Orthosymplectic unification of the Galilei group and BRST

The inclusion of BRST generators into the Poincarè group in D dimensions is known to lead IOsp[D,2|2]. Similarly, conformal symmetry gets extended into Osp[D×1,3|2]. For the non-relativistic case we find that the Galilei symmetry gets extended, by inclusion of the BRST generators, into an orthosymplectic symmetry possessing Osp[D,1|2] as a subgroup. All such extensions express the possibility of formulating the classical theories in reparametrization invariant ways. They include besides the generators of the initial kinematical symmetry (Poincarè, or conformal, or Galilei), the generators of Parisi-Sourlas transformations. The extended symmetries follow directly through BRST quantization.     

On the “covariantized light-cone” string field theory II

We present a full non-linear BRS transformation which corresponds to one of the generators of the OSp(1, 1|2) or OSp(26, 2|2) algebra using the covariantly extended joining-splitting type interaction vertex functions in open string field theory.     

OSp(1,1|4) BRST-symmetry for string field with the world-sheet metric

The Sp(2) symmetry of the ghost coordinates in the harmonic gauge for the world-sheet metric is extended to the OSp(1,1|4) group. A new set of BRST charges which form a multiplet under this OSp(1,1|4) group is found. Gauge transformations are constructed by using the Sp(4) subgroup and a gauge invariant action is proposed for the OSp(1,1|4) singlet string field.     

Heterotic σ-models and conformal supergravity in two dimensions

The (1, 0) and (2, 0) type heterotic σ-models with Wess-Zumino term are coupled to conformal supergravity in two dimensions. There are no new restrictions on the σ-model manifolds in addition to those which arise in the globally supersymmetric cases. In the (1, 0) case possible isometries of the scalar manifold are gauged. A derivation of d = 2 conformal supergravity based on the super Lie algebra OSp(2, N)⊕OSp(2, N) (N = 1, 2) is given.     

Conformally covariant nonlinear equations on tensor-spinors

We prove that to each conformally covariant equation on tensor-spinors on a Riemannian or pseudo-Riemannian manifold with spin structure one can add a nonlinear term without losing the property of conformal covariance. It follows in particular that, on a manifold of dimension n, the nonlinear Dirac equation, Pψ + λ|ψ|^1/(n?1)ψ = 0, where P is the Dirac operator and λ is a constant, is conformally covariant. This generalizes a result of Gürsey [1]. Some results of Ørsted [2], concerning a nonlinear equation associated with the Laplacian on function, and of Branson, concerning distinguished nonlinearities associated with his modified Laplacian on differential forms [3] are also derived as particular cases of this general result.     

Standard complex for quantum Lie algebras

For a quantum Lie algebra Γ, let Γ^ be its exterior extension (the algebra Γ^ is canonically defined). We introduce a differential on the exterior extension algebra Γ^ which provides the structure of a complex on Γ^. In the situation when Γ is a usual Lie algebra, this complex coincides with the “standard complex.” The differential is realized as a commutator with a (BRST) operator Q in a larger algebra Γ^[Ω], with extra generators canonically conjugated to the exterior generators of Γ^. A recurrent relation which uniquely defines the operator Q is given.     

Infinite-parameter symmetries and the Higgs effect in gravity-coupled sigma models in D+4 dimensions

We compute the mass spectra of small fluctuations of four-dimensional fields for Kaluza-Klein models in which the compactification from D+4 to 4 (flat) dimensions is induced by the scalar fields of a nonlinear sigma model defined on an S^N or CP^N manifold. The compactifications are stable for all values of N. The fact that the spectra contain no massless vector fields is traced to the absence of a local gauge invariance for the sigma-model action. We introduce a complete basis for the infinite-parameter symmetries that arise from the harmonic analysis of the higher-dimensional dynamical invariances. The spectrum of spin-one and spin-two fields is consistent with the Higgs effect associated with the breaking of the local symmetries corresponding to these generators. The commutation relations of the infinite parameter algebra for the case of CP¹ are also given. The algebra includes the spectrum-generating algebra SO(1,3) of Salam and Strathdee.     

