String Geometry Research Articles

Reflected entropy in a BCFT on a black hole background

We obtain the reflected entropy for bipartite mixed state configurations involving two disjoint and adjacent subsystems in a two dimensional boundary conformal field theory (BCFT2) in a black hole background. The bulk dual is described by an AdS3 black string geometry truncated by a Karch-Randall brane. The entanglement wedge cross section computed for this geometry matches with the reflected entropy obtained for the BCFT2 verifying the holographic duality. In this context, we also obtain the analogues of the Page curves for the reflected entropy and investigate the behaviour of the Markov gap.

Back to heterotic strings on ALE spaces. Part II. Geometry of T-dual little strings

This work is the second of a series of papers devoted to revisiting the properties of Heterotic string compactifications on ALE spaces. In this project we study the geometric counterpart in F-theory of the T-dualities between Heterotic ALE instantonic Little String Theories (LSTs) extending and generalising previous results on the subject by Aspinwall and Morrison. Since the T-dualities arise from a circle reduction one can exploit the duality between F-theory and M-theory to explore a larger moduli space, where T-dualities are realised as inequivalent elliptic fibrations of the same geometry. As expected from the Heterotic/F-theory duality the elliptic F-theory Calabi-Yau we consider admit a nested elliptic K3 fibration structure. This is central for our construction: the K3 fibrations determine the flavor groups and their global forms, and are the key to identify various T-dualities. We remark that this method works also more generally for LSTs arising from non-geometric Heterotic backgrounds. We study a first example in detail: a particularly exotic class of LSTs which are built from extremal K3 surfaces that admit flavor groups with maximal rank 18. We find all models are related by a so-called T-hexality (i.e. a 6-fold family of T-dualities) which we predict from the inequivalent elliptic fibrations of the extremal K3.

Complexity growth of BTZ black hole in massive gravity with a null string

In this paper, we investigate the complexity growth of the tensionless limit of string in the neutral BTZ black hole horizon in massive gravity. When the string approaches the horizon, we observe a novel phenomenon for the Nambu–Goto action growth that produces significant difference from tensile string geometry. The string’s tension is then suggested to partially contribute to the growth of the action. We also argue a potential proposal that reconstructs the complexity from the renormalization group (RG) flow.

Enumerative geometry of surfaces and topological strings

This survey covers recent developments on the geometry and physics of Looijenga pairs, namely pairs [Formula: see text] with [Formula: see text] a complex algebraic surface and [Formula: see text] a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to [Formula: see text], including the log Gromov–Witten invariants of the pair, the Gromov–Witten invariants of an associated higher dimensional Calabi–Yau variety, the open Gromov–Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed BPS-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.

Path integrals of perturbative superstrings on curved backgrounds from string geometry theory

String geometry theory is one of the candidates for a nonperturbative formulation of string theory. In this paper, from the string geometry theory, we derive path integrals of perturbative superstrings on all string backgrounds, ${G}_{\ensuremath{\mu}\ensuremath{\nu}}(x)$ and ${B}_{\ensuremath{\mu}\ensuremath{\nu}}(x)$, by considering fluctuations around the string background configurations, which are parametrized by the string backgrounds.

Optimal Design of Corona Ring for 132 kV Insulator at High Voltage Transmission Lines Based on Optimisation Techniques

The installation of a corona ring on an insulator string on a transmission line is one of the solutions to reduce the electric field stress surrounding the energised end of the insulator string. However, installing a corona ring with an optimum design to reduce the electric field magnitude on an insulator string is a challenging task. Therefore, in this work, a method to achieve the optimum design of a corona ring for 132 kV composite non-ceramic insulator string was proposed using two optimisation methods: the Imperialist Competitive Algorithm (ICA) and Grey Wolf Optimisation (GWO). A composite non-ceramic insulator string geometry with and without a corona ring was modelled in finite element analysis and used to obtain the electric field distribution in the model geometry. The electric field distribution was evaluated using a variation in the corona ring’s dimensions, i.e., the ring diameter, the ring tube diameter and the vertical position of the ring along the insulator string. From the results achieved, a comparison of the minimum electric field magnitude along the insulator string with a corona ring design shows that the minimum electric field magnitude is found to be lower using optimisation techniques compared to without using optimisation techniques by between 3.724% and 3.827%. Hence, this indicates the capability and effectiveness of the proposed methods in achieving the optimum design of a corona ring on an insulator string.

