Gravitational supervertices in n=1, 4D superstrings

The gravitational supermultiplet for target space-time supersymmetry of four-dimensional heterotic strings is obtained. By an explicit construction of supervertex operators it is shown that the underlying superspace geometry corresponds to the “new-minimal” formulation of N = 1, 4D supergravity. The relation between R-symmetry in target space and the U(1) symmetry of the world-sheet N = 2 superconformal algebra is outlined.     

Random matrix ensembles with random interactions: Results for EGUE(2)-SU(4)

We introduce in this paper embedded Gaussian unitary ensemble of random matrices, for m fermions in Ω number of single particle orbits, generated by random twobody interactions that are SU(4) scalar, called EGUE(2)-SU(4). Here the SU(4) algebra corresponds to Wigner’s supermultiplet SU(4) symmetry in nuclei. Formulation based on Wigner-Racah algebra of the embedding algebra U(4Ω) ? U(Ω) ? SU(4) allows for analytical treatment of this ensemble and using this analytical formulas are derived for the covariances in energy centroids and spectral variances. It is found that these covariances increase in magnitude as we go from EGUE(2) to EGUE(2)-s to EGUE(2)-SU(4) implying that symmetries may be responsible for chaos in finite interacting quantum systems.     

N = 1 complex supersymmetric theory in the harmonic superspace

The N = 1 complex supersymmetric algebra is studied using the harmonic techniques. The massless representations and the classification of their field content in terms of SU(2) n-uplets is obtained. The superspace formulation is developed and the U(1) × U(1) gauge supermultiplet is examined. Other features are discussed.     

c-Theorem for disordered systems

We find an analog of Zamolodchikov's c-theorem for disordered two-dimensional non-interacting systems in their supersymmetric field theory representation. We show that the energy momentum tensor of such field theories must be a part of a supermultiplet, and that a new parameter b can be introduced with the help of that multiplet. b flows along the renormalization group trajectories much like the central charge for unitary two-dimensional field theories. While it has not been established if this flow is irreversible, that is, if b always flows down to lower values, it does so for all the cases worked out so far. b gives a new way to label different conformal field theories for disordered systems whose central charge is always 0. b turns out to be related to the central extension of a certain algebra, a generalization of the Virasoro algebra, which we show may be present at the critical points of these theories. b is also related to the finite size corrections of the physical free energy of disordered systems. We discuss possible applications by computing b for two-dimensional Dirac fermions with random gauge potential, in other words, for U(1∣1) Kac-Moody algebra.     

On-shell and conformal N = 4 supergravity in superspace

We discuss the superspace geometries which are necessary to describe on-shell O(4) and SU(4) supergravity. The relation of central charge field strengths to physical spin-zero fields is exhibited and a “new” O(4) theory is shown to exist. The version of SU(4) supergravity which uses an antisymmetric tensor gauge field is found to require modifications of ordinary superspace. Finally the Poincaré supergeometry which admits the conformal N = 4 supermultiplet is constructed. It is shown that consistency of the Bianchi identities implies the existence of dimension zero auxiliary fields which are components of a non-linear multiplet.     

4D localization in Randall-Sundrum 2 supergravity and in Vasiliev theories

We discuss the problem of localization of 4D massless states in Randall-Sundrum 2 (one-brane) models. A Randall-Sundrum 2 construction starting from N=8 gauged supergravity in 5D anti-de Sitter space gives rise to an N=4 supergravity-matter system. We explicitly show that only the modes of the N=4 graviton supermultiplet localize on the 4D brane, streamlining and generalizing previous works. We also point out that while charged 1/4 BPS black holes do exist in the 4D theory, they are always produced in sets of total charge zero. This zero-charge configuration uplifts to a 5D metric without naked singularities, thus avoiding the curvature singularity of the 5D uplift of an isolated charged BPS black hole. Finally, we resolve a puzzle with localization of massless high spin fields on a (putative) Randall-Sundrum 2 construction based on Vasiliev?s high spin theories. We show that while high spin fields do localize, the gauge symmetry that ensures decoupling of their unphysical polarizations is anomalous. This implies that the high spin fields must acquire a mass.     

New local supersymmetry of the Vierbein formalism of Einstein gravity

The new local supersymmetry of the vierbein formalism of Einstein gravity for theN=1 case is reconsidered and the canonical quantization is carried out explicitly. The super-covariant derivative is defined with the genuine connection supermultiplet constructed from the vierbein and the ξ-field which plays the role of the Goldstone fermion of the supersymmetry. The extended BRS algebra concerning the supersymmetry is found explicitly.     

Constrained fermionic system and its equivalence with the free parafermionic theory and nonlinear sigma model

We construct the parafermionic (of orderq) representation of the Kac-Moody and Virasoro algebra and compare it with a constrained fermionic system. We find that the central charge of the Virasoro algebra of the constrained fermionic system depends on the regularization scheme. Using the path integral method, we demonstrate this dependence for theq=2 case and find that it can have the same central charge as the free parafermionic theory or the non-linear sigma model depending on the regularization scheme. We point out some ambiguity in the quantization of the constrained system in Hamiltonian formulation.     

