2D String Research Articles

Two-dimensional regular string black hole via complete alpha ^{prime } corrections

In string theory, an important challenge is to show if the singularity of black holes can be smoothed out by the complete alpha ^{prime } corrections. The simplest case is to consider a 2D string black hole or 3D black string. This problem was discussed in a gauged Wess–Zumino–Witten (WZW) model and the results are supposed to be correct to all orders in alpha ^{prime } corrections. Based on the recent remarkable progress on classifying all the alpha ^{prime } corrections, in this work, we re-study this problem with the low energy effective spacetime action, and provide classes of exact non-perturbative and non-singular solutions of the 2D black hole/3D black string via complete alpha ^{prime } corrections.

A Cooperative Implementation of Mesh Stability in Vehicular Platoons

This work studies the problem of mesh stability in connected and automated vehicles. Mesh stability, also known as 2D string stability, refers to studying how disturbances propagate in vehicular platoons in both longitudinal and lateral direction. As opposed to available decentralized results only relying on on-board sensing, the distinguishing feature of this work is a cooperative version of mesh stability, where on-board sensing is augmented by vehicle-to-vehicle communication. This cooperative version dramatically improves the state-of-the-art decentralized performance: for longitudinal control, a new cooperative non-identical protocol (i.e. with non-identical control gains) is proposed that improves the state-of-the-art decentralized non-identical protocol in terms of scalability of the control gains and strong notion of string stability. For lateral control, after showing that the non-identical approach is not necessary, a cooperative non-identical protocol is proposed to achieve another strong notion of string stability. Robustness of the proposed implementation against vehicle-to-vehicle communication delays and actuation time lags is considered. Numerical experiments, also performed with the vehicle simulator CarSim, validate the robustness and effectiveness of the proposed protocol.

BPS Algebras in 2D String Theory

We discuss a set of heterotic and type II string theory compactifications to 1+1 dimensions that are characterized by factorized internal worldsheet CFTs of the form V_1otimes bar{V}_2, where V_1, V_2 are self-dual (super) vertex operator algebras. In the cases with spacetime supersymmetry, we show that the BPS states form a module for a Borcherds–Kac–Moody (BKM) (super)algebra, and we prove that for each model the BKM (super)algebra is a symmetry of genus zero BPS string amplitudes. We compute the supersymmetric indices of these models using both Hamiltonian and path integral formalisms. The path integrals are manifestly automorphic forms closely related to the Borcherds–Weyl–Kac denominator. Along the way, we comment on various subtleties inherent to these low-dimensional string compactifications.

A New Multi-Resolution Approach to EEG Brain Modeling Using Local-Global Graphs and Stochastic Petri-Nets.

Recent modeling of brain activities encompasses the fusion of different modalities. However, fusing brain modalities requires not only the efficient and compatible representation of the signals but also the benefits associated with it. For instance, the combination of the functional characteristics of EEGs with the structural features of functional magnetic resonance imaging contributes to a better interpretation localization of brain activities. In this paper, we consider the EEG signals as parallel 2D string images from which we extract their visual abstract representations of EEG features. This representation can benefit not only the EEG modeling of the signals but also a future fusion with another modality, like fMRI. In particular, the new methodology, called Bar-LG, provides a reduced discretization of the EEG signals into selected minima/maxima in order to be used in a form of tokens for EEG brain activities of interest. A formal context-free language is used to express and represent the extracted tokens for the selected active brain regions. Then, a Generalized Stochastic Petri-Nets (GSPN) model is used for expressing the functional associations and interactions of these EEG signals as 2D image regions. An illustrative EEG example of epileptic seizure is presented to show the Bar-LG methodology's abstract capabilities.

