Results 1 - 10
of
12
IFT-P.002/2002 Towards Covariant Quantization of the Supermembrane
, 2002
"... By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the formalism recently developed for covariantly quantizing the d=10 superparticle and superstring is extended to the d=11 superparticle and supermembrane. In this formalism, kappa symmetry is replaced by a BRST-like inv ..."
Abstract
-
Cited by 26 (5 self)
- Add to MetaCart
(Show Context)
By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the formalism recently developed for covariantly quantizing the d=10 superparticle and superstring is extended to the d=11 superparticle and supermembrane. In this formalism, kappa symmetry is replaced by a BRST-like invariance using the nilpotent operator Q = ∮ λαdα where dα is the worldvolume variable corresponding to the d=11 spacetime supersymmetric derivative and λ α is an SO(10,1) pure spinor variable satisfying λΓ c λ = 0 for c = 1 to 11. Super-Poincaré covariant unintegrated and integrated supermembrane vertex operators are explicitly constructed which are in the cohomology of Q. After double-dimensional reduction of the eleventh dimension, these vertex operators are related to Type IIA superstring vertex operators where Q = QL + QR is the sum of the left and right-moving Type IIA BRST operators and the eleventh component of the pure spinor constraint, λΓ11λ = 0, replaces the b0 L −b0R constraint of the closed superstring. A conjecture is made for the computation of M-theory scattering amplitudes using these supermembrane vertex operators.
Non-Critical Pure Spinor Superstrings
, 2006
"... We construct non-critical pure spinor superstrings in two, four and six dimensions. We find explicitly the map between the RNS variables and the pure spinor ones in the linear dilaton background. The RNS variables map onto a patch of the pure spinor space and the holomorphic top form on the pure spi ..."
Abstract
-
Cited by 15 (3 self)
- Add to MetaCart
(Show Context)
We construct non-critical pure spinor superstrings in two, four and six dimensions. We find explicitly the map between the RNS variables and the pure spinor ones in the linear dilaton background. The RNS variables map onto a patch of the pure spinor space and the holomorphic top form on the pure spinor space is an essential ingredient of the mapping. A basic feature of the map is the requirement of doubling the superspace, which we analyze in detail. We study the structure of the non-critical pure spinor space, which is different from the ten-dimensional one, and its quantum anomalies. We compute the pure spinor lowest lying BRST cohomology and find an agreement with the RNS spectra. The analysis is generalized to curved backgrounds and we construct as an example the non-critical pure spinor type IIA superstring on AdS4 with RR 4-form flux.
A note on the classical BRST symmetry of the pure spinor string in a curved background,” JHEP 0607
, 2006
"... The classical pure spinor version of the heterotic superstring in a supergravity and super Yang-Mills background is considered. We obtain the BRST transformations of the world-sheet fields. They are consistent with the constraints obtained from the nilpotence of the BSRT charge and the holomorphicit ..."
Abstract
-
Cited by 11 (5 self)
- Add to MetaCart
The classical pure spinor version of the heterotic superstring in a supergravity and super Yang-Mills background is considered. We obtain the BRST transformations of the world-sheet fields. They are consistent with the constraints obtained from the nilpotence of the BSRT charge and the holomorphicity of the BRST current.
IFT-P.015.2008 Fermionic T-Duality, Dual Superconformal Symmetry, and
, 807
"... We show that tree level superstring theories on certain supersymmetric backgrounds admit a symmetry which we call “fermionic T-duality”. This is a nonlocal redefinition of the fermionic worldsheet fields similar to the redefinition we perform on bosonic variables when we do an ordinary T-duality. Th ..."
Abstract
- Add to MetaCart
(Show Context)
We show that tree level superstring theories on certain supersymmetric backgrounds admit a symmetry which we call “fermionic T-duality”. This is a nonlocal redefinition of the fermionic worldsheet fields similar to the redefinition we perform on bosonic variables when we do an ordinary T-duality. This duality maps a supersymmetric background to another supersymmetric background with different RR fields and a different dilaton. We show that a certain combination of bosonic and fermionic T-dualities maps the full superstring theory on AdS5 × S 5 back to itself in such a way that gluon scattering amplitudes in the original theory map to something very close to Wilson loops in the dual theory. This duality maps the “dual superconformal symmetry ” of the original theory to the ordinary superconformal symmetry of the dual model. This explains the dual superconformal invariance of planar scattering amplitudes of N = 4 super Yang Mills and also sheds some light on the connection between amplitudes and Wilson loops. In the appendix, we propose a simple prescription for open superstring MHV tree amplitudes in a flat background. July
Simplifying and Extending the AdS5 × S 5 Pure Spinor Formalism
, 2008
"... Although the AdS5 ×S 5 worldsheet action is not quadratic, some features of the pure spinor formalism are simpler in an AdS5 × S 5 background than in a flat background. The BRST operator acts geometrically, the left and right-moving pure spinor ghosts can be treated as complex conjugates, the zero m ..."
