arXiv subjects

Harold Erbin

Publications and source records attributed to Harold Erbin.

At least 37 records · Page 2Linked to original sources

arXiv2021

Inception Neural Network for Complete Intersection Calabi-Yau 3-folds

We introduce a neural network inspired by Google's Inception model to compute the Hodge number $h^{1,1}$ of complete intersection Calabi-Yau (CICY) 3-folds. This architecture improves largely the accuracy of the predictions over existing results, giving already 97% of accuracy with just 30% of the data for training. Moreover, accuracy climbs to 99% when using 80% of the data for training. This proves that neural networks are a valuable resource to study geometric aspects in both pure mathematics and string theory.

hep-th↗

arXiv2020

Topological defects and confinement with machine learning: the case of monopoles in compact electrodynamics

We investigate the advantages of machine learning techniques to recognize the dynamics of topological objects in quantum field theories. We consider the compact U(1) gauge theory in three spacetime dimensions as the simplest example of a theory that exhibits confinement and mass gap phenomena generated by monopoles. We train a neural network with a generated set of monopole configurations to distinguish between confinement and deconfinement phases, from which it is possible to determine the deconfinement transition point and to predict several observables. The model uses a supervised learning approach and treats the monopole configurations as three-dimensional images (holograms). We show that the model can determine the transition temperature with accuracy, which depends on the criteria implemented in the algorithm. More importantly, we train the neural network with configurations from a single lattice size before making predictions for configurations from other lattice sizes, from which a reliable estimation of the critical temperatures are obtained.

hep-lat↗

arXiv2020

Casimir effect with machine learning

Vacuum fluctuations of quantum fields between physical objects depend on the shapes, positions, and internal composition of the latter. For objects of arbitrary shapes, even made from idealized materials, the calculation of the associated zero-point (Casimir) energy is an analytically intractable challenge. We propose a new numerical approach to this problem based on machine-learning techniques and illustrate the effectiveness of the method in a (2+1) dimensional scalar field theory. The Casimir energy is first calculated numerically using a Monte-Carlo algorithm for a set of the Dirichlet boundaries of various shapes. Then, a neural network is trained to compute this energy given the Dirichlet domain, treating the latter as black-and-white pixelated images. We show that after the learning phase, the neural network is able to quickly predict the Casimir energy for new boundaries of general shapes with reasonable accuracy.

hep-lat↗

arXiv2020

Classical algebraic structures in string theory effective actions

We study generic properties of string theory effective actions obtained by classically integrating out massive excitations from string field theories based on cyclic homotopy algebras of $A_\infty$ or $L_\infty$ type. We construct observables in the UV theory and we discuss their fate after integration-out. Furthermore, we discuss how to compose two subsequent integrations of degrees of freedom (horizontal composition) and how to integrate out degrees of freedom after deforming the UV theory with a new consistent interaction (vertical decomposition). We then apply our general results to the open bosonic string using Witten's open string field theory. There we show how the horizontal composition can be used to systematically integrate out the Nakanishi-Lautrup field from the set of massless excitations, ending with a non-abelian $A_\infty$-gauge theory for just the open string gluon. Moreover we show how the vertical decomposition can be used to construct effective open-closed couplings by deforming Witten OSFT with a tadpole given by the Ellwood invariant. Also, we discuss how the effective theory controls the possibility of removing the tadpole in the microscopic theory, giving a new framework for studying D-branes deformations induced by changes in the closed string background.

hep-th↗

arXiv2020

BRST cohomology of timelike Liouville theory

We compute the Hermitian sector of the relative BRST cohomology of the spacelike and timelike Liouville theories with generic real central charge $c_L$ in each case, coupled to a spacelike Coulomb gas and a generic transverse CFT. This paper is a companion of arXiv:1905.12689, and its main goal is to completely characterize the cohomology of the timelike theory with $c_L \le 1$ which was defined there. We also apply our formulas to revisit the BRST cohomology of the spacelike Liouville theory with $c_L > 1$, which includes generalized minimal gravity. We prove a no-ghost theorem for the Hermitian sector in the timelike theory and for some spacelike models.

