Simplifying and extending the AdS(5) x S-5 pure spinor formalism

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Explaining the pure spinor formalism for the superstring

After adding a pair of non-minimal fields and performing a similarity transformation, the BRST operator in the pure spinor formalism is expressed as a conventional-looking BRST operator involving the Virasoro constraint and (b, c) ghosts, together with 12 fermionic constraints. This BRST operator can be obtained by gauge-fixing the Green-Schwarz superstring where the 8 first-class and 8 second-class Green-Schwarz constraints are combined into 12 first-class constraints. Alternatively, the pure spinor BRST operator can be obtained from the RNS formalism by twisting the ten spin-half RNS fermions into five spin-one and five spin-zero fermions, and using the SO(10)/U(5) pure spinor variables to parameterize the different ways of twisting. GSO(-) vertex operators in the pure spinor formalism are constructed using spin fields and picture-changing operators in a manner analogous to Ramond vertex operators in the RNS formalism.

Black hole partition function using the hybrid formalism of superstrings

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Ab initio study of high tridymite by the formalism generator coordinate Hartree-Fock

The Generator Coordinate Hartree-Fock (GCHF) Method is applied to generate extended 14s 8p and 17s 11p Gaussian basis sets for the atoms O and Si, respectively. The role of the weight functions in the assessment of the numerical integration range of the GCHF is shown. The Gaussian basis sets are contracted to [6s4p] O atom and [8s5p] Si atom by the Dunning's segmented contraction scheme. To evaluate the quality of our contracted [6s4p] and [8s5p] bases in molecular calculations we accomplish calculations of total and orbital energies in the Hartree-Fock-Roothaan method for O-2 and SiO molecules. We compare the results obtained with the our (14s 8p) and (17s 11p) bases sets with the of 6-311G basis and with values from the literature. The addition of one d polarization function in the silicon basis and its utilization with the basis for oxygen leads to the calculation of electronic properties and IR Spectrum of high tridymite in space group D-3d. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Multiloop superstring amplitudes from non-minimal pure spinor formalism

Using the non-minimal version of the pure spinor formalism, manifestly super-Poincare covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picture-changing operators. The only subtlety comes from regularizing the functional integral over the pure spinor ghosts. In this paper, it is shown how to regularize this functional integral in a BRST-invariant manner, allowing the computation of arbitrary multiloop amplitudes. The regularization method simplifies for scattering amplitudes which contribute to ten-dimensional F-terms, i.e. terms in the ten-dimensional superspace action which do not involve integration over the maximum number of theta's.

BFFT formalism applied to the minimal chiral Schwinger model

We consider the minimal chiral Schwinger model, by embedding the gauge non-invariant formulation into a gauge theory following the Batalin-Fradkin-Fradkina-Tyutin point of view. Within the BFFT procedure, the second-class constraints are converted into strongly involutive first-class ones, leading to an extended gauge-invariant formulation. We also show that, like the standard chiral model, in the minimal chiral model the Wess-Zumino action can be obtained by performing a q-number gauge transformation into the effective gauge non-invariant action.

COMPARISON OF THE ANOMALOUS AND NONANOMALOUS GENERALIZED SCHWINGER MODELS VIA THE FUNCTIONAL FORMALISM

We calculate the Green functions of the two versions of the generalized Schwinger model, the anomalous and the nonanomalous one, in their higher order Lagrangian density form. Furthermore, it is shown through a sequence of transformations that the bosonized Lagrangian density is equivalent to the former, at least for the bosonic correlation functions. The introduction of the sources from the beginning, leading to a gauge-invariant source term, is also considered. It is verified that the two models have the same correlation functions only if the gauge-invariant sector is taken into account. Finally, there is presented a generalization of the Wess-Zumino term, and its physical consequences are studied, in particular the appearance of gauge-dependent massive excitations.

CONTINUED-FRACTION FORMALISM APPLIED TO THE SPIN-1/2 XYZ MODEL

In this paper, we evaluate the correlation functions of the spin-1/2 XYZ model for some particular cases by using the Mori continued-fraction formalism. The results are exactly the same as those well-known ones. This removes any doubt about the convergence of the continued fraction recently raised by some authors.

Some superstring amplitude computations with the non-minimal pure spinor formalism

We use the non-minimal pure spinor formalism to compute in a super-Poincare covariant manner the four-point massless one and two-loop open superstring amplitudes, and the gauge anomaly of the six-point one-loop amplitude. All of these amplitudes are expressed as integrals of ten-dimensional superfields in a pure spinor superspace which involves five theta coordinates covariantly contracted with three pure spinors. The bosonic contribution to these amplitudes agrees with the standard results, and we demonstrate identities which show how the t(8) and epsilon(10) tensors naturally emerge from integrals over pure spinor superspace.

BRST-BFV formalism for the generalized Schwinger model

We derive the Wess-Zumino scalar term of the generalized Schwinger model both in the singular and nonsingular cases by using BRST-BFV framework. The photon propagators are also computed in the extended Lorentz gauge.

On the quantum Hamilton-Jacobi formalism

Some postulates are introduced to go from the classical Hamilton-Jacobi theory to the quantum one. We develop two approaches in order to calculate propagators, establishing the connection between them and showing the equivalence of this picture with more known ones such as the Schrödinger's and the Feynman's formalisms. Applications of the above-mentioned approaches to both the standard case of the harmonic oscillator and to the harmonic oscillator with time-dependent parameters are made. © 1991 Plenum Publishing Corporation.

Faddeev-jackiw formalism for A topological-like oscillator in planar dimensions

The problem of a harmonic oscillator coupling to an electromagnetic potential plus a topological-like (Chern-Simons) massive term, in two-dimensional space, is studied in the light of the symplectic formalism proposed by Faddeev and Jackiw for constrained systems.

Cohomology in the pure spinor formalism for the superstring

A manifestly super-Poincaré covariant formalism for the superstring has recently been constructed using a pure spinor variable. Unlike the covariant Green-Schwarz formalism, this new formalism is easily quantized with a BRST operator and tree-level scattering amplitudes have been evaluated in a manifestly covariant manner. In this paper, the cohomology of the BRST operator in the pure spinor formalism is shown to give the usual light-cone Green-Schwarz spectrum. Although the BRST operator does not directly involve the Virasoro constraint, this constraint emerges after expressing the pure spinor variable in terms of SO(8) variables.

Supersymmetric Born-Infeld from the pure spinor formalism of the open superstring

Classical BRST invariance in the pure spinor formalism for the open superstring is shown to imply the supersymmetric Born-Infeld equations of motion for the background fields. These equations are obtained by requiring that the left and right-moving BRST currents are equal on the worldsheet boundary in the presence of the background. The Born-Infeld equations are expressed in N = 1 D = 10 superspace and include all abelian contributions to the low-energy equations of motion, as well as the leading non-abelian contributions. © SISSA/ISAS 2003.

Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring

A ten-dimensional super-Poincaré covariant formalism for the superstring was recently developed which involves a BRST operator constructed from superspace matter variables and a pure spinor ghost variable. A super-Poincaré covariant prescription was defined for computing tree amplitudes and was shown to coincide with the standard RNS prescription. In this paper, picture-changing operators are used to define functional integration over the pure spinor ghosts and and to construct a suitable b ghost. A super-Poincaré covariant prescription is then given for the computation of N-point multiloop amplitudes. One can easily prove that massless N-point multiloop amplitudes vanish for N < 4, confirming the perturbative finiteness of superstring theory. One can also prove the Type IIB S-duality conjecture that R4 terms in the effective action receive no perturbative contributions above one loop. © SISSA/ISAS 2004.