Strings, branes, Schwarzian action and maximal chaos

In this article, we present explicit evidence that maximal chaos occurs for a generic, probe quark-like defect degrees of freedom, in a strongly coupled large Nc gauge theory. In holography, this corresponds to the dynamics of open string degrees of freedom, in the background of a closed string geometry. In this context, we explicitly show that a Schwarzian effective action for the soft sector emerges and couples with other modes, in the infra-red. This is manifest on an open string worldsheet, as well as a D1-brane world-volume, embedded in AdS3. The corresponding maximal chaos is governed by an intrinsic defect D-brane horizon, and an intrinsic non-linear description of the brane or the string. We also present explicit evidence of maximal chaos away from extremality on a D-brane horizon, by computing a four-point out-of-time order correlator of spin-one operators. This further suggests that a similar description of the soft sector physics of open string degrees of freedom may exist in general.

BCFT in a black hole background: an analytical holographic model

We study the entanglement phase structure of a holographic boundary conformal field theory (BCFT) in a two-dimensional black hole background. The bulk dual is the AdS3 black string geometry with a Karch-Randall brane. We compute the subregion entanglement entropy of various two-sided bipartitions to elucidate the phase space where a Page curve exists in this setup. We do fully analytical computations on both the gravity side and the field theory side and demonstrate that the results precisely match. We discuss the entanglement phase structure describing where a Page curve exists in this geometry in the context of these analytical results. This is a useful model to study entanglement entropy for quantum field theory on a curved background.

Path integrals of perturbative strings on curved backgrounds from string geometry theory

String geometry theory is one of the candidates of the nonperturbative formulation of string theory. In this paper, from the closed bosonic sector of string geometry theory, we derive path integrals of perturbative strings on all of the string backgrounds, ${G}_{\ensuremath{\mu}\ensuremath{\nu}}(x)$, ${B}_{\ensuremath{\mu}\ensuremath{\nu}}(x)$, and $\mathrm{\ensuremath{\Phi}}(x)$, by considering fluctuations around the string background configurations, which are parametrized by the string backgrounds.

Hybrid Grey Wolf and Finite Element Method (GWO-FEM) Algorithm for Enhancing High Voltage Insulator String Performance in Wet Pollution Conditions

The presence of wet pollution on the upper surface of a string insulator increases the electric field on the insulator surface, especially at the triple junction (pin-cement, cement-porcelain) as well as at the surrounding air of the insulator. The rise of the electric field leads to the ionization of the air surrounding the insulator. This phenomenon, called corona discharge, is accompanied by several consequences that are harmful to the electricity transmission network, such as electromagnetic interferences, energy losses, visible light, audible noise, and the destruction of materials by erosion. If favorable conditions are gathered, it may even cause the flashover of the insulator. Designing an optimal insulator shape that reduces this electric field value at the triple junction will be an important achievement in enhancing the performance of electrical grids. The objective of this paper is to evolve a hybrid algorithm based on the GWO-FEM for optimizing the shape and the electrical performance of a string insulator. To achieve this purpose, this work is structured in four parts. First, modeling of the insulator string geometry is conducted in Comsol-multiphysics, then FEM computation of the electric field on the polluted surface of the string insulator is completed, and the maximum electric field value at the triple junction is saved as the fitness function that will be sent to the GWO algorithm to be optimized (minimized). The third part of the work is devoted to the coding of the constrained (electrical and geometrical constraints) GWO algorithm in a Matlab interface, and finally, coupling the GWO code with the FEM code. This study is achieved in wet polluted conditions. The results are given in both 2D and 3D representations. From the obtained results we can confirm that the developed GWO-FEM hybrid algorithm for optimizing insulator strings is a very promising tool for designing and enhancing the shape and the electrical performance of insulators.

Dual D-brane actions in nonrelativistic string theory

We study worldvolume actions for D-branes coupled to the worldvolume U(1) gauge field and Ramond-Ramond (RR) potentials in nonrelativistic string theory. This theory is a self-contained corner of relativistic string theory and has a string spectrum with a Galilean-invariant dispersion relation. We therefore refer to such D-branes in nonrelativistic string theory as nonrelativistic D-branes. We focus on the bosonic fields in spacetime and also couple the D-branes to general closed string geometry, Kalb-Ramond, and dilaton background fields. We dualize nonrelativistic D-branes by performing a duality transformation on the worldvolume U(1) gauge field and uncover novel dual D-brane actions. This generalizes familiar properties, such as the SL(2, ℤ) duality in Type IIB superstring theory and the relation between Type IIA superstring and M-theory, to nonrelativistic string and M-theory. Moreover, we generalize the limit of string theory, in which nonrelativistic string theory arises, to include RR potentials. This stringy limit induces a codimension-two foliation structure in spacetime. This spacetime geometry is non-Riemannian and known as string Newton-Cartan geometry. In contrast, nonrelativistic M-theory that we probe by dualizing D2- and D4-branes in nonrelativistic string theory arises as a membrane limit of M-theory, and it is coupled to a membrane Newton-Cartan geometry with a codimension-three foliation structure. We also discuss T-duality in nonrelativistic string theory and generalize Buscher rules from earlier work to include RR potentials.

