super-Poincare Symmetry Research Articles

BPS equations in Ω-deformed N = 4 $$ \mathcal{N}=4 $$ super Yang-Mills theory

We study supersymmetry of N=4 super Yang-Mills theory in four dimensions deformed in the Omega-background. We take the Nekrasov-Shatashvili limit of the background so that two-dimensional super Poincare symmetry is recovered. We compute the deformed central charge of the superalgebra and study the 1/2 and 1/4 BPS states. We obtain the Omega-deformed 1/2 and 1/4 BPS dyon equations from the deformed supersymmetry transformation and the Bogomol'nyi completion of the energy.

Three particle superstring amplitudes with massive legs

On-shell superspaces and associated spinor helicity techniques give an efficient formulation of the Ward identities of on-shell supersymmetry for scattering amplitudes and supply tools to construct their solutions. Based on these techniques in this paper the general solutions of the Ward identities are presented for three particle scattering amplitudes with one, two or three massive legs for simple supersymmetry in ten and eight dimensions. It is shown in examples how these solutions may be used to obtain concrete amplitudes for the closed (IIB) and open superstring in a flat background. Explicit results include all three point amplitudes with one massive leg whose functional form is shown to be dictated completely by super-Poincare symmetry. The resulting surprisingly simple series only involves massive superfields labelled by completely symmetric little group representations. The extension to more general explicit three and higher point amplitudes in string theory is initiated. In appendices the field content of the fundamental massive superfields of the open and closed superstring are listed in terms of the Dynkin labels of a variety of groups which may be of independent interest.

Noncommutative associative superproduct for general supersymplectic forms

We define a noncommutative and nonanticommutative associative product for general supersymplectic forms, allowing the explicit treatment of non(anti)commutative field theories from general nonconstant string backgrounds like a graviphoton field. We propose a generalization of deformation quantization a la Fedosov to superspace, which considers noncommutativity in the tangent bundle instead of base space, by defining the Weyl super product of elements of Weyl super algebra bundles. Super Poincare symmetry is not broken and chirality seems not to be compromised in our formulation. We show that, for a particular case, the projection of the Weyl super product to the base space gives rise the Moyal product for non(anti)commutative theories.

Linearizing N=3 nonlinear supersymmetry in two dimensions

Abstract We investigate for N = 3 supersymmetry (SUSY) in D = 2 the algebraic relation between the Volkov–Akulov (VA) model of nonlinear (NL) SUSY and a (renormalizable) SO(3) vector supermultiplet of linear (L) SUSY. We derive SUSY and SO(3) invariant relations between component fields of the vector supermultiplet and Nambu–Goldstone fermions of the VA model at leading orders by using three arbitrary dimensionless parameters which can be recasted as the vacuum expectation values of auxiliary fields in the vector supermultiplet. Two different irreducible representations of SO(3) super-Poincare symmetry which appear in the same massless state are compatible with each other in the linearization of NL SUSY. The equivalence of a NL SUSY VA action to a free L SUSY action containing the Fayet–Iliopoulos D term which indicates a spontaneously SUSY breaking is also discussed explicitly according to the SUSY invariant relations.

Non-anticommutative supersymmetric field theory and quantum shift

Abstract Non-anticommutative Grassmann coordinates in four-dimensional twist-deformed N = 1 Euclidean superspace are decomposed into geometrical ones and quantum shift operators. This decomposition leads to the mapping from the commutative to the non-anticommutative supersymmetric field theory. We apply this mapping to the Wess–Zumino model in commutative field theory and derive the corresponding non-anticommutative Lagrangian. Based on the theory of twist deformations of Hopf algebras, we comment on the preservation of the (initial) N = 1 super-Poincare algebra and on the consequent super-Poincare invariant interpretation of the discussed model, but also provide a measure for the violation of the super-Poincare symmetry.

Hidden twelve-dimensional super Poincaré symmetry in eleven dimensions

First, we review a result in our previous paper, of how a ten-dimensional superparticle, taken off-shell, has a hidden eleven-dimensional superPoincare symmetry. Then, we show that the physical sector is defined by three first-class constraints which preserve the full eleven-dimensional symmetry. Applying the same concepts to the eleven dimensional superparticle, taken off-shell, we discover a hidden twelve dimensional superPoincare symmetry that governs the theory.

Superstar in noncommutative superspace via covariant quantization of the superparticle

A covariant quantization method is developed for the off-shell superparticle in 10 dimensions. On-shell it is consistent with lightcone quantization, while off-shell it gives a noncommutative superspace that realizes non-linearly a hidden 11-dimensional super Poincare symmetry. The non-linear commutation rules are then used to construct the supersymmetric generalization of the covariant Moyal star product in noncommutative superspace. As one of the possible applications, we propose this new product as the star product in supersymmetric string field theory. Furthermore, the formalism introduces new techniques and concepts in noncommutative (super)geometry.

Nonlinear realization of partially broken N=2 superconformal symmetry in four dimensions

Abstract We investigate the nonlinear realization of spontaneously broken D=4 N=2 superconformal symmetry. We particularly study Nambu-Goldstone degrees of freedom for the partial breaking of N=2 superconformal symmetry down to N=1 super-Poincare symmetry, where we get the chiral NG multiplet of dilaton and the vector NG multiplet of NG fermion of broken Q-supersymmetry. Evaluating the covariant derivatives and supervielbeins for the chiral as well as the full superspace, we obtain the nonlinear effective lagrangians.

New theories in six dimensions and matrix description of M-theory on T5 and

We present four infinite series of new quantum theories with super-Poincare symmetry in six dimensions, which are not local quantum field theories. They have string like excitations but the string coupling is of order one. Compactifying these theories on $T^5$ we find a Matrix theory description of M theory on $T^5$ and on $T^5/\IZ_2$, which is well defined and is manifestly U-duality invariant.

Gravity as a Gauge Theory with Spontaneously Broken Internal Super-Poincare Symmetry

Gravity as a Gauge Theory with Spontaneously Broken Internal Super-Poincare Symmetry

Nonlinear superfield realisations of extended supersymmetries

A superfield extension of the Volkov-Akulov method of constructing nonlinear realisations of the extended super Poincare symmetry is proposed. The formalism describes a partial supersymmetry breaking, the N=1 supersymmetry remaining unbroken. The case N=2, spontaneously broken down to N=1, is considered in detail. It is shown that in the quadratic approximation the corresponding action contains ghost fields in accordance with the general Witten discussion of supersymmetry breaking. Finally, a nonlinear superfield realisation of N=2 Poincare supersymmetry is considered with three scalar Goldstone superfields describing the U(2)/U(1) sector of the internal symmetry.

Quantisation of the non-linear super-Poincare fermion in a bag-like formulation

The quantisation of the Volkov-Akulov (1973) fermion of non-linear super-Poincare symmetry is studied using Dirac's generalised Hamiltonian method. The problem is found to be much simplified in a bag-like formulation of the model. The theory of a quark super-bag and a super-bubble is discussed.