Fredholm Property of Operators from 2D String Field Theory

In a recent study of Landau-Ginzburg model of string field theory by Gaiotto, Moore and Witten, there appears a type of perturbed Cauchy-Riemann equation, i.e. the ζ-instanton equation. Solutions of ζ-instanton equation have degenerate asymptotics. This degeneracy is a severe restriction for obtaining the Fredholm property and constructing relevant homology theory. In this article, we study the Fredholm property of a sort of differential operators with degenerate asymptotics. As an application, we verify certain Fredholm property of the linearized operator of ζ-instanton equations.

Quantum quench in non-relativistic fermionic field theory: harmonic traps and 2d string theory

We investigate a class of exactly solvable quantum quench protocols with a finite quench rate in systems of one dimensional non-relativistic fermions in external harmonic oscillator or inverted harmonic oscillator potentials, with time dependent masses and frequencies. These hamiltonians arise, respectively, in harmonic traps, and the c = 1 Matrix Model description of two dimensional string theory with time dependent string coupling. We show how the dynamics is determined by a single function of time which satisfies a generalized Ermakov-Pinney equation. The quench protocols we consider asymptote to constant masses and frequencies at early times, and cross or approach a gapless potential. In a right side up harmonic oscillator potential we determine the scaling behavior of the one point function and the entanglement entropy of a subregion by obtaining analytic approximations to the exact answers. The results are consistent with Kibble-Zurek scaling for slow quenches and with perturbation calculations for fast quenches. For cis-critical quench protocols the entanglement entropy oscillates at late times around its initial value. For end-critical protocols the entanglement entropy monotonically goes to zero inversely with time, reflecting the spread of fermions over the entire line. For the inverted harmonic oscillator potential, the dual collective field description is a scalar field in a time dependent metric and dilaton background.

Structure of methanol sub-monolayer on functionalized graphite at temperatures below the triple point

Grand canonical simulations were carried out to determine the microscopic structures of the sub-monolayer of methanol on a graphite model with two hydroxyl groups attached to the basal plane. At temperatures below the triple point temperature of methanol (176 K), the adsorption isotherm exhibits four distinct transitions: (1) saturation of the OH groups, (2) formation of 2D ring clusters floating on the basal plane, (3) transition to 2D string clusters with one end attached to the OH groups, and (4) compaction of the 2D string clusters. The variation in the molecular distribution and orientation for these transitions is studied, and correlated with the changes in isosteric heat across these transitions. It is found that the ring-to-string transition occurs more readily at low temperatures, and that the hydrogen bond length (O⋯H) within a ring or a string is constant.

Full sets of pictures to encode pictures

A picture, or two-dimensional (2D) string, is a rectangular array of symbols over a finite alphabet. In this paper, we introduce the notion of fullness for sets of strings and sets of pictures. Fullness is a local counterpart of completeness. While in 1D fullness coincides with completeness, in 2D complete sets of pictures are a subset of full ones. This new notion allows introducing the encoding of a picture. The definition of encoding is based on the one of cutting decomposition. If a set of pictures X is full then any picture has an encoding over X; furthermore, the encoding is unique if X is a univocally full set. Univocally full sets coincide with the maximal strong prefix codes of pictures that were recently introduced. At last, we show an encoding algorithm for pictures, which relies on a new tree data structure to represent univocally full sets.

Space-time in the SYK model

We consider the question of identifying the bulk space-time of the SYK model. Focusing on the signature of emergent space-time of the (Euclidean) model, we explain the need for non-local (Radon-type) transformations on external legs of n-point Green’s functions. This results in a dual theory with Euclidean AdS signature with additional legfactors. We speculate that these factors incorporate the coupling of additional bulk states similar to the discrete states of 2d string theory.

