Lower-dimensional pure-spinor superstrings

We study to what extent it is possible to generalise Berkovits' pure-spinor construction in d=10 to lower dimensions. Using a suitable definition of a ``pure'' spinor in d=4,6, we propose models analogous to the d=10 pure-spinor superstring in these dimensions. Similar models in d=2,3 are also briefly discussed.Comment: 17 page

Towards Pure Spinor Type Covariant Description of Supermembrane -- An Approach from the Double Spinor Formalism --

In a previous work, we have constructed a reparametrization invariant worldsheet action from which one can derive the super-Poincare covariant pure spinor formalism for the superstring at the fully quantum level. The main idea was the doubling of the spinor degrees of freedom in the Green-Schwarz formulation together with the introduction of a new compensating local fermionic symmetry. In this paper, we extend this "double spinor" formalism to the case of the supermembrane in 11 dimensions at the classical level. The basic scheme works in parallel with the string case and we are able to construct the closed algebra of first class constraints which governs the entire dynamics of the system. A notable difference from the string case is that this algebra is first order reducible and the associated BRST operator must be constructed accordingly. The remaining problems which need to be solved for the quantization will also be discussed.Comment: 40 pages, no figure, uses wick.sty; v2: a reference added, published versio

A New Proposal for the Picture Changing Operators in the Minimal Pure Spinor Formalism

Using a new proposal for the "picture lowering" operators, we compute the tree level scattering amplitude in the minimal pure spinor formalism by performing the integration over the pure spinor space as a multidimensional Cauchy-type integral. The amplitude will be written in terms of the projective pure spinor variables, which turns out to be useful to relate rigorously the minimal and non-minimal versions of the pure spinor formalism. The natural language for relating these formalisms is the Cech-Dolbeault isomorphism. Moreover, the Dolbeault cocycle corresponding to the tree-level scattering amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor space, which means that the origin is removed from this space. Also, the Cech-Dolbeault language plays a key role for proving the invariance of the scattering amplitude under BRST, Lorentz and supersymmetry transformations, as well as the decoupling of unphysical states. We also relate the Green's function for the massless scalar field in ten dimensions to the tree-level scattering amplitude and comment about the scattering amplitude at higher orders. In contrast with the traditional picture lowering operators, with our new proposal the tree level scattering amplitude is independent of the constant spinors introduced to define them and the BRST exact terms decouple without integrating over these constant spinors.Comment: 56 pages, typos correcte

Note About Classical Dynamics of Pure Spinor String on AdS_5 x S_5 Background

We will discuss some properties of the pure spinor string on the AdS_5 x S_5 background. Using the classical Hamiltonian analysis we will show that the vertex operator for the massless state that is in the cohomology of the BRST charges describes on-shell fluctuations around AdS_5 x S_5 background.Comment: 26. pages, added references, v2:corrected typo

Non-BPS D-Branes in Light-Cone Green-Schwarz Formalism

Non-BPS D-branes are difficult to describe covariantly in a manifestly supersymmetric formalism. For definiteness we concentrate on type IIB string theory in flat background in light-cone Green-Schwarz formalism. We study both the boundary state and the boundary conformal field theory descriptions of these D-branes with manifest SO(8) covariance and go through various consistency checks. We analyze Sen's original construction of non-BPS D-branes given in terms of an orbifold boundary conformal field theory. We also directly study the relevant world-sheet theory by deriving the open string boundary condition from the covariant boundary state. Both these methods give the same open string spectrum which is consistent with the boundary state, as required by the world-sheet duality. The boundary condition found in the second method is given in terms of bi-local fields that are quadratic in Green-Schwarz fermions. We design a special ``doubling trick'' suitable to handle such boundary conditions and prescribe rules for computing all possible correlation functions without boundary insertions. This prescription has been tested by computing disk one-point functions of several classes of closed string states and comparing the results with the boundary state computation.Comment: 47 pages, 1 figure. Typos corrected, references added and slight modification of certain explanation made. Version accepted for publication in JHE

Simplifying and Extending the AdS_5xS^5 Pure Spinor Formalism

Although the AdS_5xS^5 worldsheet action is not quadratic, some features of the pure spinor formalism are simpler in an AdS_5xS^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 AdS_5xS^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.Comment: 39 pages harvma

Ten-Dimensional Super-Twistors and Super-Yang-Mills

Four-dimensional super-twistors provide a compact covariant description of on-shell N=4 d=4 super-Yang-Mills. In this paper, ten-dimensional super-twistors are introduced which similarly provide a compact covariant description of on-shell d=10 super-Yang-Mills. The super-twistor variables are Z=(lambda^alpha, mu_alpha, Gamma^m) where lambda^alpha and mu_alpha are constrained bosonic d=10 spinors and Gamma^m is a constrained fermionic d=10 vector. The Penrose map relates the twistor superfield Phi(Z) with the d=10 super-Yang-Mills vertex operator lambda^alpha A_alpha(x,theta) which appears in the pure spinor formalism of the superstring, and the cubic super-Yang-Mills amplitude is proportional to the super-twistor integral \int dZ Phi_1 Phi_2 Phi_3.Comment: 14 pages harvmac, added short clarificatio

Origin of Pure Spinor Superstring

The pure spinor formalism for the superstring, initiated by N. Berkovits, is derived at the fully quantum level starting from a fundamental reparametrization invariant and super-Poincare invariant worldsheet action. It is a simple extension of the Green-Schwarz action with doubled spinor degrees of freedom with a compensating local supersymmetry on top of the conventional kappa-symmetry. Equivalence to the Green-Schwarz formalism is manifest from the outset. The use of free fields in the pure spinor formalism is justified from the first principle. The basic idea works also for the superparticle in 11 dimensions.Comment: 21 pages, no figure; v2: refs. adde

Pure spinor computation towards open string three-loop

Using the recent results in the pure spinor formulation, we lay out a ground-work towards the full momentum space amplitudes of open superstrings at three-loop. After briefly reviewing the one-loop amplitude, we directly work out the two-loop and reproduce the result that was obtained by a symmetry argument. For the three-loop, first we use the two-loop regulator as a warm-up exercise. The result vanishes. We then employ the regulator that has been recently proposed by Aisaka and Berkovits (AB). It is noted that the terms in higher power in $\frac{1}{\lambda\bar{\lambda}}$ that render the two-loop regulator disqualified for the three-loop do not contribute. This with a few other indications suggests a possibility that the AB regulator might also lead to a vanishing result. Nevertheless, we argue that it is possible to acquire the three-loop amplitude, and present a result that we anticipate to be the three-loop amplitude.Comment: 41 pages, latex, cosmetic change

Characterization of membrane-bound lipase from a thermophilic Rhizopus oryzae isolated from palm oil mill effluent

The characteristics of the membrane-bound lipase from a thermophilic Rhizopus oryzae were studied. The pH and temperature optima for lipase activity were at 7.0 and 37°C, respectively. The enzyme was stable and acidic conditions, retaining more than 80% of its initial activity at pH 4.0 after 30 min incubation. It was stable up to 50°C with 70% of initial activity retained after 3 h incubation. The enzyme is 1,3 specific and exhibits substrate preference. Monoacid triglyceride substrates were hydrolyzed better than methyl esters, polyoxysorbitan and sorbitan substrates