Massless Vertex Operators Research Articles

Constructing massive superstring vertex operators from massless vertex operators using the pure spinor formalism

The vertex operator for the first massive states of the open superstring is constructed in terms of d=10 super Yang-Mills superfields using the OPE's of massless vertex operators in the pure spinor formalism.

Multiparticle SYM equations of motion and pure spinor BRST blocks

In this paper a multiparticle generalization of linearized ten-dimensional super Yang--Mills superfields is proposed. Their equations of motions are shown to take the same form as in the single-particle case, supplemented by contact terms. A recursive construction of these superfields is inspired by the iterated OPEs among massless vertex operators in the pure spinor formalism. An enlarged set of BRST-covariant pure spinor blocks is then defined in a streamlined fashion and combined to multiparticle vertex operators. The latter can be used to universally describe tree-level subdiagrams in the perturbative open and closed superstring, regardless of the loop order. The inherent symmetries of the multiparticle superfields are reproduced by structure constants of the gauge group, hinting a natural appearance of the BCJ-duality between color and kinematics in the fundamentals of super Yang--Mills theory. We present one-loop applications where known scalar cohomology objects are systematically recomputed and a novel vector cohomology particularly relevant to the closed string is constructed for arbitrary multiplicity.

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

A covariant map between the Ramond-Neveu-Schwarz (RNS) and pure spinor formalisms for the superstring is found which transforms the RNS and pure spinor BRST operators into each other. The key ingredient is a dynamical twisting of the ten spin-half RNS fermions into five spin-one and five spin-zero fermions using bosonic pure spinors that parameterize an SO(10)/U(5) coset. The map relates massless vertex operators in the two formalisms, and gives a new description of Ramond states which does not require spin fields. An argument is proposed for relating the amplitude prescriptions in the two formalisms.

Symmetries of massless vertex operators in [formula omitted

The worldsheet sigma model of the superstring in AdS 5 × S 5 has a one-parameter family of flat connections parametrized by the spectral parameter. The corresponding Wilson line is not BRST invariant for an open contour, because the BRST transformation leads to boundary terms. These boundary terms define a cohomological complex associated with the endpoint of the contour. We study the cohomology of this complex for Wilson lines in some infinite-dimensional representations. We find that for these representations the cohomology is nontrivial at the ghost number 2. This implies that it is possible to define a BRST invariant open Wilson line. The central point in the construction is the existence of massless vertex operators transforming exactly covariantly under the action of the global symmetry group. In flat space, massless vertices transform covariantly only up to adding BRST-exact terms. But in AdS we show that it is possible to define vertices so that they transform exactly covariantly.

Higher-loop amplitudes in the non-minimal pure spinor formalism

We analyze the properties of the non-minimal pure spinor formalism. We show that Siegel gauge on massless vertex operators implies the primary field constraint and the level-matching condition in closed string theory by reconstructing the integrated vertex operator representation from the unintegrated ones. The pure spinor integration in the non-minimal formalism needs a regularisation. To this end we introduce a new regulator for the pure spinor integration and an extension of the regulator to allow for the saturation of the fermionic d-zero modes to all orders in perturbation. We conclude with a preliminary analysis of the properties of the four-graviton amplitude to all genus order.

COVARIANT QUANTIZATION OF THE SUPERSTRING

After reviewing the Green-Schwarz superstring using the approach of Siegel, the superstring is covariantly quantized by constructing a BRST operator from the fermionic constraints and a bosonic pure spinor ghost variable. Physical massless vertex operators are constructed and, for the first time, N-point tree amplitudes are computed in a manifestly ten-dimensional super-Poincaré covariant manner. Quantization can be generalized to curved supergravity backgrounds and the vertex operator for fluctuations around AdS5×S5 is explicitly constructed.

Superstring vertex operators in an background

A quantizable action has recently been proposed for the superstring in an AdS_5 x S^5 background with Ramond-Ramond flux. In this paper, we construct physical vertex operators corresponding to on-shell fluctuations around the AdS_5 x S^5 background. The structure of these AdS_5 x S^5 vertex operators closely resembles the structure of the massless vertex operators in a flat background.

Super-Poincare covariant quantization of the superstring

Using pure spinors, the superstring is covariantly quantized. For the first time, massless vertex operators are constructed and scattering amplitudes are computed in a manifestly ten-dimensional super-Poincar\'e covariant manner. Quantizable non-linear sigma model actions are constructed for the superstring in curved backgrounds, including the $AdS_5\times S^5$ background with Ramond-Ramond flux.

On the NSR formulation of string theory on AdS5× S5

We discuss the NSR formulation of the superstring action on AdS 5× S 5 proposed recently by Kallosh and Tseytlin in the Green-Schwarz formalism. We show that the stress-energy tensor corresponding to the NSR action for AdS superstring contains the branelike terms, corresponding to exotic massless vertex operators (referred to as the branelike vertices)- the 5-form e φ ψ m1 ⋯ ψ m5 and the 3-form ∂( e φ ψ m 1 ⋯ ψ m 3 ), multiplied by ∂X m . The corresponding sigma-model action has the manifest SO(1,3)× SO(6) invariance of superstring theory on AdS 5× S 5. We argue that adding the branelike terms is equivalent to curving the space-time to obtain the AdS 5× S 5 background. We commence the study of the proposed NSR sigma-model by analyzing the scattering amplitudes involving the branelike vertex operators. The analysis shows quite an unusual momentum dependence of these scattering amplitudes.