Related papers: Off-shell Formalism for Ali-Ilahi's ADHM Instanton…
The formalism to determine (conformal) isometries of a given curved superspace was elaborated almost two decades ago in the context of the old minimal formulation for N=1 supergravity in four dimensions (4D). This formalism is universal,…
The Drinfeld-Manin construction of U(N) instanton is reformulated in the ADHM formulism, which gives explicit general solutions of the ADHM constraints for U(N) (N>=2k-1) k-instantons. For the N<2k-1 case, implicit results are given…
We study the instanton calculus for N=4 super Yang-Mills theory in ten-dimensional Omega-background with the R-symmetry Wilson line gauge field. From the ADHM construction of instantons in the background, we obtain the deformed instanton…
We introduce N-extended (p,q) AdS superspaces in three space-time dimensions, with p+q=N and p>=q, and analyse their geometry. We show that all (p,q) AdS superspaces with X^{IJKL}=0 are conformally flat. Nonlinear sigma-models with (p,q)…
Using the harmonic superspace approach, we construct the three-dimensional N=4 supersymmetric quantum mechanics of the supermultiplet (3,4,1) coupled to an external SU(2) gauge field. The off-shell N=4 supersymmetry requires the gauge field…
In three-dimensional anti-de Sitter (AdS) space, there exist several realizations of N-extended supersymmetry, which are traditionally labelled by two non-negative integers p>=q such that p+q=N. Different choices of p and q, with N fixed,…
We study dualities in off-shell 4D N = 2 supersymmetric sigma-models, using the projective superspace approach. These include (i) duality between the real O(2n) and polar multiplets; and (ii) polar-polar duality. We demonstrate that the…
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\"ahler reduction; projective superspace; the generalized Legendre construction;…
We consider the action on instanton moduli spaces of the non-local symmetries of the self-dual Yang-Mills equations on $\mathbb{R}^4$ discovered by Chau and coauthors. Beginning with the ADHM construction, we show that a sub-algebra of the…
On-shell diagrams are gauge invariant quantities which play an important role in the description of scattering amplitudes. Based on the principles of generalized unitarity, they are given by products of elementary three-point amplitudes…
Some of the key cohomological features of the two $(1+1)$-dimensional (2D) free Abelian- and self-interacting non-Abelian gauge theories (having no interaction with matter fields) are briefly discussed first in the language of symmetry…
In this paper we propose a new supersymmetric extension of conformal mechanics. The Grassmannian variables that we introduce are the basis of the forms and of the vector-fields built over the symplectic space of the original system. Our…
The off-shell description of N=(2,2) supersymmetric non-linear sigma-models is reviewed. The conditions for ultra-violet finiteness are derived and T-duality is discussed in detail.
We review the superspace technique to determine supersymmetric spacetimes in the framework of off-shell formulations for supergravity in diverse dimensions using the case of 3D N=2 supergravity theories as an illustrative example. This…
We present a Lagrangian formulation for N=4 supersymmetric quantum-mechanical systems describing the motion in external non-Abelian self-dual gauge fields. For any such system, one can write a component supersymmetric Lagrangian by…
We discuss the construction of ADHM data for Yang-Mills instantons with the symmetries of the regular polytopes in four dimensions. We show that the case of the pentatope can be studied using a simple modification of the approach previously…
The arcane ADHM construction of Yang-Mills instantons can be very naturally understood in the framework of D-brane dynamics in string theory. In this point-of-view, the mysterious auxiliary symmetry of the ADHM construction arises as a…
The complete classification of the irreducible representations of the N-extended one-dimensional supersymmetry algebra linearly realized on a finite number of fields is presented. Off-shell invariant actions of one-dimensional…
We develop a formalism to construct supersymmetric backgrounds within the superspace formulation for five-dimensional (5D) conformal supergravity given in arXiv:0802.3953. Our approach is applicable to any off-shell formulation for 5D…
Recently, a gauged linear sigma model was proposed by Berkovits and Vafa which can be used to describe the AdS_5xS^5 superstring at finite and zero radius. In this paper we show that the model is classically integrable by constructing its…