Nonlinear Supersymmetry Research Articles

Hidden nonlinear supersymmetry of finite-gap Lamé equation

A bosonized nonlinear (polynomial) supersymmetry is revealed as a hidden symmetry of the finite-gap Lamé equation. This gives a natural explanation for peculiar properties of the periodic quantum system underlying diverse models and mechanisms in field theory, nonlinear wave physics, cosmology and condensed matter physics.

Ghost D-brane, supersymmetry and matrix model

In this note we study the world volume theory of pairs of D-brane and ghost D-brane, which is shown to have 16 linear supersymmetries and 16 nonlinear supersymmetries. In particular we study a matrix model based on the pairs of D(-1)-brane and ghost D(-1)-brane. Since such pairs are supposed to be equivalent to the closed string vacuum, we expect all 32 supersymmetries should be unbroken. We show that the world volume theory of the pairs of D-brane and ghost D-brane has unbroken 32 supersymmetries even though a half of them are nonlinearly realized.

Some systematics in the relation between linear and nonlinear global supersymmetry in curved spacetime

We focus on a nonlinear supersymmetry (NL SUSY) in curved spacetime introduced in the superon–graviton model (SGM) towards a SUSY composite unified model based on SO(10) super-Poincaré symmetry, and we consider for N=1 SUSY a systematic procedure to linearize the NL SUSY. By introducing modified superspace translations of superspace coordinates and their specific coordinate transformations both depending on a Nambu–Goldstone fermion, we show a homogeneous transformation's law of superfields which is important in the relation between linear (L) and NL SUSY. Furthermore, as a preliminary to find a L supermultiplet which is equivalent to the N=1 NL SUSY SGM multiplet, we discuss on the realization of the modified superspace translations in the construction of a supergravity-like multiplet in the superspace formalism. In particular, we find constraints on a torsion and a Lorentz transformation parameter in the superspace formalism to realize the modified supertranslations.

Nonlinear realization of supersymmetry and superconformal symmetry

Nonlinear realizations describing the spontaneous breakdown of supersymmetry and $R$-symmetry are constructed using the Goldstino and $R$-axion fields. The associated $R$-current, supersymmetry current and energy-momentum tensor are shown to be related under the nonlinear supersymmetry transformations. Nonlinear realizations of the superconformal algebra carried by these degrees of freedom are also displayed. The divergences of the $R$ and dilatation currents are related to the divergence of the superconformal currents through nonlinear supersymmetry transformations which in turn relates the explicit breakings of these symmetries.

Nonlinear supersymmetry: from classical to quantum mechanics

Quantization of the nonlinear supersymmetry faces a problem of a quantum anomaly. For some classes of superpotentials, the integrals of motion admit the corrections guaranteeing the preservation of the nonlinear supersymmetry at the quantum level. With an example of the system realizing the nonlinear superconformal symmetry, we discuss the nature of such corrections and speculate on their possible general origin.

Nonlinear supersymmetry for spectral design in quantum mechanics

Nonlinear (Polynomial, N-fold) SUSY approach to preparation of quantum systems with pre-planned spectral properties is reviewed. The full classification of ladder-reducible and irreducible chains of SUSY algebras in one-dimensional QM is given. Possible extensions of SUSY in one dimension are described. They include (no more than) ${\cal N} =2$ extended SUSY with two nilpotent SUSY charges which generate the hidden symmetry acting as a central charge. Embedding stationary quantum systems into a non-stationary SUSY QM is shown to yield new insight on quantum orbits and on spectrum generating algebras.

Non-linear supersymmetry and intersecting D-branes

We study the non-linear realization of supersymmetry. We classify all lower-dimensional operators, describing effective interactions of the Goldstino with Standard Model fields. Besides a universal coupling to the energy–momentum tensor of dimension eight, there are additional model dependent operators whose strength is not determined by non-linear supersymmetry, within the effective field theory. Their dimensionality can be lower than eight, starting with dimension six, leading in general to dominant effects at low energies. We compute their coefficients in string models with D-branes at angles. We find that the Goldstino decay constant is given by the total brane tension, while the various dimensionless couplings are independent from the values of the intersection angles.