Central Charge Extended Supersymmetric Structures for Fundamental Fermions Around Non-Abelian Vortices

Fermionic zero modes around non-abelian vortices are shown that they constitute two N = 2, d = 1 supersymmetric quantum mechanics algebras. These two algebras can be combined under certain circumstances to form a central charge extended N = 4 supersymmetric quantum algebra. We thoroughly discuss the implications of the existence of supersymmetric quantum mechanics algebras, in the quantum Hilbert space of the fermionic zero modes.     

The supersymmetry extended Weyl algebra and Casalbuoni's G4 model

We briefly review the classical version of Casalbuoni's G₄ supersummetric model (i.e. the single particle version of the scalar chiral supermultiplet) with particular emphasis on the role played by the chirality. We show that the off-mass-shell commutators of the quantum model can be derived from the Lie algebra of the Weyl (i.e. Poincaré plus dilatations) group extended by supersymmetry. The proper-time wavefunctions of the off-mass-shell states satisfy equations which clarify the role of the “auxiliary fields” of quantum field theory.     

N=2 extended superconformal algebra with “central” charges

We show how central charges may be incorporated in a superconformal (D = 4) algebra for N = 2. The charges are no longer truly central and so are at variance with the well-known theorems on (super-) symmetries of the S-matrix. We discuss the possible relevance of the algebra and justify our interest in it.     

Transformation properties of the supercurrent

It is shown that the spinor current, if correctly defined, belongs to a supermultiplet, together with the energy-momentum tensor and the axial-vector current. The transformation properties of this supermultiplet under both restricted and general supersymmetry transformations are given. The generators of special supersymmetry transformations can be obtained as first moments of the time component of the spinor current. The transformation laws of the supermultiplet containing the spinor current provide the local version of the supersymmetry algebra.     

N=1 formulation of general N=2 Yang-Mills supergravity couplings

We formulate general interactions of an N=2 Yang-Mills supermultiplet coupled to N=2 supergravity in terms of N=1 invariant functions. We show that the N=2 scalar potential of the complex scalar fields in the adjoint representation, superpartners of the Yang-Mills gauge fields, splits into a conventional gauge contribution as well as in a superpotential term contribution proportional to the SO(2) gauge coupling of N=2 de Sitter supergravity. The relation of these results to the σ model structure of N4 extended supergravities is also discussed, particularly in connection with the coset disintegration of scalar manifolds.     

C-disorder fields and Γ(2)-invariant partition functions in parafermionic conformal field theories

The character formulae for the C-disorder fields corresponding to the charge conjugation symmetry in the parafermionic conformal field theories of Zamolodchikov and Fateev are obtained. These characters span a unitary representation of the level 2 subgroup Γ(2) of the full modular group. The corresponding Γ(2)-invariant partition functions are calculated. Derivation of the character formula is based on the relation between the parafermionic theories and the twisted N = 2 superconformal algebra. A similar idea is applied to explicitly construct the highest weight modules of the twisted SU(2) Kac-Moody algebra.     

Parity,baryon number and supersymmetry

Space reflection induces a transformation in the pseudo-Lie algebra of generators of symmetries and supersymmetries. If there is a supermultiplet in the thepry in which the baryon number is zero for bosons and ± 1 for fermions then the structure of the pseudo-Lie algebra is simple and therefore the space reflection transformation can be studied in detail. It turns out that the space reflection transformation fixes uniquely the structure of the pseudo-Lie algebra as far as the generators of supersymmetries are concerned.     

Supersymmetry and classical solutions

We obtain classical solutions to the field equations of the massless supersymmetric Wess-Zumino model and to the field equations of the interacting SU(2) gauge supermultiplet. This is done by applying finite supersymmetry transformations to the known solutions of the scalar field equation with ?⁴ interaction and the Yang-Mills field equations. The relevance of supersymmetry to the solution of classical field equations involving anticommuting fermion fields is discussed.     

Quantum deformedsu(m/n) algebra and superconformal algebra on quantum superspace

We study a deformedsu(m/n) algebra on a quantum superspace. Some interesting aspects of the deformed algebra are shown. As an application of the deformed algebra we construct a deformed superconformal algebra. From the deformedsu(1/4) algebra, we derive deformed Lorentz, translation of Minkowski space,iso(2, 2) and its supersymmetric algebras as closed subalgebras with consistent automorphisms.     

Supersymmetry and electromagneticE2 transitions

We discuss the quadrupole electric transitions in the frame of the supersymmetric model for light nuclei (s —d shell). We present the construction of an isoscalar transition operator based on the assumption of the dynamicalSO ^BF (6) symmetry. Theoretical transition probabilities for nuclei belonging to the supermultiplet characterized by a particle numberN=5 show quite a good agreement with experimental data.