Semiclassical limit of Liouville Field Theory

Liouville Field Theory (LFT for short) is a two dimensional model of random surfaces, which is for instance involved in 2d string theory or in the description of the fluctuations of metrics in 2d Liouville quantum gravity. This is a probabilistic model that consists in weighting the classical Free Field action with an interaction term given by the exponential of a Gaussian multiplicative chaos. The main input of our work is the study of the semiclassical limit of the theory, which is a prescribed asymptotic regime of LFT of interest in physics literature (see [35] and references therein). We derive exact formulas for the Laplace transform of the Liouville field in the case of flat metric on the unit disk with Dirichlet boundary conditions. As a consequence, we prove that the Liouville field concentrates on the solution of the classical Liouville equation with explicit negative scalar curvature. We also characterize the leading fluctuations, which are Gaussian and massive, and establish a large deviation principle. Though considered as an ansatz in the whole physics literature, it seems that it is the first rigorous probabilistic derivation of the semiclassical limit of LFT. On the other hand, we carry out the same analysis when we further weight the Liouville action with heavy matter operators. This procedure appears when computing the n-points correlation functions of LFT.

Perturbative computation of string one-loop corrections to Wilson loop minimal surfaces in AdS5 \xd7 S5

We revisit the computation of the 1-loop string correction to the “latitude” minimal surface in AdS5 × S5 representing 1/4 BPS Wilson loop in planar mathcal{N}=4 SYM theory previously addressed in arXiv:1512.00841 and arXiv:1601.04708. We resolve the problem of matching with the subleading term in the strong coupling expansion of the exact gauge theory result (derived previously from localization) using a different method to compute determinants of 2d string fluctuation operators. We apply perturbation theory in a small parameter (angle of the latitude) corresponding to an expansion near the AdS2 minimal surface representing 1/2 BPS circular Wilson loop. This allows us to compute the corrections to the heat kernels and zeta-functions of the operators in terms of the known heat kernels on AdS2. We apply the same method also to two other examples of Wilson loop surfaces: generalized cusp and k-wound circle.

The black hole S-Matrix from quantum mechanics

We revisit the old black hole S-Matrix construction and its new partial wave expansion of 't Hooft. Inspired by old ideas from non-critical string theory & $c=1$ Matrix Quantum Mechanics, we reformulate the scattering in terms of a quantum mechanical model\textemdash of waves scattering off inverted harmonic oscillator potentials\textemdash that exactly reproduces the unitary black hole S-Matrix for all spherical harmonics; each partial wave corresponds to an inverted harmonic oscillator with ground state energy that is shifted relative to the s-wave oscillator. Identifying a connection to 2d string theory allows us to show that there is an exponential degeneracy in how a given total initial energy may be distributed among many partial waves of the 4d black hole.

Pseudo 2D String Matching Technique for High Efficiency Screen Content Coding

This paper proposes a pseudo 2D string matching (P2SM) technique for high efficiency screen content coding (SCC). The technique uses a primary reference buffer (PRB) and a secondary reference buffer (SRB) for string matching and string copying. In the encoder, optimal reference string searching is performed in both PRB and SRB, and either a PRB or an SRB string is selected as an optimal reference string on a string-by-string basis. If no reference string of at least one pixel is founded for a current pixel, then the current pixel is coded as an unmatched pixel. Compared with HM-16.4 ${+}$ SCM-4.0 reference software, the proposed P2SM technique achieves up to 37.7% Y BD-rate reduction for a screen snapshot of a spreadsheet. On average, using HEVC SCC common test condition and YUV test sequences in text and graphics with motion category, the proposed technique achieves Y BD-rate reduction of 7.7%, 5.0%, 2.6% for all intra (AI), random access (RA) and low-delay B (LB) configurations, respectively in lossy coding with both intra block copy (IBC) and P2SM having the same 4 coding tree units (CTUs) searching range, and bit-rate saving of 6.0%, 3.9%, 3.1% for AI, RA, LB configurations, respectively in lossless coding with IBC having full frame searching range while P2SM having only 2 CTUs searching range, at very low additional encoding and decoding complexity.