Nonlinear superconformal symmetry of a fermion in the field of a Dirac monopole

We study a longstanding problem of identification of the fermion–monopole symmetries. We show that the integrals of motion of the system generate a nonlinear classical Z2-graded Poisson, or quantum superalgebra, which may be treated as a nonlinear generalization of the osp(2|2)⊕su(2). In the nonlinear superalgebra, the shifted square of the full angular momentum plays the role of the central charge. Its square root is the even osp(2|2) spin generating the u(1) rotations of the supercharges. Classically, the central charge's square root has an odd counterpart whose quantum analog is, in fact, the same osp(2|2) spin operator. As an odd integral, the osp(2|2) spin generates a nonlinear supersymmetry of De Jonghe, Macfarlane, Peeters and van Holten, and may be identified as a grading operator of the nonlinear superconformal algebra.

Relation between linear and nonlinear supersymmetry in curved spacetime

Relation between linear and nonlinear supersymmetry in curved spacetime

Superconformal mechanics and nonlinear supersymmetry

We show that a simple change of the classical boson-fermion coupling constant, $2\alpha \to 2\alpha n $, $n\in \N$, in the superconformal mechanics model gives rise to a radical change of a symmetry: the modified classical and quantum systems are characterized by the nonlinear superconformal symmetry. It is generated by the four bosonic integrals which form the so(1,2) x u(1) subalgebra, and by the 2(n+1) fermionic integrals constituting the two spin-n/2 so(1,2)-representations and anticommuting for the order n polynomials of the even generators. We find that the modified quantum system with an integer value of the parameter $\alpha$ is described simultaneously by the two nonlinear superconformal symmetries of the orders relatively shifted in odd number. For the original quantum model with $|\alpha|=p$, $p\in \N$, this means the presence of the order 2p nonlinear superconformal symmetry in addition to the osp(2|2) supersymmetry.

Exactly solvable pseudoscalar periodic Dirac potentials from Darboux transformations and underlying nonlinear supersymmetry

Darboux transformation method is applied to constructing new exactly solvable periodic pseudoscalar potentials for the one-dimensional Dirac equation. Factorization properties of Darboux transformation operators are established. Underlying quadratic supersymmetry is revealed.

Nonlinear supersymmetry in quantum mechanics: algebraic properties and differential representation

We study the nonlinear (polynomial, N-fold,…) supersymmetry algebra in one-dimensional QM. Its structure is determined by the type of conjugation operation (Hermitian conjugation or transposition) and described with the help of the Hamiltonian projection on the zero-mode subspace of supercharges. We show that the SUSY algebra with transposition symmetry is always polynomial in the Hamiltonian if supercharges represent differential operators of finite order. The appearance of the extended SUSY with several (complex or real) supercharges is analyzed in details and it is established that no more than two independent supercharges may generate a nonlinear superalgebra which can be appropriately specified as N=2 SUSY. In this case we find a nontrivial hidden symmetry operator and rephrase it as a nonlinear function of the Hamiltonian on the physical state space. The full N=2 nonlinear SUSY algebra includes “central charges” both polynomial and nonpolynomial (due to a symmetry operator) in the Hamiltonian.

Derivative corrections in 10-dimensional super-Maxwell theory

We construct the supersymmetric effective action at order alpha'^4 of the abelian open superstring. It includes the alpha'^4 terms in the abelian Born-Infeld action, and in particular the leading derivative correction of the form d^4F^4. Besides linear supersymmetry this sector of the open string effective action also has a nonlinear supersymmetry. The terms d^4F^4 and their fermionic partners have an arbitrary coefficient, and we discuss the possible fate of such coefficients when higher orders in alpha' are included.

