Complete N-point superstring disk amplitude I. Pure spinor computation

In this paper the pure spinor formalism is used to obtain a compact expression for the superstring N  -point disk amplitude. The color-ordered string amplitude is given by a sum over (N−3)!$(N-3)!$ super-Yang–Mills subamplitudes multiplied by multiple Gaussian hypergeometric functions. In order to obtain this result, the cohomology structure of the pure spinor superspace is exploited to generalize the Berends–Giele method of computing super-Yang–Mills amplitudes. The method was briefly presented in Mafra et al. (2011) [1], and this paper elaborates on the details and contains higher-rank examples of building blocks and associated cohomology objects. But the main achievement of this work is to identify these field-theory structures in the pure spinor computation of the superstring amplitude. In particular, the associated set of basis worldsheet integrals is constructively obtained here and thoroughly investigated together with the structure and properties of the amplitude in Mafra et al. (2011) [2], arXiv:1106.2646 [hep-th].     

On supersymmetric Lorentzian Einstein-Weyl spaces

We consider weighted parallel spinors in Lorentzian Weyl geometry in arbitrary dimensions, choosing the weight such that the integrability condition for the existence of such a spinor implies the geometry to be Einstein-Weyl. We then use techniques developed for the classification of supersymmetric solutions to supergravity theories to characterise those Lorentzian EW geometries that allow for a weighted parallel spinor, calling the resulting geometries supersymmetric. The overall result is that they are either conformally related to ordinary geometries admitting parallel spinors (w.r.t. the Levi-Cività connection), or they are conformally related to certain Kundt spacetime. A full characterisation is obtained for the 4- and 6-dimensional cases.     

Materializing superghosts

The off-shell Batalin-Vilkovysky (BV) realization has been constructed for N = 1, d = 10 super-Yang-Mills theory with seven auxiliary fields. This becomes possible due to the materialized ghost phenomenon. Namely, supersymmetry ghosts are coordinates on a manifold B of ten-dimensional spinors with the pure spinors cut out. Auxiliary fields are sections of a bundle over B, and supersymmetry transformations are nonlinear in ghosts. By integrating out the auxiliary fields, we obtain an on-shell supersymmetric BV action with quadratic terms in the antifields. Exactly this on-shell BV action was obtained in our previous paper after integration out of auxiliary fields in the framework of a pure spinor superfield formalism. The text was submitted by the authors in English.     

Unstable behaviors of classical solutions in spinor-type conformal invariant fermionic models

It is well known that instantons are classical topological solutions existing in the context of quantum field theories that lie behind the standard model of particles. To provide a better understanding for the dynamical nature of spinor-type instanton solutions, conformal invariant pure spinor fermionic models that admit particle-like solutions for the derived classical field equations are studied in this work under cosine wave forcing. For this purpose, the effects of external periodic forcing on two systems that have different dimensions and quantum spinor numbers and have been obtained under the use of Heisenberg ansatz are investigated by constructing their Poincaré sections in phase space. As a result, bifurcations and chaos are observed depending on the excitation amplitude of the external forcing in both pure spinor fermionic models.     

Supersymmetry in Lorentzian Curved Spaces and Holography

We consider superconformal and supersymmetric field theories on four-dimensional Lorentzian curved space-times, and their five-dimensional holographic duals. As in the Euclidean signature case, preserved supersymmetry for a superconformal theory is equivalent to the existence of a charged conformal Killing spinor. Differently from the Euclidean case, we show that the existence of such spinors is equivalent to the existence of a null conformal Killing vector. For a supersymmetric field theory with an R-symmetry, this vector field is further restricted to be Killing. We demonstrate how these results agree with the existing classification of supersymmetric solutions of minimal gauged supergravity in five dimensions.     

A superloop approach to supersymmetric gauge theories

A supersymmetric extension of the loop equations of motion in gauge theories is presented. The ansatz used for solving these superloop equations has the form of an average of the superloop product — supersymmetric path-dependent phase factor. The averaging action is determined by the superloop equations themselves. An example of the abelian spinor gauge superfield is considered in some detail.     

Conformal spinor current anomalies

An anomalous divergence of the conformal spinor current is obtained for some massless supersymmetric theories. The corresponding modified Ward identities are discussed for a simple model without gauge fields.     

