4D Theory Research Articles

Automated consistent truncations and stability of flux compactifications

Classical flux compactifications contribute to a well-controlled corner of the string landscape, therefore providing an important testing ground for a variety of conjectures. We focus here on type II supergravity compactifications on 6d group manifolds towards 4d maximally symmetric spacetimes. We develop a code where the truncation to left-invariant scalars and the dimensional reduction to a 4d theory are automated, for any possible configuration of Op-planes and Dp-branes. We then prove that any such truncation is consistent. We further compute the mass spectrum and analyse the stability of many de Sitter, Minkowski or anti-de Sitter solutions, as well as their consistency with swampland conjectures.

A 5d perspective on the compactifications of 6d SCFTs to 4d mathcal{N} = 1 SCFTs

Compactifying 6d superconformal field theories (SCFTs) to 4d mathcal{N} = 1 theories on two-punctured spheres (tubes) and tori with flux is realized using duality domain walls in 5d mathcal{N} = 1 Kaluza-Klein (KK) theories, which are usually denoted by flux domain walls. We revisit this construction and study it in detail from the 5d perspective, specifically rephrasing it using the box graph description of the extended Coulomb branch phases of 5d theories. This perspective could be helpful in understanding how to equivalently realize the 4d mathcal{N} = 1 models from geometric engineering in M-theory. Along the way, we show how to recover various properties of the 4d theories from the 5d perspective, such as the flux associated to the domain wall configurations and the presence of a mathfrak{u} (1) global symmetry in the 4d theory descending from the KK symmetry on the tube, which is broken to a discrete subgroup on a flux torus. We demonstrate all of these ideas using the rank 1 E-string theory.

Pengembangan Video Powerpoint Tutorial Dalam Pembelajaran Tematik Kelas II SD Muhammadiyah 2 Pontianak

During the Covid-19 pandemic, learning process cannot be done by face-to-face so teachers are required to be creative in choosing learning media. Based on these problems, a video powerpoint tutorial product was developed in the thematic learning for the Second Grade of Muhammadiyah Elementary School 2 Pontianak in order to describe the results of validation and student responses.. The research design used in this research was Research and Development (RnD) by utilizing 4D theory from Thiagarajan that consisted of 4 steps such as define, design, develop, and dissemination. The product of this research and development was a PowerPoint Tutorial Video for Thematic teaching and Learning in which the validity had been tested by the experts. The result from the experts' validation proposed that the product scored 91.25% for its advisability in the aspect of teaching & learning (materials), 88.75% in the aspect of its media (display), and 72.5% in the aspect of language. Furthermore, the simplicity of this product also had been tested based on the 60 students' responses with the average score 3.37 in percentage of 84%. Therefore, according to the students’ responses score, it can be concluded the product was considered good and advisable to use.

Yangian Symmetry in Five Dimensions.

Quantum gravity in AdS_{7}×S^{4} is dual to a six-dimensional (6D) superconformal field theory, known as the 6D (2,0) theory, which is very challenging to describe because it lacks a conventional Lagrangian description. On the other hand, certain null reductions of the 6D (2,0) theory give rise to 5D Lagrangian theories with SU(1,3) spacetime symmetry, SO(5) R symmetry, and 24 supercharges. This appears to be closely related to the superconformal group of a 3D superconformal Chern-Simons theory known as the Aharony-Bergman-Jafferis-Maldacena theory, which is believed to be integrable in the planar limit, if one exchanges the role of conformal and R symmetry. In this Letter, we construct a representation of the 5D superconformal group using 6D supertwistors and show that it admits an infinite dimensional extension known as Yangian symmetry, which opens up the possibility that these 5D theories are exactly solvable in the planar limit.

Higgs branch, Coulomb branch, and Hall-Littlewood index

The Higgs branch of 4D $\mathcal{N}=2$ superconformal field theories can be analyzed via the Hilbert series of the Higgs branch or, in special cases, by computing the Hall-Littlewood index. For any class $\mathcal{S}$ theory corresponding to a genus-zero Riemann surface, they are conjectured to be identical. We present several families of counterexamples. We find that for any class $\mathcal{S}$ theory with four or more ${\mathbb{Z}}_{2}$-twisted punctures, they do not match. We construct 3D mirrors for such theories and analyze their Coulomb branch Hilbert series to compute the Higgs branch Hilbert series of the 4D theory. We further construct $a=c$ theories in class $\mathcal{S}$ using the twisted punctures, and these theories, which includes the ${\stackrel{^}{D}}_{4}(SU(2n+1))$ theories, have Hall-Littlewood index different from the Hilbert series of the Higgs branch. We conjecture that this is the case for all $a=c$ theories with nonempty Higgs branch, including $\mathcal{N}\ensuremath{\ge}3$ superconformal field theories.

