Working with anticommuting Weyl (or Majorana) spinors in the frame of the van der Waerden calculus is standard in supersymmetry. The natural framework of rigorous supersymmetric quantum field theory makes use of operator-valued superdistributions defined on supersymmetric test functions. This makes necessary a van der Waerden calculus in which the Grassmann variables anticommute but the fermion...

We investigate some aspects of Moyal-Weyl deformations of superspace and their compatibility with supersymmetry. For the simplest case, when only bosonic coordinates are deformed, we consider a four dimensional supersymmetric field theory which is the deformation of the Wess-Zumino renormalizable theory of a chiral superfield. We then consider the deformation of a free theory of an abelian vect...

These notes are based on lectures given by C. Callan and J. Harvey at the 1991 Trieste Spring School on String Theory and Quantum Gravity. The subject is the construction of supersymmetric soliton solutions to superstring theory. A brief review of solitons and instantons in supersymmetric theories is presented. Yang-Mills instantons are then used to construct soliton solutions to heterotic stri...

It has recently been argued that the confining vacua of Yang-Mills theory in the far infrared can have topological degrees of freedom given by magnetic Zq gauge field, both in the non-supersymmetric case and in the N = 1 supersymmetric case. In this short note we give another piece of evidence by computing and matching the supersymmetric index of the pure super Yang-Mills theory both in the ult...

In the first part of this paper we find supergravity solutions corresponding to branes on worldvolumes of the form R × Σ where Σ is a Riemann surface. These theories arise when we wrap branes on holomorphic Riemann surfaces inside K3 or CY manifolds. In some cases the theory at low energies is a conformal field theory with two less dimensions. We find some non-singular supersymmetric compactifi...

We find a regular analytic 1st order deformation of the Klebanov-Strassler background. From the dual gauge theory point of view the deformation describes supersymmetry soft breaking gaugino mass terms. We calculate the difference in vacuum energies between the supersymmetric and the non-supersymmetric solutions and find that it matches the field theory prediction. We also discuss the breaking o...

We study N = 1 supersymmetric SO(10) gauge theory with a field in the spinorial representaition and Nf (≤ 8) fields in the defining representation. It is shown that this theory for Nf = 7, 8 has a dual description, which is N = 1 supersymmetric SU(Nf − 5) gauge theory. Its matter content for Nf = 7 is different from the one for Nf = 8; for Nf = 7, it contains 8 fields in the anti-fundamental re...

In previous work we proposed a field theory model for multiple M2-branes based on an algebra with a totally antisymmetric triple product. In this paper we gauge a symmetry that arises from the algebra’s triple product. We then construct a supersymmetric theory with no free parameters that is consistent with all the continuous symmetries expected of a multiple M2-brane theory: 16 supersymmetries...

We review the substantial progress that has been made in classifying supersymmetric solutions of supergravity theories using G-structures. We also review the construction of supersymmetric black rings that were discovered using the classification of D = 5 supergravity solutions. To appear in the Proceedings of the 37th International Symposium Ahrenshoop, “Recent Developments in String/M-Theory ...