Non-anticommutative Deformation Research Articles

Twisted supersymmetry in a deformed Wess-Zumino model in (2 + 1) dimensions

Non-anticommutative deformations have been studied in the context of super-symmetry (SUSY) in three and four space-time dimensions, and the general picture is that highly nontrivial to deform supersymmetry in a way that still preserves some of its important properties, both at the formal algebraic level (e.g., preserving the associativity of the deformed theory) as well as at the physical level (e.g., maintaining renormalizability). The Hopf algebra formalism allows the definition of algebraically consistent deformations of SUSY, but this algebraic consistency does not guarantee that physical models build upon these structures will be consistent from the physical point of view. We will investigate a deformation induced by a Drinfel’d twist of the mathcal{N} = 1 SUSY algebra in three space-time dimensions. The use of the Hopf algebra formalism allows the construction of deformed mathcal{N} = 1 SUSY algebras that should still preserve a deformed version of supersymmetry. We will construct the simplest deformed version of the Wess-Zumino model in this context, but we will show that despite the consistent algebraic structure, the model in question is not invariant under SUSY transformation and is not renormalizable. We will comment on the relation of these results with previous ones discussed in the literature regarding similar four-dimensional constructions.

Supersymmetry breaking as a new source for the generalized uncertainty principle

In this letter, we will demonstrate that the breaking of supersymmetry by a non-anticommutative deformation can be used to generate the generalized uncertainty principle. We will analyse the physical reasons for this observation, in the framework of string theory. We also discuss the relation between the generalized uncertainty principle and the Lee-Wick field theories.

Supersymmetric Duality in Deformed Superloop Space

In this paper, we will analyse the superloop space formalism for a four dimensional supersymmetric Yang–Mills theory in deformed superspace. We will deform the \(\mathcal {N} =1\) superspace by imposing imposing non-anticommutativity. This non-anticommutative deformation of the superspace will break half the supersymmetry of the original theory. So, this theory will have \(\mathcal {N} =1/2\) supersymmetry. We will analyse the superloop space duality for this deformed supersymmetric Yang–Mills theory using the \(\mathcal {N} =1/2\) superspace formalism. We will demonstrate that the sources in the original theory will become monopoles in the dual theory, and the monopoles in the original theory will become sources in the dual theory.

Nonanticommutativity in the presence of a boundary

In this paper we consider nonanticommutative field theories in $\mathcal{N}=2$ superspace formalism on three-dimensional manifolds with a boundary. We modify the original Lagrangian in such a way that it preserves half the supersymmetry even in the presence of a boundary. We also analyze the partial breaking of supersymmetry caused by nonanticommutativity between fermionic coordinates. Unlike in four dimensions, in three dimensions a theory with $\mathcal{N}=1/2$ supersymmetry cannot be obtained by a nonanticommutative deformation of an $\mathcal{N}=1$ theory. However, in this paper we construct a three-dimensional theory with $\mathcal{N}=1/2$ supersymmetry by studying a combination of nonanticommutativity and boundary effects, starting from $\mathcal{N}=2$ supersymmetry.

Non-anticommutative ABJ theory

In this paper we will discuss non-anticommutative deformations of the harmonic superspace. We will analyse the non-anticommutative deformation of the superspace that break the supersymmetry from N=3 supersymmetry to N=2 supersymmetry. We will then study the ABJ theory in this non-anticommutative superspace. This deformed ABJ theory will be shown to posses N=5 supersymmetry.

Non-anticommutative solitons

Certain supersymmetric sigma models in 2+1 dimensions feature multi-soliton solutions, with and without scattering. We subject these systems to a non-anticommutative deformation by replacing the Grassmann algebra of the odd superspace coordinates with a Clifford algebra. Static CP1 and scattering U(2) solitons are constructed and carry an additional spin-1/2 degree of freedom due to the deformation. Abelian BPS solutions exist as well but have infinite action, in contrast to the Moyal case.

Physics of crypto-Hermitian and crypto-supersymmetric field theories

We discuss non-Hermitian field theories where the spectrum of the Hamiltonian involves only real energies. We make three observations. (i) The theories obtained from supersymmetric theories by nonanticommutative deformations belong in many cases to this class. (ii) When the deformation parameter is small, the deformed theory enjoys the same supersymmetry algebra as the undeformed one. Half of the supersymmetries are manifest and the existence of another half can be deduced from the structure of the spectrum. (iii) Generically, the conventionally defined $S$-matrix is not unitary for such theories.

Cryptoreality of nonanticommutative Hamiltonians

We note that, though nonanticommutative (NAC) deformations of Minkowski supersymmetric theories do not respect the reality condition and seem to lead to non-Hermitian Hamiltonians H, the latter belong to the class of ``cryptoreal'' Hamiltonians considered recently by Bender and collaborators. They can be made manifestly Hermitian via the similarity transformation H -> exp{R} H exp{-R} with a properly chosen R. The deformed model enjoys the same supersymmetry algebra as the undeformed one, though being realized differently on the involved canonical variables. Besides quantum-mechanical models, we treat, along similar lines, some NAC deformed field models in 4D Minkowski space.

