Superconformal System Research Articles

Spinning extensions of D(2, 1; \u03b1) superconformal mechanics

As is known, any realization of SU(2) in the phase space of a dynamical system can be generalized to accommodate the exceptional supergroup D(2, 1; α), which is the most general mathcal{N} = 4 supersymmetric extension of the conformal group in one spatial dimension. We construct novel spinning extensions of D(2, 1; α) superconformal mechanics by adjusting the SU(2) generators associated with the relativistic spinning particle coupled to a spherically symmetric Einstein-Maxwell background. The angular sector of the full superconformal system corresponds to the orbital motion of a particle coupled to a symmetric Euler top, which represents the spin degrees of freedom. This particle moves either on the two-sphere, optionally in the external field of a Dirac monopole, or in the SU(2) group manifold. Each case is proven to be superintegrable, and explicit solutions are given.

Nonlinear symmetries of perfectly invisible PT-regularized conformal and superconformal mechanics systems

We investigate how the Lax-Novikov integral in the perfectly invisible PT-regularized zero-gap quantum conformal and superconformal mechanics systems affects on their (super)-conformal symmetries. We show that the expansion of the conformal symmetry with this integral results in a nonlinearly extended generalized Shrödinger algebra. The PT-regularized superconformal mechanics systems in the phase of the unbroken exotic nonlinear mathcal{N} = 4 super-Poincaré symmetry are described by nonlinearly super-extended Schrödinger algebra with the osp(2|2) sub-superalgebra. In the partially broken phase, the scaling dimension of all odd integrals is indefinite, and the osp(2|2) is not contained as a sub-superalgebra.

6d Conformal matter

A single M5-brane probing G, an ADE-type singularity, leads to a system which has G x G global symmetry and can be viewed as "bifundamental" (G,G) matter. For the A_N series, this leads to the usual notion of bifundamental matter. For the other cases it corresponds to a strongly interacting (1,0) superconformal system in six dimensions. Similarly, an ADE singularity intersecting the Horava-Witten wall leads to a superconformal matter system with E_8 x G global symmetry. Using the F-theory realization of these theories, we elucidate the Coulomb/tensor branch of (G,G') conformal matter. This leads to the notion of fractionalization of an M5-brane on an ADE singularity as well as fractionalization of the intersection point of the ADE singularity with the Horava-Witten wall. Partial Higgsing of these theories leads to new 6d SCFTs in the infrared, which we also characterize. This generalizes the class of (1,0) theories which can be perturbatively realized by suspended branes in IIA string theory. By reducing on a circle, we arrive at novel duals for 5d affine quiver theories. Introducing many M5-branes leads to large N gravity duals.

New super-Calogero models and OSp(4|2) superconformal mechanics

We report on the new approach to constructing superconformal extensions of the Calogerotype systems with an arbitrary number of involved particles. It is based upon the superfield gauging of non-Abelian isometries of some supersymmetric matrix models. Among its applications, we focus on the new N = 4 superconformal system yielding the U(2)-spin Calogero model in the bosonic sector, and the one-particle case of this system, which is a new OSp(4|2) superconformal mechanics with nondynamical U(2) spin variables. The characteristic feature of thesemodels is that the strength of the conformal inverse-square potential is quantized.

POINT-SPLITTING REGULARIZATION IN N=2 SUPERCONFORMAL FIELD THEORY

In this paper, the method of point-splitting regularization is applied on the N=2 superconformal field theory, specifically the superconformal coset model formulated by Kazama and Suzuki. We obtain the correct central extensions for the N=2 superconformal algebra after many nontrivial cancellations among the various singular expressions. This shows the consistency of the point-splitting method in an N=2 superconformal system. In the process, we arrive at the Kazama–Suzuki conditions which govern the existence of an N=2 superconformal coset model in the N=1 coset model. In addition, we obtain a number of mathematical relations between the structure constants and the complex structure of the model, which allow us to simplify the U(1) current of the N=2 superconformal algebra. In the course of our analysis, we found that, at least in a two dimension conformal field theory, the operator product expansion of a composite current must be written in a way which conveys all the information of the commutator equations.