Fusion of implementers for spinors on the circle

We consider the space of odd spinors on the circle, and a decomposition into spinors supported on either the top or on the bottom half of the circle. If an operator preserves this decomposition, and acts on the bottom half in the same way as a second operator acts on the top half, then the fusion of both operators is a third operator acting on the top half like the first, and on the bottom half like the second. Fusion restricts to the Banach-Lie group of restricted orthogonal operators, which supports a central extension of implementers on a Fock space. In this article, we construct a lift of fusion to this central extension. Our construction uses Tomita-Takesaki theory for the Clifford-von Neumann algebras of the decomposed space of spinors. Our motivation is to obtain an operator-algebraic model for the basic central extension of the loop group of the spin group, on which the fusion of implementers induces a fusion product in the sense considered in the context of transgression and string geometry. In upcoming work we will use this model to construct a fusion product on a spinor bundle on the loop space of a string manifold, completing a construction proposed by Stolz and Teichner.

Impact of hole cleaning and drilling performance on the equivalent circulating density

Efficient hole cleaning in drilling operations is essential to ensure optimum penetration rates. This complex problem involves the simultaneous analysis of multiple parameters, including cuttings characteristics, fluid rheology, and annulus space geometry. The effect of the mud density increase due to the cuttings concentration, which itself is a function of the settling velocity and rate of penetration (ROP), must be considered for accurate calculations of the equivalent circulation density (ECD).Mechanical Specific Energy (MSE) models have been widely used in bit selection, drilling efficiency quantification, drilling performance monitoring, drilling performance optimization, and ROP improvement. We attempted to employ MSE for optimized hole cleaning and controlled ECD. Cuttings concentration was integrated with the drilling MSE, which was calculated to determine the effect of different drilling parameters on hole cleaning and ECD. We proposed a new model for predicting the ECD in vertical and deviated wellbores that takes fluid and formation properties, as well as wellbore and drill string geometry and drilling operational parameters, into account. The model predicts the cuttings concentration and equivalent circulation density in vertical and deviated wells. The workflow implements the critical and settling velocity models, which aids in optimizing drilling performance and hole cleaning. The developed model was used to study the effect of different drilling parameters on ECD and help engineers optimize their operational parameters. Integrating the drilling operational parameters to provide controlling options to drillers as they monitor ECD values while maintaining safety and optimizing the drilling job is critically important.

Aligned natural inflation in the Large Volume Scenario

We embed natural inflation in an explict string theory model and derive observables in cosmology. We achieve this by compactifying the type IIB string on a Calabi-Yau orientifold, stabilizing moduli via the Large Volume Scenario, and configuring axions using D7-brane stacks. In order to obtain a large effective decay constant, we employ the Kim-Nilles-Peloso alignment mechanism, with the required multiple axions arising naturally from generically anisotropic bulk geometries. The bulk volumes, and hence the axion decay constants, are stabilized by generalized one-loop corrections and subject to various conditions: the Kähler cone condition on the string geometry; the convex hull condition of the weak gravity conjecture; and the constraint from the power spectrum of scalar perturbations. We find that all constraints can be satisfied in a geometry with relatively small volume and thus heavy bulk axion mass. We also covariantize the convex hull condition for the axion-dilaton-instanton system and verify the normalization of the extremal bound.

Superstring Backgrounds in String Geometry

String geometry theory is a candidate of the nonperturbative formulation of string theory. In order to determine the string vacuum, we need to clarify how superstring backgrounds are described in string geometry theory. In this paper, we show that all the type IIA, IIB, SO(32) type I, and SO(32) and E 8 × E 8 heterotic superstring backgrounds are embedded in configurations of the fields of a single string geometry model. In particular, we show that the configurations satisfy the equations of motion of the string geometry model in α ′ ⟶ 0 if and only if the embedded string backgrounds satisfy the equations of motion of the supergravities, respectively. This means that classical dynamics of the string backgrounds are described as a part of classical dynamics in string geometry theory. Furthermore, we define an energy of the configurations in the string geometry model because they do not depend on the string geometry time. A string background can be determined by minimizing the energy.

