Class Of 4d Research Articles

Shape reconfiguring bistable structures using heat activated fibers

Engineering structures have increasingly begun to utilize mechanical instability in areas such as energy absorption, shape reconfiguration, and vibration attenuation. Most multi-stable mechanisms use 1D architectures such as pre-curved beams or inclined trusses to achieve multiple strain energy minima. These structures pose several limitations, (1) they generally require external support for functionality, (2) they often balance the competing demands of large stiffness and large amplitude in shape change, and (3) they are inherently less energetically dense compared to shell-based structures as there is negligible stretching in the material. In this work, we introduce a novel class of 4D printed bistable shell structures that morph from flat surfaces. We investigate both the formation of the structural geometry, and the mechanics of the shells once morphed. Following the precepts of 4D printing, the structural geometry is achieved in two stages. First 3D printing is used to fabricate flat polygon unit cells which are then morphed into symmetrical bistable shells. Utilizing Fused Filament Fabrication, a viscoelastic material is pre-strained as it is deposited on the print bed. By tuning the printing parameters, a predictable 2D to 3D shape morphing is triggered with heat, resulting in a height increase of up to 22.9 times the original size. Some resulting unit cells exhibit an elastic bistable response with a high peak force from a point indentation. Shape morphing and structural bistability is predicted using Finite-Element Analysis with prescribed pre-strain aligned with the fiber extrusion direction. The resulting geometries are analyzed for their mechanical behavior. Buckling simulations show good agreement with experimental results. To demonstrate an energy-dissipating metamaterial, we fabricate a planar meta-surface tiled using triangular unit cells to create an auxetic pattern. This sheet morphs to conform to a doubly curved surface globally, with each unit-cell transforming to a bistable shell locally. With this approach, we create a new generation of 4D printed bistable structures that can be applied to a variety of engineering applications.

6D SCFTs, center-flavor symmetries, and Stiefel-Whitney compactifications

The center-flavor symmetry of a gauge theory specifies the global form of consistent gauge and flavor bundle background field configurations. For 6d gauge theories which arise from a tensor branch deformation of a superconformal field theory (SCFT), we determine the global structure of such background field configurations, including possible continuous Abelian symmetry and R-symmetry bundles. Proceeding to the conformal fixed point, this provides a prescription for reading off the global form of the continuous factors of the zero-form symmetry, including possible non-trivial mixing between flavor and R-symmetry. As an application, we show that this global structure leads to a large class of 4d $\mathcal{N} = 2$ SCFTs obtained by compactifying on a $T^2$ in the presence of a topologically non-trivial flat flavor bundle characterized by a 't Hooft magnetic flux. The resulting "Stiefel--Whitney twisted" compactifications realize several new infinite families of 4d $\mathcal{N} = 2$ SCFTs, and also furnish a 6d origin for a number of recently discovered rank one and two 4d $\mathcal{N} = 2$ SCFTs.

Yoga Dark Energy: natural relaxation and other dark implications of a supersymmetric gravity sector

We construct a class of 4D 'yoga' (naturally relaxed) models for which the gravitational response of heavy-particle vacuum energies is strongly suppressed. The models contain three ingredients: (i) a relaxation mechanism driven by a scalar field (the 'relaxon'), (ii) a very supersymmetric gravity sector coupled to the Standard Model in which supersymmetry is non-linearly realised, and (iii) an accidental approximate scale invariance expressed through the presence of a low-energy dilaton supermultiplet. All three are common in higher-dimensional and string constructions and although none suffices on its own, taken together they can dramatically suppress the net vacuum-energy density. The dilaton's vev τ determines the weak scale M W ∼ M p/√τ. We compute the potential for τ and find it can be stabilized in a local de Sitter minimum at sufficiently large field values to explain the size of the electroweak hierarchy, doing so using input parameters no larger than O(60) because the relevant part of the scalar potential arises as a rational function of lnτ. The de Sitter vacuum energy at the minimum is order c M 8 W α 1/τ 4, with a coefficient c ≪ \U0001d4aa(M W -4). We discuss ways to achieve c ∼ 1/M p 4 as required by observations. Scale invariance implies the dilaton couples to matter like a Brans-Dicke scalar with coupling large enough to be naively ruled out by solar-system tests of gravity. Yet because it comes paired with an axion it can evade fifth-force bounds through the novel screening mechanism described in arXiv:2110.10352. Cosmological axio-dilaton evolution predicts a natural quintessence model for Dark Energy, whose evolution might realize recent proposals to resolve the Hubble tension, and whose axion contributes to Dark Matter. We summarize inflationary implications and some remaining challenges, including the unusual supersymmetry breaking regime used and the potential for UV completions of our approach.

