalize Smirnov’s form factor axioms, formulating them for a set of particle/hole excitations on top of the thermodynamic background...

We study the form factors of local operators of integrable QFT's between highly excited states, with finite energy density. These states arise, for example, at finite temperature, or from a generalized Gibbs ensemble. We generalize Smirnov's form factor axioms, formulating them for a set of particle/hole excitations on top of the thermodynamic back...

In (1+1)-dimensional quantum field theory, integrability is typically defined as the existence of an infinite number of local charges of different Lorentz spin, which commute with the Hamiltonian. A well known consequence of integrability is that scattering of particles is elastic and factorizable. These properties are the basis for the bootstrap p...

Machine learning algorithms often take inspiration from established results and knowledge from statistical physics. A prototypical example is the Boltzmann machine algorithm for supervised learning, which utilizes knowledge of classical thermal partition functions and the Boltzmann dis- tribution. Recently, a quantum version of the Boltzmann machin...

We study the dynamics of the sine-Gordon model after a quantum quench into the attractive regime, where the spectrum consists of solitons, antisolitons and breathers. In particular, we analyse the time-dependent expectation value of the vertex operator, $\exp\left({\rm i}\beta\Phi/2\right)$, starting from an initial state in the "squeezed state for...

At thermal equilibrium, the concept of effective central charge for massive
deformations of two-dimensional conformal field theories (CFT) is well
understood, and can be defined by comparing the partition function of the
massive model to that of a CFT. This temperature-dependent effective charge
interpolates monotonically between the central charge...

It has recently been shown that some integrable spin chains possess a set of quasilocal conserved charges, with the classic example being the spin- XXZ Heisenberg chain. These charges have been proven to be essential in order to properly describe stationary states after a quantum quench, and must be included in the generalized Gibbs ensemble (GGE)....

We study a quantum quench of an integrable quantum field theory in the planar infinite-$N$ limit. Unlike isovector-valued $O(N)$ models, matrix-valued field theories in the infinite-$N$ limit are not solvable by the Hartre-Fock approximation, and are nontrivial interacting theories. We study quenches with initial states that are color-charge neutra...

We analyse quench processes in two dimensional quantum field theories with
infinite number of conservation laws which also include fermionic charges that
close a $N=1$ supersymmetric algebra. While in general the quench protocol
induces a breaking of supersymmetry, we show that there are particular initial
states which ensure the persistence of sup...

We examine the phase structure of massive Yang-Mills theory in 1+1
dimensions. This theory is equivalent to a gauged principal chiral sigma model.
It has been previously shown that the gauged theory has only a confined phase,
and no Higgs phase in the continuum, and at infinite volume. There are no
massive gluons, but only hadron-like bound states...

We study the finite volume/temperature correlation functions of the
(1+1)-dimensional ${\rm SU}(N)$ principal chiral sigma model in the planar
limit. The exact S-matrix of the sigma model is known to simplify drastically
at large $N$, and this leads to trivial thermodynamic Bethe ansatz (TBA)
equations. The partition function, if derived using the...

Massive Yang-Mills theory is known to be renormalizable in 1+1 dimensions.
The gluon mass is introduced by coupling the gauge field to an SU(N) principal
chiral nonlinear sigma model. The proof of renormalizability relies on the
asymptotic freedom of the sigma model. However, renormalization forces the
gluon mass to infinity. The continuum theory i...

Yang Mills theory in 2+1 dimensions can be expressed as an array of coupled
(1+1)-dimensional principal chiral sigma models. The $SU(N)\times SU(N)$
principal chiral sigma model in 1+1 dimensions is integrable, asymptotically
free and has massive excitations. We calculate all the form factors and
two-point correlation functions of the Noether curre...

We study Yang Mills theory in 2+1 dimensions, as an array of coupled
(1+1)-dimensional principal chiral sigma models. This can be understood as an
anisotropic limit where one of the space-time dimensions is discrete and the
others are continuous. The $SU(N)\times SU(N)$ principal chiral sigma model in
1+1 dimensions is integrable, asymptotically fr...

The (1+1)-dimensional SU}(N) Yang-Mills Lagrangian, with bare mass M, and
gauge coupling e, naively describes gluons of mass M. In fact, renormalization
forces M to infinity. The system is in a confined phase, instead of a Higgs
phase. The spectrum of this diverging-bare-mass theory contains particles of
finite mass. There are an infinite number of...

We present results for the large-$N$ limit of the (1+1)-dimensional principal
chiral sigma model. This is an asymptotically-free $N\times N$ matrix-valued
field with massive excitations. All the form factors and the exact correlation
functions of the Noether-current operator and the energy-momentum tensor are
found, from Smirnov's form-factor axiom...

We obtain exact matrix elements of physical operators of the
(1+1)-dimensional nonlinear sigma model of an SU(N)-valued bare field, in the
't Hooft limit N goes to infinity. Specifically, all the form factors of the
Noether current and the stress-energy-momentum tensor are found with an
integrable bootstrap method. These form factors are used to fi...

We study the sigma model with $SU(N)\times SU(N)$ symmetry in 1+1 dimensions.
The two- and four-particle form factors of the Noether current operators are
found, by combining the integrable-bootstrap method with the large-$N$
expansion.

We examine the effect of quantum longitudinal rescaling of coordinates, on
the action of quantum chromodynamics (with quarks) to one loop. We use an
aspherical Wilsonian integration (previously applied to the pure Yang-Mills
theory and to quantum electrodynamics). Quantum fluctuations produce anomalous
powers of the rescaling parameter in the coeff...

We investigate quantum longitudinal rescaling of electrodynamics,
transforming coordinates as $x^{0,3}\to\lambda x^{0,3}$ and $x^{1,2}\to
x^{1,2}$, to one loop. We do this by an aspherical Wilsonian renormalization,
which was applied earlier to pure Yang-Mills theory. We find the anomalous
powers of $\lambda$ in the renormalized couplings. Our resu...