Searcharxiv⌕ Search

arXiv subjects

B. M. Zupnik

Publications and source records attributed to B. M. Zupnik.

At least 37 records · Page 2Linked to original sources
arXiv2006

Renormalizability of non-anticommutative N=(1,1) theories with singlet deformation

We study the quantum properties of two theories with a non-anticommutative (or nilpotent) chiral singlet deformation of N=(1,1) supersymmetry: the abelian model of a vector gauge multiplet and the model of a gauge multiplet interacting with a neutral hypermultiplet. In spite of the presence of a negative-mass-dimension coupling constant (deformation parameter), both theories are shown to be finite in the sense that the full effective action is one-loop exact and contains finitely many divergent terms, which vanish on-shell. The beta-function for the coupling constant is equal to zero. The divergencies can all be removed off shell by a redefinition of one of the two scalar fields of the gauge multiplet. These notable quantum properties are tightly related to the existence of a Seiberg-Witten-type transformation in both models.

hep-th↗
arXiv2005

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 Lie superalgebras are constructed in terms of the left supersymmetry generators. Non-anticommutative $\star$-products of superfields are covariant objects in the twist-deformed supersymmetries, and this covariance guarantees the manifest invariance of superfield actions using $\star$-products.

hep-th↗
arXiv2004

Non-Anticommutative Deformations of N=(1,1) Supersymmetric Theories

We discuss chirality-preserving nilpotent deformations of four-dimensional N=(1,1) Euclidean harmonic superspace and their implications in N=(1,1) supersymmetric gauge and hypermultiplet theories, basically following [hep-th/0308012] and [hep-th/0405049]. For the SO(4) x SU(2) invariant deformation, we present non-anticommutative Euclidean analogs of the N=2 gauge multiplet and hypermultiplet off-shell actions. As a new result, we consider a specific non-anticommutative hypermultiplet model with N=(1,0) supersymmetry. It involves free scalar fields and interacting right-handed spinor fields.

hep-th↗
arXiv2004

Scale Invariant Low-Energy Effective Action in N=3 SYM Theory

Using the harmonic superspace approach we study the problem of low-energy effective action in N=3 SYM theory. The candidate effective action is a scale and γ_5-invariant functional in full N=3 superspace built out of N=3 off-shell superfield strengths. This action is constructed as N=3 superfield generalization of F^4/ϕ^4 component term which is leading in the low-energy effective action and is simultaneously the first nontrivial term in scale invariant Born-Infeld action. All higher-order terms in the scale invariant Born-Infeld action are also shown to admit an off-shell superfield completion in N=3 harmonic superspace.

hep-th↗
arXiv2003

N=4 Multiplets in N=3 Harmonic Superspace

It is shown that the N=3 harmonic-superfield equations of motion are invariant with respect to the 4-th supersymmetry. The SU(3) harmonics are also used to analyze a more flexible form of superfield constraints for the Abelian N=4 vector multiplet and its N=3 decomposition. An alternative unusual representation of the N=4 supersymmetry is realized on infinite multiplets of analytic superfields in the N=3 harmonic superspace. U(1) charges of superfields in these multiplets are parametrized by an integer- valued parameter which plays the role of the discrete coordinate. Each superfield term of the N=3 Yang-Mills action has the infinite-dimensional N=4 generalization. The gauge group of this model contains an infinite number of superfield parameters.

hep-th↗
arXiv2003

New approach to nonlinear electrodynamics: dualities as symmetries of interaction

We elaborate on the duality-symmetric nonlinear electrodynamics in a new formulation with auxiliary tensor fields. The Maxwell field strength appears only in bilinear terms of the corresponding generic Lagrangian, while the self-interaction is presented by a function E depending on the auxiliary fields. Two types of dualities inherent in the nonlinear electrodynamics models admit a simple off-shell characterization in terms of this function. In the standard formulation, the continuous U(1) duality symmetry is nonlinearly realized on the Maxwell field strength. In the new setting, the same symmetry acts as linear U(1) transformations of the auxiliary field variables. The nonlinear U(1) duality condition proves to be equivalent to the linear U(1) invariance of the self-interaction E. The discrete self-duality (or self-duality by Legendre transformation) amounts to a weaker reflection symmetry of E. For a class of duality- symmetric Lagrangians we introduce an alternative representation with the auxiliary scalar field and find new explicit examples of such systems.

