arXiv subjects

E. A. Ivanov

Publications and source records attributed to E. A. Ivanov.

54 records · Page 3Linked to original sources

arXiv2007

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.

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arXiv2006

Supersymmetry at BLTP: how it started and where we are

This is a brief review of the BLTP activity in supersymmetry initiated by V.I. Ogievetsky (1928-1996) and lasting for more than 30 years. The main emphasis is made on the superspace geometric approaches and unconstrained superfield formulations. Alongside such milestones as the geometric formulation of N=1 supergravity and the harmonic superspace approach to extended supersymmetry, I sketch some other developments largely contributed by the Dubna group.

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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.

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arXiv2005

Conformal properties of hypermultiplet actions in six dimensions

We consider scale-invariant interactions of 6D N=1 hypermultiplets with the gauge multiplet. If the canonical dimension of the matter scalar field is assumed to be 1, scale-invariant lagrangians involve higher derivatives in the action. Though scale-invariant, all such lagrangians are not invariant with respect to special conformal transformations and their superpartners. If the scalar canonical dimension is assumed to be 2, conformal invariance holds at the classical, but not at the quantum level.

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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.

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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.

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arXiv2004

Symplectic sigma models in superspace

We discuss a special ``symplectic'' class of N = 4 supersymmetric sigma models in (0+1) dimension with 5r bosonic and 4r complex fermionic degrees of freedom. These models can be described off shell by N = 2 superfields (so that only half of supersymmetries are manifest) and also by N = 4 superfields in the framework of the harmonic superspace approach. Using the latter, we derive the general form of the relevant bosonic target metric.

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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.

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arXiv2002

Exact N=4 Supersymmetric Low-Energy Effective Action in N=4 Super-Yang-Mills Theory

We review a recent progress in constructing the low-energy effective action of N=4 SYM theory. This theory is formulated in terms of N=2 harmonic superfields corresponding to N=2 vector multiplet and hypermultiplet. Such a formulation possesses the manifest N=2 supersymmetry and an extra hidden on-shell supersymmetry. Exploring the hidden N=2 supersymmetry we proved that the known non-holomorphic potentials of the form ln W ln \bar{W} can be explicitly completed by the appropriate hypermultiplet-dependent terms to the entire N=4 supersymmetric form. The non-logarithmic effective potentials do not admit an N=4 completion and, hence, such potentials cannot occur in N=4 supersymmetric theory. As a result we obtain the exact N=4 supersymmetric low-energy effective action in N=4 SYM theory.

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arXiv2002

Complete Low-Energy Effective action in N=4 SYM: a Direct N=2 Supergraph Calculation

Using the covariant N=2 harmonic supergraph techniques we calculate the one-loop low-energy effective action of N=4 super-Yang-Mills theory in Coulomb branch with gauge group SU(2) spontaneously broken down to U(1). The full dependence of the low-energy effective action on both the hypermultiplet and gauge fields is determined. The direct quantum calculation confirms the correctness of the exact N=4 SYM low-energy effective action derived in hep-th/0111062 on the purely algebraic ground by invoking a hidden N=2 supersymmetry which completes the manifest N=2 one to N=4. Our results provide an exhaustive solution to the problem of finding out the exact completely N=4 supersymmetric low-energy effective action for the theory under consideration.

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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.

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arXiv2001

Complete N=4 Structure of Low-Energy Effective Action in N=4 Super Yang-Mills Theories

Using the ${\cal N}=2$ superfield approach, we construct full ${\cal N}=4$ supersymmetric low-energy effective actions for ${\cal N}=4$ SYM models, with both ${\cal N}=2$ gauge superfield strengths and hypermultiplet superfields included. The basic idea is to complete the known non-holomorphic effective potentials which depend only on ${\cal N}=2$ superfield strengths $W$ and ${\bar W}$ to the full on-shell ${\cal N}=4$ invariants by adding the appropriate superfield hypermultiplet terms. We prove that the effective potentials of the form ${ln} W {ln} \bar W$ can be ${\cal N} = 4$ completed in this way and present the precise structure of the corresponding completions. However, the effective potentials of the non-logarithmic form suggested in hep-th/9811017 and hep-th/9909020 do not admit the ${\cal N}=4$ completion. Therefore, such potentials cannot come out as (perturbative or non-perturbative) quantum corrections in ${\cal N}=4$ SYM models.

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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.

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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.

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arXiv1998

Central Charge as the Origin of Holomorphic Effective Action in N=2 Gauge Theory

We explicitly demonstrate that the perturbative holomorphic contribution to the off-shell effective action of N=2 U(1) gauge supermultiplet is an entire effect of the minimal coupling to a hypermultiplet with the mass generated by a central charge in N=2 superalgebra. The central charge is induced by a constant vacuum N=2 gauge superfield strength spontaneously breaking the automorphism U(1)_R symmetry of N=2 superalgebra. We use the manifestly off-shell supersymmetric harmonic superspace techniques of quantum calculations with the central charge-massive hypermultiplet propagator.

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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.

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arXiv1997

Effective Action of the N = 2 Maxwell Multiplet in Harmonic Superspace

We present, in the N=2, D=4 harmonic superspace formalism, a general method for constructing the off-shell effective action of an N=2 abelian gauge superfield coupled to matter hypermultiplets. Using manifestly N=2 supersymmetric harmonic supergraph techniques, we calculate the low-energy corrections to the renormalized one-loop effective action in terms of N=2 (anti)chiral superfield strengths. For a harmonic gauge prepotential with vanishing vacuum expectation value, corresponding to massless hypermultiplets, the only non-trivial radiative corrections to appear are non-holomorphic. For a prepotential with non-zero vacuum value, which breaks the U(1)-factor in the N=2 supersymmetry automorphism group and corresponds to massive hypermultiplets, only non-trivial holomorphic corrections arise at leading order. These holomorphic contribution are consistent with Seiberg's quantum correction to the effective action, while the first non-holomorphic contribution in the massless case is the N=2 supersymmetrization of the Heisenberg-Euler effective Lagrangian.

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arXiv1996

Harmonic Superspace: New Directions

We sketch recent applications of the harmonic superspace approach for off-shell formulations of $(4,4)$, $2D$ sigma models with torsion and for constructing super KdV hierarchies associated with "small" and "large" $N=4$ superconformal algebras.

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