hep-th↗

arXiv2020

Localization of effective actions in Heterotic String Field Theory

We consider the algebraic couplings in the tree level effective action of the heterotic string. We show how these couplings can be computed from closed string field theory. When the light fields we are interested in are charged under an underlying ${\mathcal N}=2$ $R$-charge in the left-moving sector, their quartic effective potential localizes at the boundary of the worldsheet moduli space, in complete analogy to the previously studied open string case. In particular we are able to compute the quartic closed string field theory potential without resorting to any explicit expression for the 3- and the 4-strings vertices but only using the $L_\infty$ relations between them. As a non trivial example we show how the heterotic Yang-Mills quartic potential arises in this way.

hep-th↗

arXiv2020

A short note on dynamics and degrees of freedom in $2d$ classical gravity

We comment on some peculiarities of matter with and without Weyl invariance coupled to classical $2d$ Einstein-Hilbert gravity for several models, in particular, related to the counting of degrees of freedom and on the dynamics. We find that theories where the matter action is Weyl invariant has generically more degrees of freedom than action without the invariance. This follows from the Weyl invariance of the metric equations of motion independently of the invariance of the action. Then, we study another set of models with scalar fields and show that solutions to the equations of motion are either trivial or inconsistent. To our knowledge, these aspects of classical $2d$ gravity have not been put forward and can be interesting to be remembered when using it as a toy model for $4d$ gravity. The goal of this note is also as a pedagogical exercise: our results follow from standard methods, but we emphasize more direct computations.

gr-qc↗

arXiv2019

Conformality of $1/N$ corrections in SYK-like models

The Sachdev--Ye--Kitaev is a quantum mechanical model of $N$ Majorana fermions which displays a number of appealing features -- solvability in the strong coupling regime, near-conformal invariance and maximal chaos -- which make it a suitable model for black holes in the context of the AdS/CFT holography. In this paper, we show for the colored SYK model and several of its tensor model cousins that the next-to-leading order in the large $N$ expansion preserves the conformal invariance of the $2$-point function in the strong coupling regime, up to the contribution of the pseudo-Goldstone bosons due to the explicit breaking of the symmetry and which are already seen in the leading order $4$-point function. We also comment on the composite field approach for computing correlation functions in colored tensor models.

hep-th↗

arXiv2019

Quantum Gravity from Timelike Liouville theory

A proper definition of the path integral of quantum gravity has been a long-standing puzzle because the Weyl factor of the Euclidean metric has a wrong-sign kinetic term. We propose a definition of two-dimensional Liouville quantum gravity with cosmological constant using conformal bootstrap for the timelike Liouville theory coupled to supercritical matter. We prove a no-ghost theorem for the states in the BRST cohomology. We show that the four-point function constructed by gluing the timelike Liouville three-point functions is well defined and crossing symmetric (numerically) for external Liouville energies corresponding to \textit{all} physical states in the BRST cohomology with the choice of the Ribault-Santachiara contour for the internal energy.

hep-th↗

arXiv2019

Two-Point String Amplitudes

We show that the two-point tree level amplitude in string theory in flat space is given by the standard free particle expression.

hep-th↗

arXiv2019

Analyticity and Crossing Symmetry of Superstring Loop Amplitudes

Bros, Epstein and Glaser proved crossing symmetry of the S-matrix of a theory without massless fields by using certain analyticity properties of the off-shell momentum space Green's function in the complex momentum plane. The latter properties follow from representing the momentum space Green's function as Fourier transform of the position space Green's function, satisfying certain properties implied by the underlying local quantum field theory. We prove the same analyticity properties of the momentum space Green's functions in superstring field theory by directly working with the momentum space Feynman rules even though the corresponding properties of the position space Green's function are not known. Our result is valid to all orders in perturbation theory, but requires, as usual, explicitly subtracting / regulating the non-analyticities associated with massless particles. These results can also be used to prove other general analyticity properties of the S-matrix of superstring theory.

