Relating the Green-Schwarz and pure spinor formalisms for the superstring

Although it is not known how to covariantly quantize the Green-Schwarz (GS) superstring, there exists a semi-light-cone gauge choice in which the GS superstring can be quantized in a conformally invariant manner. In this paper, we prove that BRST quantization of the GS superstring in semi-light-cone gauge is equivalent to BRST quantization using the pure spinor formalism for the superstring © SISSA/ISAS 2005.

Pure spinor formalism as an N ≤ 2 topological string

Following suggestions of Nekrasov and Siegel, a non-minimal set of fields are added to the pure spinor formalism for the superstring. Twisted ĉ ≤ 3 N ≤ 2 generators are then constructed where the pure spinor BRST operator is the fermionic spin-one generator, and the formalism is interpreted as a critical topological string. Three applications of this topological string theory include the super-Poincaré covariant computation of multiloop superstring amplitudes without picture-changing operators, the construction of a cubic open superstring field theory without contact-term problems, and a new four-dimensional version of the pure spinor formalism which computes F-terms in the spacetime action. © SISSA 2005.

Four-point one-loop amplitude computation in the pure spinor formalism

The massless 4-point one-loop amplitude computation in the pure spinor formalism is shown to agree with the computation in the RNS formalism. © SISSA 2006.

One-loop conformal invariance of the type II pure spinor superstring in a curved background

We compute the one-loop beta functions for the Type II superstring using the pure spinor formalism in a generic supergravity background. It is known that the classical pure spinor BRST symmetry puts the background fields on-shell. In this paper we show that the one-loop beta functions vanish as a consequence of the classical BRST symmetry of the action. © SISSA 2007.

Superstring Amplitudes in the Pure Spinor Formalism

Among other things, the pure spinor formalism has been used to rederive some particular superstring scattering amplitudes in the last few years. I will briefly review how the computations were done and show that the kinematical factors of these amplitudes can be simply written as integrals in a pure spinor superspace. © 2007 Elsevier B.V. All rights reserved.

Yang-Mills Chern-Simons corrections from the pure spinor superstring

Nilpotency of the pure spinor BRST operator in a curved background implies superspace equations of motion for the background. By computing one-loop corrections to nilpotency for the heterotic sigma model, the Yang-Mills Chern-Simons corrections to the background are derived. © 2008 SISSA.

Unfolding physics from the algebraic classification of spinor fields

After reviewing the Lounesto spinor field classification, according to the bilinear covariants associated to a spinor field, we call attention and unravel some prominent features involving unexpected properties about spinor fields under such classification. In particular, we pithily focus on the new aspects - as well as current concrete possibilities. They mainly arise when we deal with some non-standard spinor fields concerning, in particular, their applications in physics. © 2012 Elsevier B.V.

Harmonic superspace from the AdS5 × S5 pure spinor formalism

On-shell supergravity vertex operators in an AdS 5 × S 5 background are described in the pure spinor formalism by the zero mode cohomology of a BRST operator. After expanding the pure spinor BRST operator in terms of the AdS 5 radius variable, this cohomology is computed using $ \mathcal{N}=4 $ harmonic superspace variables and explicit super-field expressions are obtained for the behavior of supergravity vertex operators near the boundary of AdS 5. © 2013 SISSA, Trieste, Italy.

Divergences of generalized quantum electrodynamics on the Lorenz gauge

In this paper we study the Generalized Quantum Electrodynamics (GQED4) on the Lorenz gauge condition and show that divergences are still present in the theory. © 2013 American Institute of Physics.

Correspondence between the self-dual model and the topologically massive electrodynamics: A new view

Following the study of the Topologically Massive Theories under the Hamilton-Jacobi, we now analyze the constraint structure of the Self-Dual model as well as its correspondence with the Topologically Massive Electrodynamics. © 2013 American Institute of Physics.

Nilpotency of the b ghost in the non-minimal pure spinor formalism

The b ghost in the non-minimal pure spinor formalism is not a fundamental field. It is based on a complicated chain of operators and proving its nilpotency is nontrivial. Chandia proved this property in arXiv:1008.1778, but with an assumption on the nonminimal variables that is not valid in general. In this work, the b ghost is demonstrated to be nilpotent without this assumption. © 2013 SISSA, Trieste, Italy.

Dynamical twisting and the b ghost in the pure spinor formalism

After adding an RNS-like fermionic vector ψ m to the pure spinor formalism, the non-minimal b ghost takes a simple form similar to the pure spinor BRST operator. The N=2 superconformal field theory generated by the b ghost and the BRST current can be interpreted as a dynamical twisting of the RNS formalism where the choice of which spin 1/2 ψ m variables are twisted into spin 0 and spin 1 variables is determined by the pure spinor variables that parameterize the coset SO(10)/U(5). © 2013 SISSA, Trieste, Italy.

Notes on the pure spinor b ghost

In this work, a particular BRST-exact class of deformations of the b ghost in the non-minimal pure spinor formalism is investigated and the impact of this construction in the N= 2 ĉ = 3 topological string algebra is analysed. As an example, a subclass of deformations is explicitly shown, where the U (1) current appears in a conventional form, involving only the ghost number currents. Furthermore, a c ghost like composite field is introduced, but with an unusual construction. © 2013 SISSA, Trieste, Italy.

Batalin-Fradkin-Vilkovisky quantization of the generalized scalar electrodynamics

This work comprises a study upon the quantization and the renormalizability of the generalized electrodynamics of spinless charged particles (mesons), namely, the generalized scalar electrodynamics (GSQED4). The theory is quantized in the covariant framework of the Batalin-Fradkin-Vilkovisky method. Thereafter, the complete Green's functions are obtained through functional methods and a proper discussion on the theory's renormalizability is also given. Next, we present the computation and further discussion on the radiative correction at α order; and, as it turns out, an unexpected mP-dependent divergence on the mesonic sector of the theory is found. Furthermore, in order to show the effectiveness of the renormalization procedure on the present theory, we also give a diagrammatic discussion on the photon self-energy at α2 order, where we observe contributions from the meson self-energy function. Afterwards, we present the expressions of the counterterms and effective coupling of the theory, obtaining from the latter an energy range where the theory is defined by m2≤k2

Some mathematical aspects and scattering amplitudes in the pure spinor formalism

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