Holographic Duals of Argyres-Douglas Theories.

We propose the first explicit holographic duals for a class of superconformal field theories of Argyres-Douglas type, which are inherently strongly coupled and provide a window onto remarkable nonperturbative phenomena (such as mutually nonlocal massless dyons and relevant operators of fractional dimension). The theories under examination are realized by a stack of M5-branes wrapped on a sphere with one irregular puncture and one regular puncture. In the dual 11d supergravity solutions, the irregular puncture is realized as an internal M5-brane source.

Schur correlation functions from q -deformed Yang-Mills theory

We construct the wave functions in the $q$-deformed 2D Yang-Mills theory that compute torus correlation functions of affine currents in the vertex operator algebra associated to a class of 4D $\mathcal{N}=2$ superconformal field theory. These wave functions are then shown to reduce to the topological correlators of a set of Coulomb branch operators in the $T[SU(N)]$ theory, from which those correlators in the 3D mirror dual of the 4D ${T}_{N}$ theories can be computed.

Machine learning of Calabi-Yau volumes

We employ machine learning techniques to investigate the volume minimum of Sasaki-Einstein base manifolds of non-compact toric Calabi-Yau 3-folds. We find that the minimum volume can be approximated via a second order multiple linear regression on standard topological quantities obtained from the corresponding toric diagram. The approximation improves further after invoking a convolutional neural network with the full toric diagram of the Calabi-Yau 3-folds as the input. We are thereby able to circumvent any minimization procedure that was previously necessary and find an explicit mapping between the minimum volume and the topological quantities of the toric diagram. Under the AdS/CFT correspondence, the minimum volumes of Sasaki-Einstein manifolds correspond to central charges of a class of 4d N=1 superconformal field theories. We therefore find empirical evidence for a function that gives values of central charges without the usual extremization procedure.

Phase space quantization, noncommutativity, and the gravitational field

In this paper we study the structure of the phase space in noncommutative geometry in the presence of a nontrivial frame. Our basic assumptions are that the underlying space is a symplectic and parallelizable manifold. Furthermore, we assume the validity of the Leibniz rule and the Jacobi identities. We consider noncommutative spaces due to the quantization of the symplectic structure and determine the momentum operators that guarantee a set of canonical commutation relations, appropriately extended to include the nontrivial frame. We stress the important role of left vs. right acting operators and of symplectic duality. This enables us to write down the form of the full phase space algebra on these noncommutative spaces, both in the noncompact and in the compact case. We test our results against the class of 4D and 6D symplectic nilmanifolds, thus presenting a large set of nontrivial examples that realize the general formalism.

Bipartite field theories from D-branes

We develop tools for determining the gauge theory resulting from a configuration of Type IIB D3-branes probing a non-compact, toric Calabi-Yau 3-fold, in the presence of additional flavor D7-branes with general embeddings. Two main ingredients of our approach are dimer models and mirror symmetry. D7-branes with general embeddings are obtained by recombination of elementary D7-brane constituents. These tools are then used to engineer a large set of Bipartite Field Theories, a class of 4d, N=1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces. Several explicit examples, including infinite families of models, associated to both planar and non-planar graphs are presented.