Conformal field theory and the symmetries of string field theory

The two-dimensional conformal field theory representation of Witten's bosonic string field theory is discussed. The basic overlap equations, K_n symmetry and BRST invariance are proved directly, without the usual expansion in oscillators. The conformal field theory approach naturally provides local overlap identities which (when integrated over half the string) can be used to verify properties of the cubic action. In particular, a recently proposed diffeomorphism invariance is shown to be free of anomalies. Finally, a new class of symmetries, including generalizations of the K_n symmetries which are local in spacetime, are presented.     

Nilpotent Symmetries in Jackiw-Pi Model: Augmented Superfield Approach

We derive the complete set of off-shell nilpotent \(\left (s^{2}_{(a)b} = 0\right )\) and absolutely anticommuting (s_bs_ab+s_abs_b=0) Becchi-Rouet-Stora-Tyutin (BRST) (s_b) as well as anti-BRST symmetry transformations (s_ab) corresponding to the combined Yang-Mills and non-Yang-Mills symmetries of the (2+1)-dimensional Jackiw-Pi model within the framework of augmented superfield formalism. The absolute anticommutativity of the (anti-)BRST symmetries is ensured by the existence of two sets of Curci-Ferrari (CF) type of conditions which emerge naturally in this formalism. The presence of CF conditions enables us to derive the coupled but equivalent Lagrangian densities. We also capture the (anti-)BRST invariance of the coupled Lagrangian densities in the superfield formalism. The derivation of the (anti-)BRST transformations of the auxiliary field ρ is one of the key findings which can neither be generated by the nilpotent (anti-)BRST charges nor by the requirements of the nilpotency and/or absolute anticommutativity of the (anti-)BRST transformations. Finally, we provide a bird’s-eye view on the role of auxiliary field for various massive models and point out few striking similarities and some glaring differences among them.     

Abelian 3-form gauge theory: Superfield approach

We discuss a D-dimensional Abelian 3-form gauge theory within the framework of Bonora-Tonin’s superfield formalism and derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for this theory. To pay our homage to Victor I. Ogievetsky (1928–1996), who was one of the inventors of Abelian 2-form (antisymmetric tensor) gauge field, we go a step further and discuss the above D-dimensional Abelian 3-form gauge theory within the framework of BRST formalism and establish that the existence of the (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions is the hallmark of any arbitrary p-form gauge theory (discussed within the framework of BRST formalism).     

AdS branes from partial breaking of superconformal symmetries

It is shown how the static-gauge world-volume superfield actions of diverse superbranes on the AdS_d+1 superbackgrounds can be systematically derived from nonlinear realizations of the appropriate AdS supersymmetries. The latter are treated as superconformal symmetries of flat Minkowski superspaces of the bosonic dimension d. Examples include the N = 1 AdS₄ supermembrane, which is associated with the 1/2 partial breaking of the OSp(1|4) supersymmetry down to the N = 1, d = 3 Poincaré supersymmetry, and the T-duality related L3-brane on AdS₅ and scalar 3-brane on AdS₅ × S¹, which are associated with two different patterns of 1/2 breaking of the SU(2, 2|1) supersymmetry. Another (closely related) topic is the AdS/CFT equivalence transformation. It maps the world-volume actions of the codimension-one AdS_d+1 (super)branes onto the actions of the appropriate Minkowski (super)conformal field theories in the dimension d.     

Structure constants for the osp(1|2) current algebra

We study the free field realization of the two-dimensional osp(1|2) current algebra. We consider the case in which the level of the affine osp(1|2) symmetry is a positive integer. Using the Coulomb gas technique we obtain integral representations for the conformal blocks of the model. In particular, from the behaviour of the four-point function, we extract the structure constants for the product of two arbitrary primary operators of the theory. From this result we derive the fusion rules of the osp(1|2) conformal field theory and we explore the connections between the osp(1|2) affine symmetry and the N = 1 superconformal field theories.     

