Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism

Abstract

Using the non-minimal version of the pure spinor formalism, manifestly super-Poincare covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picture-changing operators. The only subtlety comes from regularizing the functional integral over the pure spinor ghosts. In this paper, it is shown how to regularize this functional integral in a BRST-invariant manner, allowing the computation of arbitrary multiloop amplitudes. The regularization method simplifies for scattering amplitudes which contribute to ten-dimensional F-terms, i.e. terms in the ten-dimensional superspace action which do not involve integration over the maximum number of $\theta$'s.

23 pages harvmac, added acknowledgement

References in corpus (28)

• String Theory and Noncommutative Geometry
• Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
• Super-Poincare Covariant Quantization of the Superstring
• Two Dimensional Gauge Theories Revisited
• Duality, Quotients, and Currents
• Topological Amplitudes in String Theory
• Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories
• N=4 Topological Strings
• Pure Spinor Formalism as an N=2 Topological String
• Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring
• ABCD of instantons
• Current Algebras and Differential Geometry
• Towards Covariant Quantization of the Supermembrane
• Covariant Quantization of Superstrings Without Pure Spinor Constraints
• Covariant One-Loop Amplitudes in D=11
• On maximally supersymmetric Yang-Mills theories
• Dilaton shift under duality and torsion of elliptic complex
• A New First Class Algebra, Homological Perturbation and Extension of Pure Spinor Formalism for Superstring
• Mirror symmetry in two steps: A-I-B
• Higher-Dimensional Twistor Transforms using Pure Spinors
• Dirac Sigma Models
• The Character of Pure Spinors
• On First Order Formalism in String Theory
• Y-formalism in Pure Spinor Quantization of Superstrings
• On the b-antighost in the Pure Spinor Quantization of Superstrings
• Wakimoto realizations of current algebras: an explicit construction
• Noncommutative instantons: a new approach
• Covariant Multiloop Superstring Amplitudes

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• Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization
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• One-loop Superstring Amplitude From Integrals on Pure Spinors Space
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• BRST quantization of the pure spinor superstring
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• A New Proposal for the Picture Changing Operators in the Minimal Pure Spinor Formalism
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• Pure spinor computation towards open string three-loop
• Pure Spinor Integration from the Collating Formula
• Analytical solutions of pure-spinor superstring field theory
• D=5 Holomorphic Chern-Simons and the Pure Spinor Superstring
• Geometrical framework for picture changing operators in the pure spinor formalism