Complete N-point superstring disk amplitude II. Amplitude and hypergeometric function structure

Using the pure spinor formalism in part I (Mafra et al., preprint [1]) we compute the complete tree-level amplitude of N massless open strings and find a striking simple and compact form in terms of minimal building blocks: the full N  -point amplitude is expressed by a sum over (N−3)!$(N-3)!$ Yang–Mills partial subamplitudes each multiplying a multiple Gaussian hypergeometric function. While the former capture the space–time kinematics of the amplitude the latter encode the string effects. This result disguises a lot of structure linking aspects of gauge amplitudes as color and kinematics with properties of generalized Euler integrals. In this part II the structure of the multiple hypergeometric functions is analyzed in detail: their relations to monodromy equations, their minimal basis structure, and methods to determine their poles and transcendentality properties are proposed. Finally, a Gröbner basis analysis provides independent sets of rational functions in the Euler integrals.     

Supergravity and the spinor dual model

We find that the spinor dual model is locally supersymmetric not only in the two-dimensional surface spanned by the string, but also with respect to the embedding space-time.     

Algebraic spinors and SUSY

Using the Dirac-Kaehler formalism, we formulate the supersymmetric Wess-Zumino model. Special attention is paid to the proper definition of a two-dimensional spinor, its adjoint, and its generalization to other dimensions.     

Quantization of superparametrized monopoles

Classical finite-energy solutions of the SU(2) Yang-Mills-Higgs system in four-dimensional space-time are embedded in the supersymmetric extension of the theory. Finite supertranslations are constructed and are used to obtain a family of solutions to the supersymmetric field equations, parametrized by fermionic Majorana spinor parameters. The quantum theory around arbitrary classical solutions, parametrized by arbitrary bosonic (global and local) as well as fermionic (global) parameters, is constructed and discussed.     

Spinor Bose–Einstein condensates

An overview of the physics of spinor and dipolar Bose–Einstein condensates (BECs) is given. Mean-field ground states, Bogoliubov spectra, and many-body ground and excited states of spinor BECs are discussed. Properties of spin-polarized dipolar BECs and those of spinor–dipolar BECs are reviewed. Some of the unique features of the vortices in spinor BECs such as fractional vortices and non-Abelian vortices are delineated. The symmetry of the order parameter is classified using group theory, and various topological excitations are investigated based on homotopy theory. Some of the more recent developments in a spinor BEC are discussed.     

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.     

Super Yang–Mills theory from nonlinear supersymmetry

The relation between a nonlinear supersymmetric (NLSUSY) theory and a SUSY Yang–Mills (SYM) theory is studied for N=3$N=3$ SUSY in two-dimensional space–time. We explicitly show the NL/L SUSY relation for the (pure) SYM theory by means of cancellations among Nambu–Goldstone fermion self-interaction terms.     

Bound-state solutions of the Dirac-Rosen-Morse potential with spin and pseudospin symmetry<Superscript>⋆</Superscript>

The energy spectra and the corresponding two-component spinor wave functions of the Dirac equation for the Rosen-Morse potential with spin and pseudospin symmetry are obtained. The s -wave ( k \kappa = 0 state) solutions for this problem are obtained by using the basic concept of the supersymmetric quantum mechanics approach and function analysis (standard approach) in the calculations. Under the spin symmetry and pseudospin symmetry, the energy equation and the corresponding two-component spinor wave functions for this potential and other special types of this potential are obtained. The extension of this result to the k \kappa 1 \neq 0 state is suggested.     

Point-splitting derivation of anomalous divergence for the spinor current

The anomaly for the divergence of the spinor current in the supersymmetric Yang-Mills theory is obtained by the point-splitting regularization method. The results agree with those of the lowest order perturbation theory. The anomaly is removed by redifinition of the gauge invariant conserved current.     

De Sitter cosmic strings and supersymmetry

We study massive spinor fields in the geometry of a straight cosmic string in a de Sitter background. We find a hidden N = 2 supersymmetry in the fermionic solutions of the equations of motion. We connect the zero mode solutions to the heat-kernel regularized Witten index of the supersymmetric algebra.