We study the interplay between T-duality, compactification and supersymmetry. We prove that when the original configuration has unbroken space-time supersymmetries, the dual configuration also does if a special condition is met: the Killing spinors of the original configuration have to be independent on the coordinate which corresponds to the isometry direction of the bosonic fields used for du...

We find M-theory (Type IIA) duals for compactifications of the 9d CHL string to 5d (4d) on K3 (K3 × S 1). The IIA duals are Calabi-Yau orbifolds with nontrivial RR U (1) In ten dimensions, the consistent critical string theories with (at least) sixteen super-charges have been known since the 1980s. There are (after accounting for the S-duality of the two SO(32) theories) four. In D = 9, in addi...

[A] M. Svensson, On holomorphic harmonic morphisms, Manuscripta Math. 107 (2002), 1–13. [B] M. Svensson, Harmonic morphisms from even-dimensional hyperbolic spaces, Math. Scand. 92 (2003), 246–260. [C] M. Svensson, Holomorphic foliations, harmonic morphisms and the Walczak formula, J. London Math. Soc. 68 (2003), 781–794. [D] M. Svensson, Harmonic morphisms in Hermitian geometry, J. Reine Angew...

In this note we look at a number of infinite-dimensional R-vector spaces that arise in analysis, and we consider their dual and double dual spaces. As an application, we give an example of an infinite-dimensional vector space V for which the natural map η : V → V ∗∗ is not an isomorphism. In analysis, duals and double duals of vector spaces are often defined differently than in algebra, by cons...

We find regular string duals of three dimensional N = 1 SYM with a Chern-Simons interaction at level k for SO and Sp gauge groups. Using the string dual we exactly reproduce the conjectured pattern of supersymmetry breaking proposed by Witten by showing that there is dynamical supersymmetry breaking for k < h/2 while supersymmetry remains unbroken for k ≥ h/2, where h is the dual Coxeter number...

We consider the question of determining the higher weights or the generalized Hamming weights of affine Grassmann codes and their duals. Several initial as well as terminal higher weights of affine Grassmann codes of an arbitrary level are determined explicitly. In the case of duals of these codes, we give a formula for many initial as well as terminal higher weights. As a special case, we obta...

Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R4 can be described as certain 2-morphisms in the 2-category of ‘2-tangles in 4 dimensions’. Using the work of Carter, Rieger and Saito, we prove that this 2-category is the ‘free semistrict braided monoidal 2-category with duals on one un...

In this work we study the duality for a general multiobjective optimization problem. Considering, first, a scalar problem, different duals using the conjugacy approach are presented. Starting from these scalar duals, we introduce six different multiobjective dual problems to the primal one, one depending on certain vector parameters. The existence of weak and, under certain conditions, of stron...

We construct metastable configurations of branes and anti-branes wrapping 2-spheres inside local Calabi-Yau manifolds and study their large N duals. These duals are CalabiYau manifolds in which the wrapped 2-spheres have been replaced by 3-spheres with flux through them, and supersymmetry is spontaneously broken. The geometry of the nonsupersymmetric vacuum is exactly calculable to all orders o...

We study the black hole black string phase transitions of gravitational theories compactified on a circle using the holographic duality conjecture. The gauge theory duals of these theories are maximally supersymmetric and strongly coupled 1 + 1 dimensional SU(N) Yang-Mills theories compactified on a circle, in the large N limit. We perform the strongly coupled finite temperature gauge theory ca...