Hamiltonian reduction of supersymmetric WZNW models on bosonic groups and superstrings

It is shown that an alternative supersymmetric version of the Liouville equation extracted from D = 3 Green-Schwarz superstring equations naturally arises as a super-Toda model obtained from a properly constrained supersymmetric WZNW theory based on the sl(2, R) algebra. Hamiltonian reduction is performed by imposing a non-linear superfield constraint which turns out to be a mixture of a first- and second-class constraint on supercurrent components. Supersymmetry of the model is realized non-linearly and is spontaneously broken. The set of independent current fields which survive the Hamiltonian reduction contains (in the holomorphic sector) one bosonic current of spin 2 (the stress tensor of the spin-0 Liouville mode) and two fermionic fields of spin 3 2 and −1 2 . The n = 1 superconformal system thus obtained is of the same kind as one describing non-critical fermionic strings in a universal string theory. The generalization of this procedure allows one to produce from any bosonic Lie algebra super-Toda models and associated super- W algebras together with their non-standard realizations.

A locally supersymmetric action for the bosonic string

Recently Berkovits and Vafa have shown that the bosonic string can be viewed as a fermionic string propagating in a particular background. Such a background is described by a somewhat unusual N=1 superconformal system. By coupling it to N=1 supergravity I construct a local supersymmetric action for the bosonic string.

Four-dimensional gravitational backgrounds based on [formula omitted], superconformal systems

We propose two new realizations of the N = 4, c ̂ = 4 superconformal system based on the compact and non- compact versions of parafermionic algebras. The target space interpretation of these systems is given in terms of four- dimensional target spaces with non-trivial metric and topology different from the previously known four-dimensional semi-wormhole realization. The proposed c ̂ = 4 systems can be used as a building block to construct perturbatively stable superstring solutions with covariantized target space supersymmetry around non-trivial gravitational and dilation backgrounds.

More about superconformal field theory. Hamiltonian formalism

The Hamiltonian formalism for theN=1,d=4 superconformal system is given. The first-order formalism is found by starting from the canonical covariant one. As the conformal supergravity is a higher-derivative theory, to analyze the second-order Hamiltonian formalism the Ostrogradski transformation is introduced to define canonical momenta.

Higher symmetries in the spin-one Zamolodchikov-Fateev hamiltonian with a finite number of sites and toroidal boundary conditions. Spectra and operator content of N = 1 superconformal systems

The finite-size scaling spectra of the antiferromagnetic Zamolodchikov-Fateev hamiltonian with toroidal boundary conditions are given up to macroscopic momenta, by a Z(2) parafermion combined with a free boson. We show how to project out from this spectra various N = 1 superconformal systems. We give the operator content corresponding to the various sectors of these systems determined by internal symmetries and boundary conditions. In particular we recover all the modular invariants of Cappelli in two different ways. We next apply the same projection mechanism to finite chains. This is possible due to some special symmetry properties of the finite chains. In this way we get the spectra of various systems. In particular the spectra of the tricritical Ising model (c = 7 10 ) obtained from the spin-one chain coincides with those obtained from the spectra of the spin-1/2 XXZ Heisenberg chain. Through a simple generalization the number of states for some higher SU(2) × SU(2)/SU(2) coset models are obtained.

N = 3 AND N = 4 SUPERCONFORMAL WZNW SIGMA MODELS IN SUPERSPACE II: THE N = 4 CASE

The issues related to the U (1) × O (4) N = 4 superconformal WZNW sigma models [with the bosonic target spaces U (1) × SU (2) and U (1) × U (1) × O (4)] are investigated in the framework of a 2D N = 4 superspace. We define the corresponding N = 4 supercurrents, both on classical and quantum levels, in terms of the basic primary N = 4 WZNW superfields and show that the generalized Sugawara form for the dimension 3/2 and 2 component currents directly follows from the constraints on the basic superfields. The N = 4 superfield analog of the Knizhnik–Zamolodchikov equation for conformal blocks in WZNW sigma models is derived. We also analyze the N = 4 WZNW superfields from the standpoint of two SU(2) N = 4 SCAs entering as subalgebras into the underlying U (1) × O (4) N = 4 SCA. We demonstrate that in the linearizing limit the U (1) × SU (2) WZNW model reproduces the recently discussed SU(2) N = 4 superconformal system of free chiral superfields.

