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B. M. Zupnik

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

49 records · Page 3Linked to original sources
arXiv1999

Partial spontaneous breakdown of 3-dimensional N=2 supersymmetry

The superfield models with the partial spontaneous breaking of the global D=3, N=2 supersymmetry are discussed. The abelian gauge model describes low-energy interactions of the real scalar field with the 3D vector and fermion fields. We introduce the new Goldstone-Maxwell representation of the 3D gauge superfield and show that 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 considered. These models have the constant vacuum solutions and describe, respectively, the interactions of the N=1 Goldstone multiplets of the D2-brane or supermembrane with the additional massive multiplets.

hep-th↗
arXiv1998

Background Harmonic Superfields in N=2 Supergravity

A modification of the harmonic superfield formalism in $D=4, N=2$ supergravity using a subsidiary condition of covariance under the background supersymmetry with a central charge ($B$-covariance) is considered. Conservation of analyticity together with the $B$-covariance leads to the appearance of linear gravitational superfields. Analytic prepotentials arise in a decomposition of the background linear superfields in terms of spinor coordinates and transform in a nonstandard way under the background supersymmetry. The linear gravitational superfields can be written via spinor derivatives of nonanalytic spinor prepotentials. The perturbative expansion of the extended supergravity action in terms of the $B$-covariant superfields and the corresponding version of the differential-geometric formalism are considered. We discuss the dual harmonic representation of the linearized extended supergravity, which corresponds to the dynamical condition of Grassmann analyticity.

hep-th↗
arXiv1998

Harmonic Superspaces For Three-Dimensional Theories

Three-dimensional field theories with N=3 and N=4 supersymmetries are considered in the framework of the harmonic-superspace approach. Analytic superspaces of these supersymmetries are similar; however, the geometry of gauge theories with the manifest N=3 is richer and admits construction of the topological mass term.

hep-th↗
arXiv1997

Induced hypermultiplet self-interactions in N=2 gauge theories

We calculate the charged hypermultiplet low-energy effective action in the Coulomb branch of the 4D, N=2 gauge theory, by using the harmonic superspace approach. We find that the unique leading contribution is given by the harmonic-analytic Lagrangian of the fourth order in the hypermultiplet superfields, with the induced coupling constant being proportional to central charges of N=2 SUSY algebra. The central charges are identified with Cartan generators of the internal symmetry, and they give BPS masses to the hypermultiplets. The induced hyper-K"ahler metrics appear to be the Taub-NUT metric or its higher-dimensional generalizations. Simultaneously, non-trivial scalar potentials are produced. Within the harmonic superspace method, we show an equivalence between the two known approaches to the 4D central charges. In the first one, the central charges are obtained via the Scherk-Schwarz dimensional reduction from six dimensions, whereas in the second one they are generated by a covariantly-constant background gauge superfield. Our analysis is extended to a more general situation with the non-vanishing Fayet-Iliopoulos (FI) terms. The perturbatively-induced Taub-NUT self-coupling in the Coulomb branch is found to be stable against adding the FI term, whereas the non-perturbatively generated (Eguchi-Hanson type) hypermultiplet self-interaction is proposed for the Higgs branch.

hep-th↗
arXiv1996

Zero-Curvature Representation and Dual Formulations of $N=2$ Supersymmetric Gauge Theory in Harmonic Superspace

Analytical harmonic superfields are the basic variables of a standard harmonic formalism of SYM^2_4-theory. We consider superfield actions for alternative formulations of this theory using the unconstrained harmonic prepotentials. The corresponding equations of motion are equivalent to the component field equations of SYM^2_4-theory. The analyticity condition appears only on-shell as the zero-curvature equation in the alternative formulations.

hep-th↗
arXiv1995

Zero-curvature representation for harmonic-superspace equations of motion in $N=1, D=6$ supersymmetric gauge theory

We consider the $SYM^1_6$ harmonic-superspace system of equations that contains superfield constraints and equations of motion for the simplest six-dimensional supersymmetric gauge theory. A special $A$-frame of the analytic basis is introduced where a kinematic equation for the harmonic connection $A^{\s--}$ can be solved . A dynamical equation in this frame is equivalent to the zero-curvature equation corresponding to the covariant conservation of analyticity. Using a simple harmonic gauge condition for the gauge group $SU(2)$ we derive the superfield equations that produce the general $SYM^1_6$ solution . An analogous approach for the analysis of integrability conditions for the $SYM^2_4$-theory and $SYM$-supergravity-matter systems in harmonic superspace is discussed briefly.