Abstract
- Add to MetaCart
(Show Context)
Although the AdS5 ×S 5 worldsheet action is not quadratic, some features of the pure spinor formalism are simpler in an AdS5 × S 5 background than in a flat background. The BRST operator acts geometrically, the left and right-moving pure spinor ghosts can be treated as complex conjugates, the zero mode measure factor is trivial, and the b ghost does not require non-minimal fields. Furthermore, a topological version of the AdS5 × S 5 action with the same worldsheet variables and BRST operator can be constructed by gauge-fixing a G/G principal chiral model where G = PSU(2, 2|4). This topological model is argued to describe the zero radius limit that is dual to free N = 4 super-Yang-Mills and can also be interpreted as an “unbroken phase ” of superstring theory.
IFT-P.002/2002 Covariant Quantization of the Supermembrane
, 2002
"... By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the formalism recently developed for covariantly quantizing the d=10 superparticle and superstring is extended to the d=11 superparticle and supermembrane. In this formalism, kappa symmetry is replaced by a BRST-like inv ..."
Abstract
- Add to MetaCart
(Show Context)
By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the formalism recently developed for covariantly quantizing the d=10 superparticle and superstring is extended to the d=11 superparticle and supermembrane. In this formalism, kappa symmetry is replaced by a BRST-like invariance using the nilpotent operator Q = ∮ λαdα where dα is the worldvolume variable corresponding to the d=11 spacetime supersymmetric derivative and λ α is an SO(10,1) pure spinor variable satisfying λΓ c λ = 0 for c = 1 to 11. Super-Poincaré covariant unintegrated and integrated supermembrane vertex operators are explicitly constructed which are in the cohomology of Q. After double-dimensional reduction of the eleventh dimension, these vertex operators are related to Type IIA superstring vertex operators where Q = QL + QR is the sum of the left and right-moving Type IIA BRST operators and the eleventh component of the pure spinor constraint, λΓ11λ = 0, replaces the b0 L −b0R constraint of the closed superstring. A conjecture is made for the computation of M-theory scattering amplitudes using these supermembrane vertex operators.
IFT-P.063/2002 ICTP Lectures on Covariant Quantization of the Superstring
, 2002
"... These ICTP Trieste lecture notes review the pure spinor approach to quantizing the superstring with manifest D=10 super-Poincaré invariance. The first section discusses covariant quantization of the superparticle and gives a new proof of equivalence with the Brink-Schwarz superparticle. The second s ..."
Abstract
- Add to MetaCart
(Show Context)
These ICTP Trieste lecture notes review the pure spinor approach to quantizing the superstring with manifest D=10 super-Poincaré invariance. The first section discusses covariant quantization of the superparticle and gives a new proof of equivalence with the Brink-Schwarz superparticle. The second section discusses the superstring in a flat background and shows how to construct vertex operators and compute tree amplitudes in a manifestly super-Poincaré covariant manner. And the third section discusses quantization of the superstring in curved backgrounds which can include Ramond-Ramond flux.
The Superembedding Origin of the Berkovits Pure Spinor Covariant Quantization of Superstrings
, 2002
"... We show that the pure spinor formalism proposed by Berkovits to covariantly quantize superstrings is a gauge fixed, twisted version of the complexified n = 2 superembedding formulation of the superstring. This provides the Berkovits approach with a geometrical superdiffeomorphism invariant ground. A ..."
Abstract
- Add to MetaCart
(Show Context)
We show that the pure spinor formalism proposed by Berkovits to covariantly quantize superstrings is a gauge fixed, twisted version of the complexified n = 2 superembedding formulation of the superstring. This provides the Berkovits approach with a geometrical superdiffeomorphism invariant ground. As a consequence, the absence of the worldsheet (super)diffeomorphism ghosts in the pure spinor quantization prescription and the nature of the Berkovits BRST charge and antighost are clarified. Since superembedding is classically equivalent to the Green–Schwarz formulation, we thus also The superembedding is a geometrical description of the dynamics of superbranes by means of a specific embedding of worldvolume supersurfaces into target superspaces. It has proved to be a powerful method for studying various aspects of superbranes at the classical level (see [1] for a review). For instance, the superembedding description has explained the geometrical
IFT-P.044/2004 BRST Cohomology and Nonlocal Conserved Charges
, 2004
"... A relation is found between nonlocal conserved charges in string theory and certain ghost-number two states in the BRST cohomology. This provides a simple proof that the nonlocal conserved charges for the superstring in an AdS5 × S5 background are BRST-invariant in the pure spinor formalism and are ..."
Abstract
- Add to MetaCart
(Show Context)
A relation is found between nonlocal conserved charges in string theory and certain ghost-number two states in the BRST cohomology. This provides a simple proof that the nonlocal conserved charges for the superstring in an AdS5 × S5 background are BRST-invariant in the pure spinor formalism and are κ-symmetric in the Green-Schwarz formalism.