On the moduli space of c=0 topological conformal field theories

We studied the marginal deformation of the c=0 topological conformal field theories (TCFT). We showed that topological SL(2) Wess-Zumino-Witten (WZW) models, topological superconformal ghost systems, TCFT constructed from the N=2 superconformal system and two dimensional topological gravity belong to the same one parameter family (moduli space) of the c=0 TCFTs. We conjectured that the N=2 TCFT constructed from the Wolf space realization of N=4 superconformal algebra belongs to another family.

Quaternionic manifolds for type II superstring vacua of Calabi-Yau spaces

In type II theories compactified on Calabi-Yau manifolds the moduli fields are accompanied by (Ramond-Ramond) scalar superpartners. N = 2 space-time supersymmetry requires the low-energy effective mutual interaction of these excitations be described by a quaternionic σ-model in target space. In this paper we explicitly construct these manifolds from the restricted Kähler geometry of the moduli space of arbitrary (2,2) superconformal systems.

Strings on hyperelliptic supersurfaces

Starting from a definition of a hyperelliptic superRiemann surface (HESS), we study its supermoduli space and the “superVirasoro” algebra on it. We map that algebra into a Z 4 p=2 parafermionic algebra on CP 1,1. Using explicitly supersymmetric bosonization of the first-order superconformal systems, we construct explicitly the primary fields of the parafermionic algebra: the branching and the spin operators. We give a simple prescription for the calculation of sdet D γ on HESS through correlation functions of these branching operators. As an example, we calculate the g = 2 superstring partition function and verify that the cosmological constant vanishes, after integration over the moduli space.

GEOMETRY OF TYPE II SUPERSTRINGS AND THE MODULI OF SUPERCONFORMAL FIELD THEORIES

We study general properties of the low-energy effective theory for 4D type II superstrings obtained by the compactification on an abstract (2,2) superconformal system. This is the basic step towards the construction of their moduli space. We give an explicit and general algorithm to convert the effective Lagrangian for the type IIA into that of type IIB superstring defined by the same (2,2) superconformal system (and vice versa). This map converts Kahler manifolds into quaternionic ones (and quaternionic into Kahlerian ones) and has a deep geometrical meaning. The relationship with the theory of normal quaternionic manifolds (and algebras), as well as with Jordan algebras, is outlined. It turns out that only a restricted class of quarternionic geometries is allowed in the string case. We derive a general and explicit formula for the (fully nonlinear) couplings of the vector-multiplets (IIA case) in terms of the basic three-point functions of the underlying superconformal theory. A number of illustrative examples is also presented.

CHARACTER FORMULAE AND THE STRUCTURE OF THE REPRESENTATIONS OF THE N=1, N=2 SUPERCONFORMAL ALGEBRAS

The unitary representations of the N=1 and N=2 superconformal algebras are analyzed. The embedding structure of all the degenerate representations is studied. Character formulae are derived for the degenerate representations including those which [Formula: see text]. The relation between characters and the exact partition functions of 2-d critical statistical systems is explored. The [Formula: see text], N=2 superconformal system is analyzed from the group theoretic point of view and it is shown to be a subsector of the N=1, ĉ=2/3 theory.

The c=2/3 minimal N=1 superconformal system and its realisation in the critical O(2) Gaussian model

The structure of the c=2/3 minimal N=1 superconformal system is analysed in detail. The primary operators are constructed as operators in the critical O(2) Gaussian model at some specific fixed radius. The operator algebra is verified explicitly. Operator product coefficients and some superspace correlation functions are calculated exactly.

Modular invariance in superconformal models

The constraints of modular invariance on the field content of two-dimensional superconformal systems are explored. The constraints take the form of sum rules on the number of superconformal highest weight states and a requirement of integer spin. Models which satisfy these constraints are given.