hep-th↗
arXiv1995

Harmonic-Superspace Integrability of N=1, D=6 Supersymmetric Gauge Theory

We consider the harmonic-superspace ($HS$) system of equations that contains superfield $SYM^1_6$ constraints and equations of motion. A dynamical equation in the special $A$-frame is equivalent to the zero-curvature equation corresponding to a covariant conservation of $HS$-analyticity. Properties of a general $SYM^1_6$ solution for the gauge group $SU(2)$ are studied in the simplest harmonic gauge. An analogous approach to the integrability interpretation of $SYM$-$SG$-matter systems in $HS$ is discussed briefly.

hep-th↗
arXiv1995

Quantum Deformations of the Self-Duality Equation and Conformal Twistors

A noncommutative algebra of the complex $q$-twistors and their differentials is considered on the basis of the quantum $GL_q (4)\times SL_q (2)$ group. Real and pseudoreal $q$-twistors are discussed too. We consider the quantum-group self-duality equation in the framework of the local gauge algebra of differential forms on $q$-twistor spaces. Quantum deformations of the general multi-instanton solutions are constructed. The corresponding noncommutative algebras of moduli are introduced. The general $q$-instanton connection is a function of the $q$-twistors and the $q$-moduli .

q-alg↗
arXiv1994

Differential Calculus on the Quantum Sphere and Deformed Self-Duality Equation

We discuss the left-covariant 3-dimensional differential calculus on the quantum sphere $SU_q (2)/U(1) $. The $SU_q (2)$-spinor harmonics are treated as coordinates of the quantum sphere. We consider the gauge theory for the quantum group $SU_q (2)\times U(1) $ on the deformed Euclidean space $E_q (4)$. A $q$-generalization of the harmonic-gauge-field formalism is suggested . This formalism is applied for the harmonic (twistor) interpretation of the quantum-group self-duality equation (QGSDE). We consider the zero-curvature representation and the general construction of QGSDE-solutions in terms of the analytic prepotential.

q-alg↗
arXiv1994

Solution of Self-Duality Equation in Quantum-Group Gauge Theory and Quantum Harmonics

We discuss the gauge theory for quantum group $SU_q (2)\times U(1) $ on the quantum Euclidean space. This theory contains three physical gauge fields and one$\; U(1)-$gauge field with a zero field strength. We construct the quantum-group self-duality equation (QGSDE) in terms of differential forms and with the help of the field-strength decomposition. A deformed analog of the BPST-instanton solution is obtained. We consider a harmonic (twistor) interpretation of QGSDE in terms of $SU_q (2)/U(1) $ quantum harmonics. The quantum harmonic gauge equations are formulated in the framework of a left-covariant 3D differential calculus on the quantum group $SU_q (2)$.

hep-th↗
arXiv1993

Quantum deformations for the diagonal R-matrices

We consider two different types of deformations for the linear group $ GL(n)$ which correspond to using of a general diagonal R-matrix. Relations between braided and quantum deformed algebras and their coactions on a quantum plane are discussed. We show that tensor-grading-preserving differential calculi can be constructed on braided groups , quantum groups and quantum planes for the case of the diagonal R-matrix.

hep-th↗
arXiv1992

Minimal deformations of the commutative algebra and the linear group GL(n)

We consider the relations of generalized commutativity in the algebra of formal series $ M_q (x^i ) $, which conserve a tensor $ I_q $-grading and depend on parameters $ q(i,k) $ . We choose the $ I_q $-preserving version of differential calculus on $ M_q$ . A new construction of the symmetrized tensor product for $ M_q $-type algebras and the corresponding definition of minimally deformed linear group $ QGL(n) $ and Lie algebra $ qgl(n) $ are proposed. We study the connection of $ QGL(n) $ and $ qgl(n) $ with the special matrix algebra $ \mbox{Mat} (n,Q) $ containing matrices with noncommutative elements. A definition of the deformed determinant in the algebra $ \mbox{Mat} (n,Q) $ is given. The exponential parametrization in the algebra $ \mbox{Mat} (n,Q) $ is considered on the basis of Campbell-Hausdorf formula.

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