Couplings in pseudosupersymmetry

We analyze theories in which a supersymmetric sector is coupled to a supersymmetry-breaking sector described by a non-linear realization. We show how to consistently couple N = 1 supersymmetric matter to non-supersymmetric matter in such a way that all interactions are invariant under non-linear supersymmetry transformations. We extend this formalism to couple N = 2 supersymmetric matter to N = 1 superfields that lack N = 2 partners but transform in a non-linear representation of the N = 2 algebra. In particular, we show how to couple an N = 2 vector to N = 1 chiral fields in a consistent way. This has important applications to effective field theories describing the interactions of D-brane world-volume fields with bulk fields. We apply our method to study systems where different sectors break different halves of supersymmetry, which appear naturally in models of intersecting branes.

D-brane models with non-linear supersymmetry

We study a class of type I string models with supersymmetry broken on the world-volume of some D-branes and vanishing tree-level potential. Despite the non-supersymmetric spectrum, supersymmetry is non-linearly realized on these D-branes, while it is spontaneously broken in the bulk by Scherk–Schwarz boundary conditions. These models can easily accommodate 3-branes with interesting gauge groups and chiral fermions. We also study the effective field theory and in particular we compute the four-fermion couplings of the localized goldstino with the matter fermions on the brane.

Nonlinear supersymmetry and unification of space-time and matter

Based upon the geometrical arguments of nonlinear SUSY in curved higher symmetric (SGM) space-time a new Einstein-Hilbert type action of superon-graviton model(SGM) for space-time and matter is obtained. SGM action is invariant under $$[global NL SUSY] \otimes [local GL(4,R)] \otimes [local Lorentz] \otimes [global SO(N)]$$ The explicit form of SGM action is given in terms of the fields of the graviton and superons by using the spin connection formalism. Some characteristic structures of the gravitational coupling of superons are manifested (in two dimensional space-time) with some details of the calculations. SGM cosmology is discussed briefly.

On linearization of N=1 nonlinear supersymmetry

The N=1 Volkov-Akulov model of nonlinear supersymmetry is explicitly related to a vector supermultiplet model with a Fayet-Iliopoulos D term of linear supersymmetry. The physical significance of the results is discussed briefly.

Nonlinear supersymmetry on the plane in magnetic field and quasi-exactly solvable systems

The nonlinear n-supersymmetry with holomorphic supercharges is investigated for the 2D system describing the motion of a charged spin-1/2 particle in an external magnetic field. The universal algebraic structure underlying the holomorphic n-supersymmetry is found. It is shown that the essential difference of the 2D realization of the holomorphic n-supersymmetry from the 1D case recently analysed by us consists in appearance of the central charge entering non-trivially into the superalgebra. The relation of the 2D holomorphic n-supersymmetry to the 1D quasi-exactly solvable (QES) problems is demonstrated by means of the reduction of the systems with hyperbolic or trigonometric form of the magnetic field. The reduction of the n-supersymmetric system with the polynomial magnetic field results in the family of the one-dimensional QES systems with the sextic potential. Unlike the original 2D holomorphic supersymmetry, the reduced 1D supersymmetry associated with x 6+⋯ family is characterized by the non-holomorphic supercharges of the special form found by Aoyama et al.

Free conical dynamics: charge-monopole as a particle with spin, anyon and nonlinear fermion-monopole supersymmetry

We discuss the origin of the effectively free dynamics of the charge in the magnetic monopole field to apply it for finding the alternative treatment of the charge-monopole as a particle with spin, for tracing out the relation of the charge-monopole to the free relativistic anyon and for clarifying the nature of the non-standard nonlinear supersymmetry of the fermion-monopole system.

D = 10 super-Yang-Mills at O(α′2)

Using superspace techniques, the complete and most general action of D=10 super-Yang--Mills theory is constructed at the alpha'^2 level. No other approximations, e.g., keeping only a subset of the allowed derivative terms, are used. The Lorentz structure of the alpha'^2 corrections is completely determined, while (depending on the gauge group) there is some freedom in the adjoint structure, which is given by a totally symmetric four-index tensor. We examine the second, non-linearly realised supersymmetry that may be present when the gauge group has a U(1) factor, and find that the constraints from linear and non-linear supersymmetry to a large extent coincide. However, the additional restrictions on the adjoint structure of the order alpha'^2 interactions following from the requirement of non-linear supersymmetry do not completely specify the symmetrised trace prescription.