hep-th↗
arXiv2002

Invariance of interaction terms in new representation of self-dual electrodynamics

A new representation of Lagrangians of 4D nonlinear electrodynamics is considered. In this new formulation, in parallel with the standard Maxwell field strength F, an auxiliary bispinor (tensor) field V is introduced. The gauge field strength appears only in bilinear terms of the full Lagrangian, while the interaction Lagrangian E depends on the auxiliary fields, E = E(V). Two types of self-duality inherent in the nonlinear electrodynamics models admit a simple characterization in terms of the function E. The continuous SO(2) duality symmetry between nonlinear equations of motion and Bianchi identities amounts to requiring E to be a function of the SO(2) invariant quartic combination |V|^4. The discrete self-duality (or self-duality under Legendre transformation) amounts to a weaker condition E(V)= E(iV). This approach can be generalized to a system of n Abelian gauge fields exhibiting U(n) duality. The corresponding interaction Lagrangian should be U(n) invariant function of n bispinor auxiliary fields.

hep-th↗
arXiv2002

Harmonic superpotentials and symmetries in gauge theories with eight supercharges

Models of interactions of D-dimensional hypermultiplets and supersymmetric gauge multiplets with $\mathcal{N}=8$ supercharges $(D{\leq} 6)$ can be formulated in the framework of harmonic superspaces. The effective Coulomb low-energy action for D=5 includes the free and Chern-Simons terms. We consider also the non-Abelian superfield D=5 Chern-Simons action. The biharmonic $D=3,\mathcal{N}=8$ superspace is introduced for a description of l and r supermultiplets and the mirror symmetry. The D=2,(4,4) gauge theory and hypermultiplet interactions are considered in the triharmonic superspace. Constraints for $D{=}1,\mathcal{N}{=}8$ supermultiplets are solved with the help of the $SU(2){\times}Spin(5)$ harmonics. Effective gauge actions in the full $D{\leq}3,\mathcal{N}{=}8$ superspaces contain constrained (harmonic) superpotentials satisfying the (6-D) Laplace equations for the gauge group U(1) or corresponding (6-D)p-dimensional equations for the gauge groups $[U(1)]^p$. Generalized harmonic representations of superpotentials connect equivalent superfield structures of these theories in the full and analytic superspaces. The harmonic approach simplifies the proofs of non-renormalization theorems.

hep-th↗
arXiv2002

New representation for Lagrangians of self-dual nonlinear electrodynamics

We elaborate on a new representation of Lagrangians of 4D nonlinear electrodynamics including the Born-Infeld theory as a particular case. In this new formulation, in parallel with the standard Maxwell field strength $F_{αβ}, \bar{F}_{\dotα\dotβ}$, an auxiliary bispinor field $V_{αβ}, \bar{V}_{\dotα\dotβ}$ is introduced. The gauge field strength appears only in bilinear terms of the full Lagrangian, while the interaction Lagrangian $E$ depends on the auxiliary fields, $E = E(V^2, \bar V^2)$. The generic nonlinear Lagrangian depending on $F,\bar{F}$ emerges as a result of eliminating the auxiliary fields. Two types of self-duality inherent in the nonlinear electrodynamics models admit a simple characterization in terms of the function $E$. The continuous SO(2) duality symmetry between nonlinear equations of motion and Bianchi identities amounts to requiring $E$ to be a function of the SO(2) invariant quartic combination $V^2\bar V^2$, which explicitly solves the well-known self-duality condition for nonlinear Lagrangians. The discrete self-duality (or self-duality under Legendre transformation) amounts to a weaker condition $E(V^2, \bar{V}^2) = E(-V^2, -\bar{V}^2)$. We show how to generalize this approach to a system of $n$ Abelian gauge fields exhibiting U(n) duality. The corresponding interaction Lagrangian should be U(n) invariant function of $n$ bispinor auxiliary fields.

hep-th↗
arXiv2001

N=3 supersymmetric Born-Infeld theory

We construct an off-shell N=3 supersymmetric extension of the abelian D=4 Born-Infeld action starting from the action of supersymmetric Maxwell theory in N=3 harmonic superspace. A crucial new feature of the N=3 super BI action is that its interaction part contains only terms of the order 4k in the N=3 superfield strengths. The correct component bosonic BI action arises as the result of elimination of auxiliary tensor field which is present in the off-shell N=3 vector multiplet in parallel with the gauge field strength. In this new Legendre-type representation, the bosonic BI action is fully specified by a real function of the single variable quartic in the auxiliary tensor field. The generic choice of this function amounts to a wide set of self-dual nonlinear extensions of the Maxwell action. All of them admit an off-shell N=3 supersymmetrization.

