Four-dimensional supersymmetric black holes of type IIA superstring

We systematically construct a large class of four-dimensional supersymmetric black hole solutions of toroidally compactified type IIA superstring theory by explicitly solving the Killing spinor equations. They correspond to orthogonally intersecting configurations in ten dimensions. With the Kaluza-Klein monopole, they are parameterized by four charges and preserve of the N = 8 supersymmetry. We found a simple map to associate each charge with the corresponding Killing spinor constraints. The embedding of the N = 4 supersymmetry of a toroidally compactified heterotic string into the N = 8 supersymmetry of the IIA superstring was explicitly shown. We also found explicitly the configurations with only Ramond-Ramond charges, and those with both Neveu-Schwarz Neveu-Schwarz charges and Ramond-Ramond charges, including the dilaton and the internal metrics. The T-dual of these configurations were shown to satisfy the Killing spinor equations as well.     

Gauge fixing in fully gauge-invariant field theory of closed bosonic and Neveu-Schwarz strings

The gauge fixing procedure is reanalyzed in our fully gauge-invariant closed bosonic and Neveu-Schwarz string field theory which does not have any constraint on string functionals and gauge parameters. The relations to other formulations are clarified; in particular, it is shown that our theory recovers other formulation with constraints L₊ − L₋ = 0 after partial gauge fixing but without any truncation. Complete gauge fixing is also made and the expected propagator is obtained. The constraint L₊ − L₋ = 0 appears as a field equation in our formulation.     

On the Structure of Verma Modules over Virasoro and Neveu-Schwarz Algebras

In the paper we present a different proof of the theorem of B. L. Feigin and D. B. Fuchs about the structure of Verma modules over Virasoro algebra. We state some new results about the structure of Verma modules over Neveu-Schwarz. The proof has two advantages: First, it is simpler in the most interesting cases (for example in the so called minimal models), second, it can be generalized for Neveu-Schwarz algebra for some class of Verma modules. Received: 15 December 1995 / Accepted: 4 March 1996     

Superconformal algebras and transitive group actions on quadrics

A classification of “physical” superconformal algebras is given. The list consists of seven algebras: the Virasoro algebra, the Neveu-Schwarz algebra, theN = 2,3 and 4 algebras, the superalgebra of all vector fields on theN = 2 supercircle, and a new algebraCK ₆ constructed in [3]. The proof relies heavily on the classification of all connected subgroups ofSO _n(C) which act transitively on the quadric (v, v) = 1. To Ernest Borisovich Vinberg on his 60_th birthday Partially supported by NSF grant DMS-9622870     

A Super Generalization of KdV6 Equation

In this paper, we propose a fermionic generalization of KdV6 equation and study its integrability. Moreover, we show that this equation is a constraint Hamiltonian flow on the coadjoint orbit of Neveu-Schwarz superalgebra.     

Spectrum generating algebra and no-ghost theorem for fermionic massive string

The covariant operator quantization of the ordinary free spinning BDH string modified by adding the supersymmetric Liouville sector is analysed in the even target space dimensions d = 2, 4, 6, 8. The spectrum generating algebra for this model is constructed and a general version of the no-ghost theorem is proven. The counterpart of the GSO projection leads to a family of tachyon-free unitary free string theories. One of these models is equivalent to the non-critical Ramond-Neveu-Schwarz spinning string truncated in the Neveu-Schwarz sector to the tachyon-free eigenspace of the fermion parity operator.     

Diffractive dissociation in the dual model

We study the one twisted loop contribution to the five-point function in the Neveu-Schwarz model. The formulation obtained incorporates the requirements of duality and analyticity (Steinmann relations), provides a low-mass vector-pseudoscalar system predominantly as an S-wave J^P = 1⁺ state near threshold, conserves approximately t-channel helicity and thus is an interesting candidate for the phenomenology of diffractive dissociation.     

A presentation for the Virasoro and super-Virasoro algebras

It is shown that the entire Virasoro, Ramond and Neveu-Schwarz algebras can each be constructed from a finite number of well-chosen generators satisfying a small number of conditions. The most economical sets consist of just two starting generators in all cases, subject to eight conditions for the Virasoro case, five conditions for the Ramond case, and nine conditions for the Neveu-Schwarz case.Work supported by the U.S. Department of Energy, Division of High Energy Physics, Contract W-31-109-ENG-38     

Highest weight representations of the Neveu-Schwarz and Ramond algebras

We construct a family of representationsK ^,w of the Neveu-Schwarz and Ramond algebras, which generalize the Fock representations of the Virasoro algebra. We show that the representationsK ^,w are intertwined by a vertex operator.The above results are used to give the proof of the conjectured formulas for the determinant of the contravariant form on the highest weight representations of the Neveu-Schwarz and Ramond algebras. Further results on the representation theory of the latter are derived from the determinant formulas.Partially supported by the National Science Foundation through the Mathematical Sciences Research InstitutePartially supported by NSF grant MCS-8201260     

Perturbation of pulsating strings

We discuss semiclassical quantization of circular pulsating strings in \( \text {AdS}_3 \times \text {S}^3 \) background with and without the Neveu-Schwarz–Neveu-Schwarz (NS–NS) flux. We find the equations of motion corresponding to the quadratic action in bosonic sector in terms of scalar quantities and invariants of the geometry. The general equations for studying physical perturbations along the string in an arbitrary curved spacetime are written down using covariant formalism. We discuss the stability of these string configurations by studying the solutions of the linearized perturbed equations of motion.     

