Notes on beta-deformations of the pure spinor superstring in AdS(5) x S(5)

We study the properties of the vertex operator for the beta-deformation of the superstring in AdS(5) x S(5) in the pure spinor formalism. We discuss the action of supersymmetry on the infinitesimal beta-deformation, the application of the homological perturbation theory, and the relation between the worldsheet description and the spacetime supergravity description. (C) 2011 Elsevier B.V. All rights reserved.

Ten-dimensional supergravity constraints from the pure spinor formalism for the superstring

It has recently been shown that the ten-dimensional superstring can be quantized using the BRST operator Q = philambda(alpha)d(alpha), where lambda(alpha) is a pure spinor satisfying; lambdagamma(m)lambda = 0 and dalpha is the fermionic supersymmetric derivative. In this paper, the pure spinor version of superstring theory is formulated in a curved supergravity background and it is shown that nilpotency and holomorphicity of the pure spinor BRST operator imply the on-shell superspace constraints of the supergravity background. This is shown to lowest order in alpha' for the heterotic and Type II superstrings, thus providing a compact pure spinor version of the ten-dimensional superspace constraints for N = 1 Type IIA and Type IIB supergravities. Since quantization is straightforward using the pure spinor version of the superstring, it is expected that these methods can also be used to compute higher-order alpha' corrections to the ten-dimensional superspace constraints. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Lorentz invariance of the pure spinor BRST cohomology for the superstring

In a previous Letter. The BRST cohomology in the pure spinor formalism of the superstring was shown to coincide with the light-cone Green-Schwarz spectrum by using an SO(8) parameterization of the pure spinor. In this Letter, the SO(9, 1) Lorentz generators are explicitly constructed using this SO(8) parameterization, proving the Lorentz invariance of the pure spinor BRST cohomology. (C) 2001 Published by Elsevier B.V. B.V.

Path integral quantization of generalized quantum electrodynamics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Notes on beta-deformations of the pure spinor superstring in AdS(5) x S-5

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

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.

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.

The Hilbert space of the Chern-Simons theory on a cylinder: a loop quantum gravity approach

As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define at the quantum level the constraints appearing in the canonical approach and completely solve them, thus constructing a gauge and diffeomorphism invariant physical Hilbert space for the theory. This space turns out to be infinite dimensional, but separable.

STRONG COUPLING LIMITS and QUANTUM ISOMORPHISMS of THE GAUGED THIRRING MODEL

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Matsubara-Fradkin thermodynamical quantization of Podolsky electrodynamics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Renormalization of the ladder light-front Bethe-Salpeter equation in the Yukawa model

The reduction of the two-fermion Bethe-Salpeter equation in the framework of light-front dynamics is studied for the Yukawa model. It yields auxiliary three-dimensional quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded in powers of the coupling constant gs allowing a defined number of boson exchanges; it is divergent and needs renormalization; it also includes the instantaneous term of the Dirac propagator. One possible solution of the renormalization problem of the boson exchanges is shown to be provided by expanding the effective interaction beyond single boson exchange. The effective interaction in ladder approximation up to order g4 s is discussed in detail. It is shown that the effective interaction naturally yields the box counterterm required to be introduced ad hoc previously. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional quantities.

Canonical Quantization of a Massive Weyl Field

We construct a consistent theory of a quantum massive Weyl field. We start with the formulation of the classical field theory approach for the description of massive Weyl fields. It is demonstrated that the standard Lagrange formalism cannot be applied for the studies of massive first-quantized Weyl spinors. Nevertheless we show that the classical field theory description of massive Weyl fields can be implemented in frames of the Hamilton formalism or using the extended Lagrange formalism. Then we carry out a canonical quantization of the system. The independent ways for the quantization of a massive Weyl field are discussed. We also compare our results with the previous approaches for the treatment of massive Weyl spinors. Finally the new interpretation of the Majorana condition is proposed.

The Ramond sector of open superstring field theory

Although the equations of motion for the Neveu-Schwarz (NS) and Ramond (R) sectors of open superstring field theory can be covariantly expressed in terms of one NS and one R string field, picture-changing problems prevent the construction of an action involving these two string fields. However, a consistent action can be constructed by dividing the NS and R states into three string fields which are real, chiral and antichiral. The open superstring field theory action includes a WZW-like term for the real field and holomorphic Chern-Simons-like terms for the chiral and antichiral fields. Different versions of the action can be constructed with either manifest d = 8 Lorentz covariance or manifest TV = 1 d = 4 super-Poincaré covariance. The lack of a manifestly d = 10 Lorentz covariant action is related to the self-dual five-form in the type-IIB R-R sector.

Covariant map between Ramond-Neveu-Schwarz and pure spinor formalisms for the superstring

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Problem with the superstring action of Deriglazov and Galajinsky

Deriglazov and Galajinsky have recently proposed a new covariant action for the Green-Schwarz superstring which can be constructed in any spacetime dimension. In this Comment, I show that their action contains extra on-shell degrees of freedom as compared with the standard action and is therefore inequivalent. ©1999 The American Physical Society.