Supersymmetric gauge theory, (2,0) theory and twisted 5d Super-Yang-Mills

Twisted compactification of the 6d N=(2,0) theories on a punctured Riemann surface give a large class of 4d N=1 and N=2 gauge theories, called class S. We argue that nonperturbative dynamics of class S theories are described by 5d maximal Super-Yang-Mills (SYM) twisted on the Riemann surface. In a sense, twisted 5d SYM might be regarded as a "Lagrangian" for class S theories on R^{1,2} times S^1. First, we show that twisted 5d SYM gives generalized Hitchin's equations which was proposed recently. Then, we discuss how to identify chiral operators with quantities in twisted 5d SYM. Mesons, or holomorphic moment maps, are identified with operators at punctures which are realized as 3d superconformal theories T_rho[G] coupled to twisted 5d SYM. "Baryons" are identified qualitatively through a study of 4d N=2 Higgs branches. We also derive a simple formula for dynamical superpotential vev which is relevant for BPS domain wall tensions. With these tools, we examine many examples of 4d N=1 theories with several phases such as confining, Higgs, and Coulomb phases, and show perfect agreements between field theories and twisted 5d SYM. Spectral curve is an essential tool to solve generalized Hitchin's equations, and our results clarify the physical information encoded in the curve.

Cluster transformations from bipartite field theories

Bipartite field theories (BFTs) are a new class of 4d N=1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces. In this paper we derive, purely in terms of the gauge theory, the cluster transformations of face weights under square moves in the graph. In this context, we obtain them by connecting regular parametrizations of the master space of the associated BFTs. For BFTs on a disk, these transformations follow from the properties of coordinates in the Grassmannian. This represents a new addition to the list of combinatorial objects for the Grassmannian, such as matching and matroid polytopes, that have been shown to emerge from BFT dynamics.

New directions in bipartite field theories

We perform a detailed investigation of Bipartite Field Theories (BFTs), a general class of 4d N=1 gauge theories which are defined by bipartite graphs. This class of theories is considerably expanded by identifying a new way of assigning gauge symmetries to graphs. A new procedure is introduced in order to determine the toric Calabi-Yau moduli spaces of BFTs. For graphs on a disk, we show that the matroid polytope for the corresponding cell in the Grassmannian coincides with the toric diagram of the BFT moduli space. A systematic BFT prescription for determining graph reductions is presented. We illustrate our ideas in infinite classes of BFTs and introduce various operations for generating new theories from existing ones. Particular emphasis is given to theories associated to non-planar graphs.

On algebraically special vacuum spacetimes in five dimensions

Vacuum solutions admitting a hypersurface-orthogonal repeated principal null direction are an important class of 4D algebraically special spacetimes. We investigate the 5D analogues of such solutions: vacuum spacetimes admitting a hypersurface-orthogonal multiple Weyl aligned null direction (WAND). Such spacetimes fall into four families determined by the rank of the 3 × 3 matrix that defines the expansion and shear of the multiple WAND. The rank 3 and rank 0 cases have been studied previously. We investigate the two remaining families. We show how to define coordinates which lead to a considerable simplification of the Einstein equation with cosmological constant. The rank 2 case gives warped product and Kaluza–Klein versions of the 4D Robinson–Trautman solutions as well as some new solutions. The rank 1 case gives product, or analytically continued Schwarzschild, spacetimes.