Vector-multiplet effective action in the non-anticommutative charged hypermultiplet model

We investigate the quantum aspects of a charged hypermultiplet in deformed N = ( 1 , 1 ) superspace with singlet non-anticommutative deformation of supersymmetry. This model is a “star” modification of the hypermultiplet interacting with a background Abelian vector superfield. We prove that this model is renormalizable in the sense that the divergent part of the effective action is proportional to the N = ( 1 , 0 ) non-anticommutative super-Yang–Mills action. We also calculate the finite part of the low-energy effective action depending on the vector multiplet, which corresponds to the (anti)holomorphic potential. The holomorphic piece is just deformed to the star-generalization of the standard holomorphic potential, while the antiholomorphic piece is not. We also reveal the component structure and find the deformation of the mass and the central charge.

Deformations of Euclidean supersymmetries

We consider quantum supergroups that arise in non-anticommutative deformations of N=(1/2,1/2) and N=(1,1) four-dimensional Euclidean supersymmetric theories. Twist operators in the corresponding deformed algebras of superfields contain left spinor generators. We show that non-anticommutative $\star$-products of superfields transform covariantly in the deformed supersymmetries. This covariance guarantees the invariance of deformed superfield actions of models involving $\star$-products of superfields.

Nonanticommutative deformation of Script N = 4 SYM theory: the Myers effect and vacuum states

We propose a deformation of ${\cal N}=4$ SYM theoery induced by nonanticommutative star product. The deformation introduces new bosonic terms which we identify with the corresponding Myers terms of a stack of D3-branes in the presence of a five-form RR flux. We take this as an indication that the deformed lagrangian describes D3-branes in such a background. The vacuum states of the theory are also examined. In a specific case where the U(1) part of the gauge field is nonvanishing the (anti)holomorphic transverse coordinates of the brane sit on a fuzzy two sphere. For a supersymmetric vacuum the antiholomorphic coordinates must necessarily commute. However, we also encounter non-supersymmetric vacua for which the antiholomorphic coordinates do not commute.

Twist-deformed supersymmetries in non-anticommutative superspaces

We consider a quantum group interpretation of the non-anticommutative deformations in Euclidean supersymmetric theories. Twist deformations in the corresponding superspaces and supergroups are constructed in terms of the left supersymmetry generators. Non-anticommutative ⋆-products of superfields are covariant objects in the twist-deformed supersymmetries, and this covariance guarantees the manifest invariance of superfield actions using ⋆-products.

Summing up non-anticommutative Kähler potential

We offer a simple non-perturbative formula for the component action of a generic N=1/2 supersymmetric chiral model in terms of an arbitrary number of chiral superfields in four dimensions, which is obtained by the non-anticommutative (NAC) deformation of a generic four-dimensional N=1 supersymmetric non-linear sigma-model (NLSM) described by arbitrary Kähler superpotential and scalar superpotential. The auxiliary integrations responsible for fuzziness are eliminated in the case of a single chiral superfield. The scalar potential in components is derived by eliminating the auxiliary fields. The NAC-deformation of the CP1 Kähler NLSM with an arbitrary scalar superpotential is calculated as an example.

Script N = 1/2 quiver gauge theories from open strings with R-R fluxes

We consider a four dimensional N=1 gauge theory with bifundamental matter and a superpotential, defined on stacks of fractional branes. By turning on a flux for the R-R graviphoton field strength and computing open string amplitudes with insertions of R-R closed string vertices, we introduce a non-anticommutative deformation and obtain the N=1/2 version of the theory. We also comment on the appearance of a new structure in the effective Lagrangian.

On nonanticommutative Script N = 2 sigma-models in two dimensions

We study nonanticommutative deformations of N=2 two-dimensional Euclidean sigma models. We find that these theories are described by simple deformations of Zumino's Lagrangian and the holomorphic superpotential. Geometrically, this deformation can be interpreted as a fuzziness in target space controlled by the vacuum expectation value of the auxiliary field. In the case of nonanticommutative deformations preserving Euclidean invariance, we find that a continuation of the deformed supersymmetry algebra to Lorentzian signature leads to a rather intriguing central extension of the ordinary (2,2) superalgebra.

Stochastic versus semiclassical approach to quantum chaotic scattering: C. H. Lewenkopf and H. A. Weidenmüller. Max-Planck-Institut für Kernphysik, D-6900 Heidelberg, Germany

We offer a simple non-perturbative formula for the component action of a generic N=1/2 supersymmetric chiral model in terms of an arbitrary number of chiral superfields in four dimensions, which is obtained by the non-anticommutative (NAC) deformation of a generic four-dimensional N=1 supersymmetric non-linear sigma-model (NLSM) described by arbitrary Kähler superpotential and scalar superpotential. The auxiliary integrations responsible for fuzziness are eliminated in the case of a single chiral superfield. The scalar potential in components is derived by eliminating the auxiliary fields. The NAC-deformation of the CP1 Kähler NLSM with an arbitrary scalar superpotential is calculated as an example.