Superstrings from Hamiltonian reduction

In any string theory there is a hidden, twisted superconformal symmetry algebra, part of which is made up by the BRST current and the anti-ghost. We investigate how this algebra can be systematically constructed for strings with N − 2 supersymmetries, via quantum Hamiltonian reduction of the Lie superalgebras osp(N|2). The motivation is to understand how one could systematically construct generalized string theories from superalgebras. We also briefly discuss the BRST algebra of the topological string, which is a doubly twisted N = 4 superconformal algebra.     

Canonical BRST quantisation of worldsheet gravities

We reformulate the BRST quantisation of chiral Virasoro and W₃ worldsheet gravities. Our approach follows directly the classic BRST formulation of Yang-Mills theory in employing a derivative gauge condition instead of the conventional conformal gauge condition, supplemented by an introduction of momenta in order to put the ghost action back into first-order form. The consequence of these simple changes is a considerable simplification of the BRST formulation, the evaluation of anomalies and the expression of Wess-Zumino consistency conditions. In particular, the transformation rules of all fields now constitute a canonical transformation generated by the BRST operator Q, and we obtain in this reformulation a new result that the anomaly in the BRST Ward identity is obtained by application of the anomalous operator Q², calculated using operator products, to the gauge fermion.     

Strings in the harmonic gauge

The bosonic string is quantized in a path-integral formulation in harmonic gauge. The BRST transformations are identified and the stress tensor is constructed. The conformal anomaly is computed, and has the standard (D−26) form. The ghost number current is shown to have no anomalies, even on a curved world sheet.     

Nilpotency ofQBRST and the vanishing ß-function in string theories

We study the conformal Ward identities following from the BRST invariance in string theories and show that the nilpotency of Q_BRST implies a vanishing ß-function and vice versa.     

The Map Between Conformal Hypercomplex/ Hyper-Kähler and Quaternionic(-Kähler) Geometry

We review the general properties of target spaces of hypermultiplets, which are quaternionic-like manifolds, and discuss the relations between these manifolds and their symmetry generators. We explicitly construct a one-to-one map between conformal hypercomplex manifolds (i.e. those that have a closed homothetic Killing vector) and quaternionic manifolds of one quaternionic dimension less. An important role is played by `ξ-transformations', relating complex structures on conformal hypercomplex manifolds and connections on quaternionic manifolds. In this map, the subclass of conformal hyper-Kähler manifolds is mapped to quaternionic-Kähler manifolds. We relate the curvatures of the corresponding manifolds and furthermore map the symmetries of these manifolds to each other.     

Classical hamiltonian reduction on D(2|1;α) Chern–Simons gauge theory and large N=4 superconformal symmetry

3d Chern–Simons gauge theory has a strong connection with 2d CFT and link invariants in knot theory. We impose some constraints on the D(2|1;α) CS theory in the similar context of the hamiltonian reduction of 2d superconformal algebras. There Hilbert states in D(2|1;α) CS theory are partly identified with characters of the large N=4 SCFT by their transformation properties.     

Quaternion-Octonion Unitary Symmetries and Analogous Casimir Operators

An attempt has been made to investigate the global SU(2) and SU(3) unitary flavor symmetries systematically in terms of quaternion and octonion respectively. It is shown that these symmetries are suitably handled with quaternions and octonions in order to obtain their generators, commutation rules and symmetry properties. Accordingly, Casimir operators for SU(2) and SU(3) flavor symmetries are also constructed for the proper testing of these symmetries in terms of quaternions and octonions.     

Anisotropy of positron wave function in 4d transition metals

The positron wave functions have been calculated employing the method of expansion of symmetrized plane waves in some 4d transition metals. Systematics of the positron wave functions along the three symmetry directions [100], [110], [111] in these metals, have been discussed. The anisotropies of the ψ₊ have been found to be strongly dependent upon the crystal symmetries. The results of the band structure calculation of 2γ-angular correlation in Rh and Ag are presented.