AGT correspondence, (q-)Painlevè equations and matrix models

Painlevè equation for conformal blocks is a combined corollary of integrability and Ward identities, which can be explicitly revealed in the matrix model realization of AGT relations. We demonstrate this in some detail, both for q-Painlevè equations for the q-Virasoro conformal block, or AGT dual gauge theory in 5d, and for ordinary Painlevè equations, or AGT dual gauge theory in 4d. Especially interesting is the continuous limit from 5d to 4d and its description at the level of equations for eight τ-functions. Half of these equations are governed by integrability and another half by Ward identities.

Higher form symmetries TFT in 6d

Symmetries and anomalies of a d-dimensional quantum field theory are often encoded in a (d + 1)-dimensional topological action, called symmetry topological field theory (TFT). We derive the symmetry TFT for the 2-form and 1-form symmetries of 6d (1, 0) field theories, focusing on theories with a single tensor multiplet (rank 1). We implement this by coupling the low-energy tensor branch action to the background fields for the higher-form symmetries and by looking at the symmetry transformation rules on dynamical and background fields. These transformation rules also imply a mixing of the higher-form symmetries in a 3-group structure. For some specific and related higher rank cases, we also derive the symmetry TFT from the holographic dual IIA supergravity solutions. The symmetry TFT action contains a coupling between the 2-form symmetry and the 1-form symmetry backgrounds, which leads to a mixed anomaly between the 1-form symmetries of the 5d KK-theory obtained by circle compactification. We confirm this by a pure 5d analysis provided by the 5d effective low-energy Coulomb branch Lagrangian coupled to background fields. We also derive the symmetry TFT for 5d SU(p) supersymmetric gauge theories with Chern-Simons level q and for 5d theories without non-abelian gauge theory description at low-energy. Finally, we discuss the fate of the 2-form and 1-form symmetry of rank 1 6d field theories when coupled to gravity.

2-Group symmetries and M-theory

Quantum Field Theories engineered in M-theory can have 2-group symmetries, mixing 0-form and 1-form symmetry backgrounds in non-trivial ways. In this paper we develop methods for determining the 2-group structure from the boundary geometry of the M-theory background. We illustrate these methods in the case of 5d theories arising from M-theory on ordinary and generalised toric Calabi-Yau cones, including cases in which the resulting theory is non-Lagrangian. Our results confirm and elucidate previous results on 2-groups from geometric engineering.

Pairwise Multiparticle States and the Monopole Unitarity Puzzle.

We suggest a novel resolution for a decades old mystery-what happens when a positron scatters off a minimal grand-unification-theory monopole in an s wave, a puzzle first discussed by Callan in 1983. Using the language of on shell amplitudes and pairwise helicity we suggest that the final state contains two up quarks and a down quark in an entangled "pairwise" multiparticle state-the only particle final state that satisfies angular momentum and gauge charge conservation. The cross section for this process is as large as in the original Rubakov-Callan effect, only suppressed by the QCD scale. The final state we find cannot be seen in Callan's truncated 2D theory, since our new pairwise state appears only in more than two dimensions.

Holonomy saddles and 5d BPS quivers

We study the Seberg-Witten geometry of 5d mathcal{N} = 1 pure Yang-Mills theories compactified on a circle. The concept of the holonomy saddle implies that there are multiple 4d limits of interacting Seiberg-Witten theories from a single 5d theory, and we explore this in the simplest case of pure SU(N) theories. The compactification leads to N copies of locally indistinguishable 4d pure SU(N) Seiberg-Witten theories in the infrared, glued together in a manner dictated by the Chern-Simons level. We show how this picture naturally builds the 5d BPS quivers which agree with the D0 probe dynamics previously proposed via the geometrically engineered local Calabi-Yau. We work out various SU(2) and SU(3) examples through a detailed look at the respective spectral curves. We also note a special ℤ2N feature of SU(N)N spectral curves and the resulting BPS quivers, with emphasis on how the 4d holonomy saddles are affected.

Two 6D origins of 4D SCFTs: Class S and 6D (1, 0) on a torus

We consider all 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$ arising from the compactification of exceptional 6d $(2,0)$ SCFTs on a three-punctured sphere with a simple puncture. We find that each of these 4d theories has another origin as a 6d $(1,0)$ SCFT compactified on a torus, which we check by identifying and comparing the central charges and the flavor symmetry. Each 6d theory is identified with a complex structure deformation of $(\mathfrak{e}_n,\mathfrak{e}_n)$ minimal conformal matter, which corresponds to a Higgs branch renormalization group flow. We find that this structure is precisely replicated by the partial closure of the punctures in the class $\mathcal{S}$ construction. We explain how the plurality of origins makes manifest some aspects of 4d SCFTs, including flavor symmetry enhancements and determining if it is a product SCFT. We further highlight the string theoretic basis for this identification of 4d theories from different origins via mirror symmetry.