Bipartite field theories: from D-brane probes to scattering amplitudes

Abstract We introduce and initiate the investigation of a general class of 4d, $\mathcal{N}=1$ quiver gauge theories whose Lagrangian is defined by a bipartite graph on a Riemann surface, with or without boundaries. We refer to such class of theories as Bipartite Field Theories (BFTs). BFTs underlie a wide spectrum of interesting physical systems, including: D3-branes probing toric Calabi-Yau 3-folds, their mirror configurations of D6-branes, cluster integrable systems in (0 + 1) dimensions and leading singularities in scattering amplitudes for $\mathcal{N}=4$ SYM. While our discussion is fully general, we focus on models that are relevant for scattering amplitudes. We investigate the BFT perspective on graph modifications, the emergence of Calabi-Yau manifolds (which arise as the master and moduli spaces of BFTs), the translation between square moves in the graph and Seiberg duality and the identification of dual theories by means of the underlying Calabi-Yaus, the phenomenon of loop reduction and the interpretation of the boundary operator for cells in the positive Grassmannian as higgsing in the BFT. We develop a technique based on generalized Kasteleyn matrices that permits an efficient determination of the Calabi-Yau geometries associated to arbitrary graphs. Our techniques allow us to go beyond the planar limit by both increasing the number of boundaries of the graphs and the genus of the underlying Riemann surface. Our investigation suggests a central role for Calabi-Yau manifolds in the context of leading singularities, whose full scope is yet to be uncovered.

Network and Seiberg duality

We define and study a new class of 4d N=1 superconformal quiver gauge theories associated with a planar bipartite network. While UV description is not unique due to Seiberg duality, we can classify the IR fixed points of the theory by a permutation, or equivalently a cell of the totally non-negative Grassmannian. The story is similar to a bipartite network on the torus classified by a Newton polygon. We then generalize the network to a general bordered Riemann surface and define IR SCFT from the geometric data of a Riemann surface. We also comment on IR R-charges and superconformal indices of our theories.

On a class of 4D Kähler bases and AdS5supersymmetric black holes

We construct a class of toric Kahler manifolds, M_4, of real dimension four, a subset of which corresponds to the Kahler bases of all known 5D asymptotically AdS_5 supersymmetric black-holes. In a certain limit, these Kahler spaces take the form of cones over Sasaki spaces, which, in turn, are fibrations over toric manifolds of real dimension two. The metric on M_4 is completely determined by a single function H(x), which is the conformal factor of the two dimensional space. We study the solutions of minimal five dimensional gauged supergravity having this class of Kahler spaces as base and show that in order to generate a five dimensional solution H(x) must obey a simple sixth order differential equation. We discuss the solutions in detail, which include all known asymptotically AdS_5 black holes as well as other spacetimes with non-compact horizons. Moreover we find an infinite number of supersymmetric deformations of these spacetimes with less spatial isometries than the base space. These deformations vanish at the horizon, but become relevant asymptotically.

Singularities, gauge dynamics, and non-perturbative superpotentials in string theory

We describe a class of 4D N = 1 compactifications of the SO(32) heterotic/type I string theory which are destabilized by non-perturbatively generated superpotentials. In the type I description, the destabilizing superpotential is generated by a one instanton effect or gaugino condensation in a non-perturbative SU(2) gauge group. The dual, heterotic description involves destabilization due to world-sheet instanton or half world-sheet instanton effects in the two cases. A genericity argument suggests that a (global) supersymmetry-breaking model of Intriligator and Thomas might be typical in a class of string theory models. Our analysis also suggests that the tensionless strings which arise in the E 8 × E 8 theory in six dimensions when an instanton shrinks to zero size should, in some cases, have supersymmetry breaking dynamics upon further compactification to four dimensions. We provide explicit examples, constructed using F-theory, of the two cases of dynamically generated superpotentials.

Anisotropic spacetimes in homogeneous string cosmology

The dynamics of the early universe may have been profoundly influenced by spatial anisotropies. A search for such backgrounds in the context of string cosmology has uncovered the existence of an entire class of 4D spatially homogeneous but not necessarily isotropic spacetimes, analogous to the class of Bianchi-type models in general relativity. Leading-order solutions with vanishing cosmological constant but with non-vanishing dilaton and antisymmetric field are explicitly found for all types. This is a new class of solutions, whose isotropy limits reproduce all known and, further, all possible FRW-type of models in the string effective-action context considered. There is always an initial singularity and no inflation. Other features of the general solutions, including their behavior under abelian T duality are also discussed.