hep-th↗

arXiv2018

Universality of tunnelling particles in Hawking radiation

The complex path (or Hamilton-Jacobi) approach to Hawking radiation corresponds to the intuitive picture of particles tunnelling through the horizon and forming a thermal radiation. This method computes the tunnelling rate of a given particle from its equation of motion and equates it to the Boltzmann distribution of the radiation from which the Hawking temperature is identified. In agreement with the original derivation by Hawking and the other approaches, it has been checked case by case that the temperature is indeed universal for a number of backgrounds and the tunnelling of particles from spins $0$ to $1$ mostly, spins $3/2$ and $2$ in some instances. In this letter, we give a general proof that the temperature is indeed equal for all (massless and massive) particles with spins from $0$ to $2$ on an arbitrary background (limited to be Einstein for spin greater than $1$) in any number of dimensions. Moreover, we propose a general argument to extend this result to any spin greater than $2$.

gr-qc↗

arXiv2018

GANs for generating EFT models

We initiate a way of generating models by the computer, satisfying both experimental and theoretical constraints. In particular, we present a framework which allows the generation of effective field theories. We use Generative Adversarial Networks to generate these models and we generate examples which go beyond the examples known to the machine. As a starting point, we apply this idea to the generation of supersymmetric field theories. In this case, the machine knows consistent examples of supersymmetric field theories with a single field and generates new examples of such theories. In the generated potentials we find distinct properties, here the number of minima in the scalar potential, with values not found in the training data. We comment on potential further applications of this framework.

cs.LG↗

arXiv2018

Minisuperspace computation of the Mabuchi spectrum

It was shown recently that, beside the traditional Liouville action, other functionals appear in the gravitational action of two-dimensional quantum gravity in the conformal gauge, the most important one being the Mabuchi functional. In a letter we proposed a minisuperspace action for this theory and used it to perform its canonical quantization. We found that the Hamiltonian of the Mabuchi theory is equal to the one of the Liouville theory and thus that the spectrum and correlation functions match in this approximation. In this paper we provide motivations to support our conjecture.

hep-th↗

arXiv2017

Closed Superstring Field Theory and its Applications

We review recent developments in the construction of heterotic and type II string field theories and their various applications. These include systematic procedures for determining the shifts in the vacuum expectation values of fields under quantum corrections, computing renormalized masses and S-matrix of the theory around the shifted vacuum and a proof of unitarity of the S-matrix. The S-matrix computed this way is free from all divergences when there are more than 4 non-compact space-time dimensions, but suffers from the usual infrared divergences when the number of non-compact space-time dimensions is 4 or less.

hep-th↗

arXiv2017

Domain wall seeds in CSO-gauged supergravity

Gravitational domain wall solutions in gauged supergravity are often constructed within truncations that do not include vectors. As a consequence the gauge group is only a global symmetry of this truncation. The consistency of the truncation requires the restriction to solutions with vanishing Noether charge under this global symmetry, since otherwise vector fields are sourced. We show that this has interesting consequences for the orbit structure of the solutions under the global symmetries. We investigate this for $\text{CSO}(p,q,r)$-gaugings in various dimensions with scalar fields truncated to the $\text{SL}(n,\mathbb{R})/\text{SO}(n)$ subcoset. We prove that the seed solution $-$ which generates all other solutions using only global transformations $-$ has a diagonal coset matrix. This means that there exists a transformation at the boundary of the geometry that diagonalises the coset matrix and that this same transformation also diagonalises the whole flow as a consequence of the vanishing charge.

hep-th↗

arXiv2017

Janis-Newman algorithm: generating rotating and NUT charged black holes

In this review we present the most general form of the Janis--Newman algorithm. This extension allows to generate configurations which contain all bosonic fields with spin less than or equal to two (real and complex scalar fields, gauge fields, metric field) and with five of the six parameters of the Plebański-Demiański metric (mass, electric charge, magnetic charge, NUT charge and angular momentum). Several examples are included to illustrate the algorithm. We also discuss the extension of the algorithm to other dimensions.

gr-qc↗

arXiv2016

Mabuchi spectrum from the minisuperspace

It was recently shown that other functionals contribute to the effective action for the Liouville field when considering massive matter coupled to two-dimensional gravity in the conformal gauge. The most important of these new contributions corresponds to the Mabuchi functional. We propose a minisuperspace action that reproduces the main features of the Mabuchi action in order to describe the dynamics of the zero-mode. We show that the associated Hamiltonian coincides with the (quantum mechanical) Liouville Hamiltonian. As a consequence the Liouville theory and our model of the Mabuchi theory both share the same spectrum, eigenfunctions and - in this approximation - correlation functions.

hep-th↗