$$p$$-Adic Fractal Strings of Arbitrary Rational Dimensions and Cantor Strings

The local theory of complex dimensions for real and $$p$$ -adic fractal strings describes oscillations that are intrinsic to the geometry, dynamics and spectrum of archimedean and nonarchimedean fractal strings. We aim to develop a global theory of complex dimensions for adèlic fractal strings in order to reveal the oscillatory nature of adèlic fractal strings and to understand the Riemann hypothesis in terms of the vibrations and resonances of fractal strings. We present a simple and natural construction of self-similar $$p$$ -adic fractal strings of any rational fractal (i.e., Minkowski) dimension in the closed unit interval $$[0,1]$$ . Moreover, as a first step towards a global theory of complex dimensions for adèlic fractal strings, we construct an adèlic Cantor string in the set of finite adèles $$\mathbb{A}_0$$ as an infinite Cartesian product of every $$p$$ -adic Cantor string, as well as an adèlic Cantor-Smith string in the ring of adèles $$\mathbb{A}$$ as a Cartesian product of the general Cantor string and the adèlic Cantor string.

HEE and HSC for flavors: perturbative structure in open string geometries

Introduction of electric field in the D-brane worldvolume induces a horizon in the open string geometry perceived by the brane fluctuations. We study the holographic entanglement entropy (HEE) and subregion complexity (HSC) in these asymptotically AdS geometries in three, four and five dimensions aiming to capture these quantities in the flavor sector introduced by the D-branes. Both the strip and spherical subregions have been considered. We show that the Bekenstein-Hawking entropy associated with the open string horizon, which earlier failed to reproduce the thermal entropy in the boundary, now precisely matches with the entanglement entropy at high temperatures. We check the validity of embedding function theorem while computing the HEE and attempt to reproduce the first law of entanglement thermodynamics, at least at leading order. On the basis of obtained results, we also reflect upon consequences of applying Ryu-Takayanagi proposal on these non-Einstein geometries.

Effects of Cornell-type scalar potential on a generalized KG-oscillator field in Kaluza–Klein theory

We study a generalized KG-oscillator in the five-dimensional cosmic string geometry background with a magnetic field and quantum flux using Kaluza–Klein theory under the effects of a Cornell-type scalar potential, and observe the gravitational analogue of the Aharonov–Bohm effect. We see that the scalar potential allows the formation of bound states solution, and the energy eigenvalue depends on the global parameter characterizing the space–time. We also see that the magnetic field depends on quantum numbers of the relativistic system which shows a quantum effect.

String cosmology backgrounds from classical string geometry

We introduce a very early universe model based on the thermodynamics of a gas of closed strings in a background which is non-perturbative in $\alpha'$. Upon considering the fully $\alpha'$-corrected equations extended to include certain anisotropic cosmological backgrounds, we describe the evolution of the system in three different stages parametrized by the gas' equation of state. Using standard string thermodynamical arguments, we start with an isotropic 10-dimensional universe inside the string scale and evolve it towards a universe with four large spacetime dimensions and six stabilized internal dimensions in the Einstein frame.

Equivalence of solutions between the four-dimensional novel and regularized EGB theories in a cylindrically symmetric spacetime

Recently, a novel four-dimensional Einstein–Gauss–Bonnet (EGB) theory was presented to bypass the Lovelock’s theorem and to give nontrivial effects on the four-dimensional local gravity. The main mechanism is to introduce a redefinition alpha rightarrow alpha /(D-4) and to take the limit Drightarrow 4. However, this theory does not have standard four-dimensional field equations. Some regularization procedures are then proposed to address this problem (http://arxiv.org/abs/2003.11552, http://arxiv.org/abs/2003.12771, http://arxiv.org/abs/2004.08362, http://arxiv.org/abs/2004.09472, http://arxiv.org/abs/2004.10716). The resultant regularized four-dimensional EGB theory has the same on-shell action as the original theory. Thus it is expected that the novel four-dimensional EGB theory is equivalent to its regularized version. However, the equivalence of these two theories is symmetry-dependent. In this paper, we test the equivalence in a cylindrically symmetric spacetime. The well-defined field equations of the two theories are obtained, with which our follow-up analysis shows that they are equivalent in such spacetime. Cylindrical cosmic strings are then considered as specific examples of the metric. Three sets of solutions are obtained and the corresponding string mass densities are evaluated. The results reveal how the Gauss–Bonnet term in four dimensions contributes to the string geometry in the new theory.