Dark dimension, the swampland, and the dark matter fraction composed of primordial black holes

Very recently, it was suggested that combining the Swampland program with the smallness of the dark energy and confronting these ideas to experiment lead to the prediction of the existence of a single extra-dimension (dubbed the dark dimension) with characteristic length-scale in the micron range. We show that the rate of Hawking radiation slows down for black holes perceiving the dark dimension and discuss the impact of our findings in assessing the dark matter fraction that could be composed of primordial black holes. We demonstrate that for a species scale of ${\cal O}(10^{10}~{\rm GeV})$, an all-dark-matter interpretation in terms of primordial black holes should be feasible for masses in the range $10^{14} \leq M_{BH}/{\rm g}\leq 10^{21}$. This range is extended compared to that in the 4D theory by 3 orders of magnitude in the low mass region. We also show that PBHs with $M_{\rm BH} \sim 10^{12}~{\rm g}$ could potentially explain the well-known Galactic 511 keV gamma-ray line if they make up a tiny fraction of the total dark matter density.

Can one hear the shape of a wormhole?

A large class of flat big bang-big crunch cosmologies with negative cosmological constant are related by analytic continuation to asymptotically AdS traversable wormholes with planar cross section. In recent works (arXiv:2102.05057, arXiv:2203.11220) it was suggested that such wormhole geometries may be dual to a pair of 3D holographic CFTs coupled via auxiliary degrees of freedom to give a theory that confines in the infrared. In this paper, we explore signatures of the presence of such a wormhole in the state of the coupled pair of 3D theories. We explain how the wormhole geometry is reflected in the spectrum of the confining theory and the behavior of two-point functions and entanglement entropies. We provide explicit algorithms to reconstruct the wormhole scale factor (which uniquely determines its geometry) from entanglement entropies, heavy operator two-point functions, or light operator two-point functions (which contain the spectrum information). In the last case, the physics of the bulk scalar field dual to the light operator is closely related to the quantum mechanics of a one-dimensional particle in a potential derived from the scale factor, and the problem of reconstructing the scale factor from the two-point function is directly related to the problem of reconstructing this Schrödinger potential from its spectrum.

The geometry of decoupling fields

We consider 4d field theories obtained by reducing the 6d (1,0) SCFT of N M5-branes probing a ℂ2/ℤk singularity on a Riemann surface with fluxes. We follow two different routes. On the one hand, we consider the integration of the anomaly polynomial of the parent 6d SCFT on the Riemann surface. On the other hand, we perform an anomaly inflow analysis directly from eleven dimensions, from a setup with M5-branes probing a resolved ℂ2/ℤk singularity fibered over the Riemann surface. By comparing the 4d anomaly polynomials, we provide a characterization of a class of modes that decouple along the RG flow from six to four dimensions, for generic N, k, and genus. These modes are identified with the flip fields encountered in the Lagrangian descriptions of these 4d models, when they are available. We show that such fields couple to operators originating from M2-branes wrapping the resolution cycles. This provides a geometric origin of flip fields. They interpolate between the 6d theory in the UV, where the M2-brane operators are projected out, and the 4d theory in the IR, where these M2-brane operators are part of the spectrum.

M5 branes on ℝ1,1×Taub-NUT

We study M5 branes on ℝ1,1×Taub-NUT that we view as a singular fibration. Reducing the M5 branes along the fiber gives 5d SYM. Due to the singularity, this 5d theory has a gauge anomaly and it is not supersymmetric. To cure these problems we add a supersymmetric gauged chiral WZW theory on the 2d submanifold where the circle fiber vanishes. In addition we add a mass term for the five scalar fields located on this submanifold. With all this, we obtain a fully supersymmetric and gauge invariant theory.

Multi-channel Luttinger Liquids at the Edge of Quantum Hall Systems

We consider the edge transport properties of a generic class of interacting quantum Hall systems on a cylinder, in the infinite volume and zero temperature limit. We prove that the large-scale behavior of the edge correlation functions is effectively described by the multi-channel Luttinger model. In particular, we prove that the edge conductance is universal, and equal to the sum of the chiralities of the non-interacting edge modes. The proof is based on rigorous renormalization group methods, that allow to fully take into account the effect of backscattering at the edge. Universality arises as a consequence of the integrability of the emergent multi-channel Luttinger liquid combined with lattice Ward identities for the microscopic 2d theory.