Complex Gaussian Multiplicative Chaos

In this article, we study complex Gaussian multiplicative chaos. More precisely, we study the renormalization theory and the limit of the exponential of a complex log-correlated Gaussian field in all dimensions (including Gaussian Free Fields in dimension 2). Our main working assumption is that the real part and the imaginary part are independent. We also discuss applications in 2D string theory; in particular we give a rigorous mathematical definition of the so-called Tachyon fields, the conformally invariant operators in critical Liouville Quantum Gravity with a c=1 central charge, and derive the original KPZ formula for these fields.

Minimizing gauge functional for 2d gravity and string theory

We show the existence of a minimizing procedure for selecting a unique representative on the orbit of any given Riemann surface that contributes to the string partition function. As it must, the procedure reduces the string path integral to a final integration over a particular fundamental domain, selected by the choice of the minimizing functional. This construction somehow demystifies the Gribov question.

Algorithms for discovery of spatial co-orientation patterns from images

Image mining is an important task to discover interesting and meaningful patterns form large image databases. In this paper, we introduce the spatial co-orientation patterns in image databases. Spatial co-orientation patterns refer to objects that frequently occur with the same spatial orientation, e.g. left, right, below, etc. among images. For example, an object P is frequently left to an object Q among images. We utilize the data structure, 2D string, to represent the spatial orientation of objects in an image. Two approaches, Apriori-based and pattern-growth approaches, are proposed for mining co-orientation patterns. An experimental evaluation with synthetic datasets shows the advantage and disadvantage between these two algorithms.

Ensemble clustering using semidefinite programming with applications

In this paper, we study the ensemble clustering problem, where the input is in the form of multiple clustering solutions. The goal of ensemble clustering algorithms is to aggregate the solutions into one solution that maximizes the agreement in the input ensemble. We obtain several new results for this problem. Specifically, we show that the notion of agreement under such circumstances can be better captured using a 2D string encoding rather than a voting strategy, which is common among existing approaches. Our optimization proceeds by first constructing a non-linear objective function which is then transformed into a 0-1 Semidefinite program (SDP) using novel convexification techniques. This model can be subsequently relaxed to a polynomial time solvable SDP. In addition to the theoretical contributions, our experimental results on standard machine learning and synthetic datasets show that this approach leads to improvements not only in terms of the proposed agreement measure but also the existing agreement measures based on voting strategies. In addition, we identify several new application scenarios for this problem. These include combining multiple image segmentations and generating tissue maps from multiple-channel Diffusion Tensor brain images to identify the underlying structure of the brain.

Modelling and simulations of DRIE including a footing effect

An improved model for surface evolvement of Deep Reactive Ion Etching (DRIE) is developed, which is based on Time Multiplexed Deep Etching (TMDE). It couples the advanced plasma sheath approximation and has the simplex data structure due to 2D string algorithm, so as to achieve an acceptable arithmetic speed. Furthermore, after some reasonable descriptions for footing surface are assumed, a simple module for footing effect simulations is added to this model. The simulations of DRIE and footing effect are also performed, and the simulated results are in accordance with the experiments.

Zero-norm states and stringy symmetries

We identify spacetime symmetry charges of 26D open bosonic string theory from an infinite number of zero-norm states (ZNS) with arbitrary high spin in the old covariant first quantized string spectrum. We give various evidences to support this identification. These include massive sigma-model calculation, Witten string field theory calculation, 2D string theory calculation and, most importantly, three methods of high-energy stringy scattering amplitude calculations. The last calculations explicitly prove Gross's conjectures in 1988 on high energy symmetry of string theory.

C= 1 matrix model from string field theory

We show that the boundary string field theory (BSFT) on unstable D0-branes in 2d string theory is equivalent to the double scaled c=1 matrix model (i.e. quadratic action), even though we naively expect many interaction terms in BSFT. It is checked that S-matrices are trivial in the open string theory on the D0-branes. We discuss how to take the closed string decoupling limit in our model in order to make its holographic interpretation clear. We also find some useful lessons from our results in 2d string toward the further understanding of the higher dimensional BSFT action.