We discuss an orbifold of the toroidally compactified heterotic string which gives a global reduction of the dimension of the moduli space while preserving the supersymmetry. This construction yields the moduli space of the first of a series of reduced rank theories with maximal supersymmetry discovered recently by Chaudhuri, Hockney, and Lykken. Such moduli spaces contain nonsimply-laced enhanced symmetry points in any spacetime dimension D<10. Precisely in D=4 the set of allowed gauge groups is invariant under electricmagnetic duality, providing further evidence for S-duality of the D=4 heterotic string.

The existence of maximally supersymmetric solutions to heterotic string theory that are not toroidal compactifications of the ten-dimensional superstring is established. We construct an exact fermionic realization of an % = 1 supersymmetric string theory in D = 8 with non-simply-laced gauge group Sp(20). Toroidal compactification to six and four dimensions gives maximally extended supersymmetric theories with reduced rank (4, 12) and (6, 14), respectively. PACS numbers: 11.25.Mj, 11. 25.Hf Finiteness is a robust property of the perturbative amplitudes of the known superstring theories. N = 4 supersymmetric Yang-Mills theory is known to be finite in four dimensions [1], and there is growing evidence that the theory exhibits an extension of Olive-Montonen strong-weak coupling duality known as 5 duality [2,3]. A generalization of the Olive-Montonen duality of N = 4 theories has also been identified in N = 1 supersymmetric Yang-Mills theory [4]. In string theory, conjectures for 5 duality have mostly been explored in the context of toroidal compactifications of the ten-dimensional heterotic string to spacetime dimensions D ( 10 [5].It would be helpful to have insight into the generic moduli space, and the generic duality group, of such maximally supersymmetric string theories. We will therefore consider the possibility of exact solutions to string theory beyond those obtained by dimensional reduction from a ten-dimensional superstring.These solutions are exact in the sigma model (n') expansion but are perturbative in the string coupling constant. To be specific, we will construct solutions to heterotic string theory, i.e. , with (NR, Nt ) = (2, 0) superconformal invariance on the world sheet. Our construction is, however, quite general, and the conclusions can be adapted to solutions of any closed string theory in any spacetime dimension.Toroidal compactification of the ten-dimensional N = I heterotic string to six (four) dimensions results in a lowenergy effective N = 2 (N = 4) supergravity coupled to 20 (22) Abelian vector multiplets, giving a total of 24 (28) Abelian vector gauge fields with gauge group (U(1)) ((U(1)) ), respectively. Four (six) of these Abelian multiplets are contained within the N = 2 (N = 4) supergravity multiplets. At enhanced symmetry points in the moduli space the Abelian group (U(1))zo ((U(1))z2) is enlarged to a simply laced group of rank 20 (22). The lowenergy field theory limit of such a solution has maximally extended spacetime supersymmetry.Since all of the elementary scalars appear in the adjoint representation of the gauge group, symmetry breaking via the Higgs mecha-nism is adequate in describing the moduli space of vacua with a fixed number of Abelian multiplets.In this Letter we show that there exist maximally supersymmetric vacua with four-, six-, and eight-dimensional Lorentz invariance that are not obtained by toroidal compactification of a ten-dimensional heterotic string. The total number of Abelian vector multiplets in the fourdimensional theory can be reduced to just six, n...

This paper introduces a deep architecture for segmenting 3D objects into their labeled semantic parts. Our architecture combines image-based Fully Convolutional Networks (FCNs) and surface-based Conditional Random Fields (CRFs) to yield coherent segmentations of 3D shapes. The image-based FCNs are used for efficient view-based reasoning about 3D object parts. Through a special projection layer, FCN outputs are effectively aggregated across multiple views and scales, then are projected onto the 3D object surfaces. Finally, a surface-based CRF combines the projected outputs with geometric consistency cues to yield coherent segmentations. The whole architecture (multi-view FCNs and CRF) is trained end-to-end. Our approach significantly outperforms the existing stateof-the-art methods in the currently largest segmentation benchmark (ShapeNet). Finally, we demonstrate promising segmentation results on noisy 3D shapes acquired from consumer-grade depth cameras.

Figure 1: Given 100 training airplanes (green), our probabilistic model synthesizes 1267 new airplanes (blue). AbstractWe present an approach to synthesizing shapes from complex domains, by identifying new plausible combinations of components from existing shapes. Our primary contribution is a new generative model of component-based shape structure. The model represents probabilistic relationships between properties of shape components, and relates them to learned underlying causes of structural variability within the domain. These causes are treated as latent variables, leading to a compact representation that can be effectively learned without supervision from a set of compatibly segmented shapes. We evaluate the model on a number of shape datasets with complex structural variability and demonstrate its application to amplification of shape databases and to interactive shape synthesis.

We obtain three generation SU (3) c ×SU (2) L ×U (1) Y string models in all of the exactly solvable (0, 2) constructions sampled by fermionization. None of these examples, including those that are symmetric abelian orbifolds, rely on the Z 2 ×Z 2 orbifold underlying the NAHE basis. We present the first known three generation models for which the hypercharge normalization, k 1 , takes values smaller than that obtained from an SU (5) embedding, thus lowering the effective gauge coupling unification scale. All of the models contain fractional electrically charged and vectorlike exotic matter that could survive in the light spectrum.10/95 †