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.

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.

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.

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.

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.

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.

Some mathematical aspects and scattering amplitudes in the pure spinor formalism

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

Harmonic superspace from the Ad'S IND. 5' × 'S POT. 5' pure spinor formalism

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

Princípio de ação quântica de Schwinger

The Schwinger quantum action principle is a dynamic characterization of the transformation functions and is based on the algebraic structure derived from the kinematic analysis of the measurement processes at the quantum level. As such, this variational principle, allows to derive the canonical commutation relations in a consistent way. Moreover, the dynamic pictures of Schrödinger, Heisenberg and a quantum Hamilton-Jacobi equation can be derived from it. We will implement this formalism by solving simple systems such as the free particle, the quantum harmonic oscillator and the quantum forced harmonic oscillator.