Distinguishing 6D (1, 0) SCFTs: An extension to the geometric construction

We provide a new extension to the geometric construction of 6d $(1,0)$ SCFTs that encapsulates Higgs branch structures with identical global symmetry but different spectra. In particular, we find that there exist distinct 6d $(1,0)$ SCFTs that may appear to share their tensor branch description, flavor symmetry algebras, and central charges. For example, such subtleties arise for the very even nilpotent Higgsing of $(\mathfrak{so}_{4k}, \mathfrak{so}_{4k})$ conformal matter; we propose a method to predict at which conformal dimension the Higgs branch operators of the two theories differ via augmenting the tensor branch description with the Higgs branch chiral ring generators of the building block theories. Torus compactifications of these 6d $(1,0)$ SCFTs give rise to 4d $\mathcal{N}=2$ SCFTs of class $\mathcal{S}$ and the Higgs branch of such 4d theories are captured via the Hall--Littlewood index. We confirm that the resulting 4d theories indeed differ in their spectra in the predicted conformal dimension from their Hall--Littlewood indices. We highlight how this ambiguity in the tensor branch description arises beyond the very even nilpotent Higgsing of $(\mathfrak{so}_{4k}, \mathfrak{so}_{4k})$ conformal matter, and hence should be understood for more general classes of 6d $(1,0)$ SCFTs.

Deformed integrable models from holomorphic Chern-Simons theory

We study the approaches to two-dimensional integrable field theories via a six-dimensional(6D) holomorphic Chern-Simons theory defined on twistor space. Under symmetry reduction, it reduces to a four-dimensional Chern-Simons theory, while under solving along fibres it leads to four-dimensional(4D) integrable theory, the anti-self-dual Yang-Mills or its generalizations. From both four-dimensional theories, various two-dimensional integrable field theories can be obtained. In this work, we try to investigate several two-dimensional integrable deformations in this framework. We find that the $\lambda$-deformation, the rational $\eta$-deformation and the generalized $\lambda$-deformation can not be realized from 4D integrable model approach, even though they could be obtained from 4D Chern-Simons theory. The obstacle stems from the incompatibility between the symmetry reduction and the boundary conditions. Nevertheless, we show that a coupled theory of $\lambda$-deformation and the $\eta$-deformation in the trigonometric description could be obtained from the 6D theory in both ways, by considering the case that $(3,0)$-form in the 6D theory is allowed to have zeros.

Exceptional moduli spaces for exceptional mathcal{N} = 3 theories

It is expected on general grounds that the moduli space of 4d mathcal{N} = 3 theories is of the form ℂ3r/Γ, with r the rank and Γ a crystallographic complex reflection group (CCRG). As in the case of Lie algebras, the space of CCRGs consists of several infinite families, together with some exceptionals. To date, no 4d mathcal{N} = 3 theory with moduli space labelled by an exceptional CCRG (excluding Weyl groups) has been identified. In this work we show that the 4d mathcal{N} = 3 theories proposed in [1], constructed via non-geometric quotients of type- mathfrak{e} 6d (2,0) theories, realize nearly all such exceptional moduli spaces. In addition, we introduce an extension of this construction to allow for twists and quotients by outer automorphism symmetries. This gives new examples of 4d mathcal{N} = 3 theories going beyond simple S-folds.

Meshfree dynamic analysis of functionally graded carbon nanotube reinforced polymer sandwich beams under harmonic moving loads

ABSTRACT A new generation of advanced composite materials has recently emerged through the use of Carbon Nanotubes (CNTs) as the reinforcing constituent in polymer matrix. In this paper, the dynamic response of polymer sandwich beams with functionally graded face sheets subject to two successive harmonic moving loads has been studied. Three different patterns of CNT’s distributions for the face sheets have been investigated: Uniform Distribution (UD), Symmetrically Functionally Graded (SFG) distribution, and Unsymmetrically Functionally Graded (USFG) distribution. A thorough study on the effects of velocity, position, excitation frequency, and the phase angles of loads has been carried out using the Radial Point Interpolation Meshfree (RPIM) method based on the 2D theory of elasticity. The SFG is found to result in the highest stiffness of all three distribution patterns. Increasing the volume fraction of the reinforcement is seen to have resulted in an increase of around 33% in the flexural rigidity of the SFG beam. Also, decreasing the frequency is seen to have suppressed the deflection of the USFG type up to 90%. The current research presents a reliable computational framework to help provide an insight into the design of an optimum sandwich structure subject to a complicated state of loading.