hep-th↗
arXiv2001

Geometry of solutions of N=2 SYM-theory in harmonic superspace

In harmonic superspace, the classical equations of motion of $D=4, N=2$ supersymmetric Yang-Mills theory for Minkowski and Euclidean spaces are analyzed. We study dual superfield representations of equations and subsidiary conditions corresponding to classical SYM-solutions with different symmetries. In particular, alternative superfield constructions of self-dual and static solutions are described in the framework of the harmonic approach.

hep-th↗
arXiv2001

N=4 Super-Yang-Mills Equations In Harmonic Superspace

We analyze the superfield equations of the 4-dimensional N=4 SYM-theory using light-cone gauge conditions and the harmonic-superspace approach. The harmonic superfield equations of motion are drastically simplified in this gauge, in particular, the basic harmonic-superfield matrices and the corresponding harmonic analytic gauge connections become nilpotent on-shell.

hep-th↗
arXiv2000

Short harmonic superfields and light-cone gauge in super-Yang-Mills equations

We analyze the superfield equations of the 4-dimensional N=2 and N=4 SYM-theories using light-cone gauge conditions and the harmonic-superspace approach. The harmonic superfield equations of motion are drastically simplified in this gauge, in particular, the basic harmonic-superfield matrices and the corresponding harmonic analytic gauge connections become nilpotent on-shell.

hep-th↗
arXiv2000

Solving N=3 super-Yang-Mills equations in harmonic superspace

We analyze the superfield constraints of the D=4, N=3 SYM-theory using light-cone gauge conditions. The SU(3)/U(1)xU(1) harmonic variables are interpreted as auxiliary spectral parameters, and the transform to the harmonic-superspace representation is considered. Our nilpotent gauge for the basic harmonic superfield simplifies the SYM-equations of motion. A partial Grassmann decomposition of these equations yields the solvable linear system of iterative equations.

hep-th↗
arXiv1999

Goldstone-type superfields and partial spontaneous breaking of D=3, N=2 supersymmetry

We consider the modified superfield constraints with constant terms for the D=3, N=2 Goldstone-Maxwell gauge multiplet which contains Goldstone fermions, real scalar and vector fields. The partial spontaneous breaking N=2 to N=1 is possible for the non-minimal self-interaction of this modified gauge superfield including the linear Fayet-Iliopoulos term. The dual description of the partial breaking in the model of the self-interacting Goldstone chiral superfield is also discussed.

hep-th↗
arXiv1999

Constrained superpotentials in harmonic gauge theories with 8 supercharges

We consider D-dimensional supersymmetric gauge theories with 8 supercharges (D<6,$~\mathcal{N}=8$) in the framework of harmonic superspaces. The effective Abelian low-energy action for D=5 contains the free and Chern-Simons terms. Effective $\mathcal{N}=8$ superfield actions for D<4 can be written in terms of the superpotentials satisfying the superfield constraints and (6-D)-dimensional Laplace equations. The role of alternative harmonic structures is discussed.

hep-th↗
arXiv1999

Modified N=2 supersymmetry and Fayet-Iliopoulos terms

We study peculiarities of realization of N=2 supersymmetry in N=2 abelian gauge theory with two sorts of FI terms, electric and magnetic ones, within manifestly supersymmetric formulations via the Mezincescu and harmonic-analytic prepotentials. We obtain a `magnetic', duality- transformed superfield form of the N=2 Maxwell effective holomorphic action with standard electric $FI$ term and demonstrate that in such a system off-shell N=2 supersymmetry is inevitably realized in an unusual Goldstone mode corresponding to the {\it partial} spontaneous breaking down to N=1. On shell, the standard total breaking occurs. In a system with the two sorts of FI terms, off-shell N=2 supersymmetry is realized in the partial breaking mode both in the electric and magnetic representations. This regime is retained on shell due to the Antoniadis- Partouche-Taylor mechanism. We show that the off-shell algebra of N=2 supersymmetry in the partial breaking realization is modified on gauge-variant objects like potentials and prepotentials. The closure of spinor charges involves some special gauge transformations before any gauge-fixing.

hep-th↗