Singular vectors of the Neveu-Schwarz algebra

We give an explicit expression for some singular vectors of highest weight representations of the Neveu-Schwarz algebra.     

The Multi-Pole Neveu-Schwarz Algebra on Riemann Supersphere

According to the Riemann-Roch theorem, we construct bases H_-n⁽ⁱ⁾ and N_-m^(f), for the meromorphic λ = -1 and λ = -1/2 differentials on the Riemann sphere S². The dual bases, A_-n⁽ⁱ⁾, and D_-m^(j), of these meromorphic λ differentials on C_r curves are defined. Expanding the component fields TB(z) and TF(z) of the stress-energy tensor T(z) in the superconformal field theory by the dual bases A_-n⁽ⁱ⁾, and D_-m^(j), respectively, we obtain a series of expanding coefficients. The commutation relations among these coefficients are given explicitly, which,is just the multi-pole Neveu-Schwarz algebra with central extensions on the Riemann supersphere S. Physical implics tions of the algebra are also discussed.     

Manifestly dual formulation of the Ramond-model

The interacting-string formalism is extended to the Neveu-Schwarz and Ramond models. The duality properties of the latter model are more transparent than in the older formulation, and ghost-free amplitudes with an arbitrary number of external fermions can be calculated.     

Towards the large N limit of pure Nu = 1 super Yang-Mills theory

We find the gravity solution corresponding to a large number of Neveu-Schwarz or D5-branes wrapped on a two sphere so that we have pure Nu = 1 super Yang-Mills in the IR. The supergravity solution is smooth, it shows confinement, and it breaks the U(1)(R) chiral symmetry in the appropriate way. When the gravity approximation is valid the masses of glueballs are comparable to the masses of Kaluza-Klein (KK) states on the 5-brane, but if we could quantize strings on this background it looks like we should be able to decouple the KK states.     

Equivalence of two-loop superstring amplitudes in the pure spinor and Ramond-Neveu-Schwarz formalisms

The pure spinor formalism for the superstring has recently been used to compute massless four-point two-loop amplitudes in a manifestly super-Poincaré covariant manner. In this Letter, we show that when all four external states are Neveu-Schwarz states, the two-loop amplitude coincides with the Ramond-Neveu-Schwarz result.     

Covariant fermionic vertex in superstrings

A covariant fermionic vertex is constructed in terms of Ramond spinors and ghost operators, starting from the Neveu-Schwarz model. Correlation functions of spinors and ghosts are defined. The supersymmetry algebra is realized as the algebra of massless vertices with zero momentum.     

The Mixed Kuper-Camassa-Holm-Hunter-Saxton Equations

In this paper, a mixed Kuper-CH-HS equation by a Kupershmidt deformation is introduced and its integrable properties are studied. Moreover, that the equation can be viewed as a constraint Hamiltonian flow on the coadjoint orbit of Neveu-Schwarz superalgebra is shown.     

Spontaneous symmetry breakdown and Regge intercepts

By Regge slope methods we exhibit a Nambu-Goldstone spontaneous symmetry breakdown and a Higgs mechanism inherent in a unit-intercept dual meson amplitude. Introducing an Abelian gauge group corresponding to conservation of a pseudocharge, Regge intercept shifts are calculated; to lowest order the leading Regge intercept of the Neveu-Schwarz model is lowered from $\text{α(0) = 1}\text{to}\text{α(0) =}\text{1}\text{2}$. Our method has the advantage over Bardakci's spurion method that massless scalar are not required at any stage.     

Spectral Triples and the Super-Virasoro Algebra

We construct infinite dimensional spectral triples associated with representations of the super-Virasoro algebra. In particular the irreducible, unitary positive energy representation of the Ramond algebra with central charge c and minimal lowest weight h = c/24 is graded and gives rise to a net of even θ-summable spectral triples with non-zero Fredholm index. The irreducible unitary positive energy representations of the Neveu-Schwarz algebra give rise to nets of even θ-summable generalised spectral triples where there is no Dirac operator but only a superderivation.     

Multiplet classification of the indecomposable highest weight modules over the Neveu-Schwarz and Ramond superalgebras

All multiplets of reducible (and indecomposable) highest weight modules (HWM) over the Neveu-Schwarz and Ramond superalgebras are classified and parametrized. The reducible HWM are given a simple explicit parametrization. The homogeneity degrees of all singular vectors of the reducible HWM are explicitly given.Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria