Lectures on Two-Loop Superstrings

Abstract

In these lectures, recent progress on multiloop superstring perturbation theory is reviewed. A construction from first principles is given for an unambiguous and slice-independent two-loop superstring measure on moduli space for even spin structure. A consistent choice of moduli, invariant under local worldsheet supersymmetry is made in terms of the super-period matrix. A variety of subtle new contributions arising from a careful gauge fixing procedure are taken into account. The superstring measure is computed explicitly in terms of genus two theta-functions and reveals the importance of a new modular object of weight 6. For given even spin structure, the measure exhibits a behavior under degenerations of the worldsheet that is consistent with physical principles. The measure allows for a unique modular covariant GSO projection. Under this GSO projection, the cosmological constant, the 1-, 2- and 3- point functions of massless supergravitons vanish pointwise on moduli space. A certain disconnected part of the 4-point function is shown to be given by a convergent integral on moduli space. A general consistent formula is given for the two-loop cosmological constant in compactifications with central charge c=15 and with N=1 worldsheet supersymmetry. Finally, some comments are made on possible extensions of this work to higher loop order.

37 pages, 3 figures, Lectures delivered at Hangzhou and Beijing 2002

References in corpus (6)

• Large N Field Theories, String Theory and Gravity
• U-duality and M-Theory
• Two-Loop Superstrings II, The Chiral Measure on Moduli Space
• Vacuum Energy Cancellation in a Non-supersymmetric String
• Chiral splitting and world-sheet gravitinos in higher-derivative string amplitudes
• Momentum Analyticity and Finiteness of the 1-Loop Superstring Amplitude

Cited by in corpus (45)

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• Superstring Perturbation Theory Revisited
• Automorphic properties of low energy string amplitudes in various dimensions
• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• Two-Loop Superstrings V: Gauge Slice Independence of the N-Point Function
• Analytical Solutions of Open String Field Theory
• Higher genus modular graph functions, string invariants, and their exact asymptotics
• Tropical Amplitudes
• Asyzygies, modular forms, and the superstring measure II
• Eisenstein series and automorphic representations
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• The Overall Coefficient of the Two-loop Superstring Amplitude Using Pure Spinors
• The LQG -- String: Loop Quantum Gravity Quantization of String Theory I. Flat Target Space
• Two-Loop Superstrings VII, Cohomology of Chiral Amplitudes
• Two-Loop Superstrings on Orbifold Compactifications
• On the Construction of Asymmetric Orbifold Models
• Two loop superstring amplitudes and S_6 representations
• Comments on BRST quantization of strings
• Two-loop vacuum energy for Calabi-Yau orbifold models
• Multi-loop open string amplitudes and their field theory limit
• Ambitwistor Integrands from Tensionless Chiral Superstring Integrands
• Higher genus partition functions of meromorphic conformal field theories
• One-Dimensional Super Calabi-Yau Manifolds and their Mirrors
• The Super Period Matrix with Ramond Punctures in the supergravity formulation
• Obstructed Thickenings and Supermanifolds
• Factorization of the Two Loop Four-Particle Amplitude in Superstring Theory Revisited
• Superstring field theory in the democratic picture
• Topics in Two-Loop Superstring Perturbation Theory
• Asymptotics of the $D^8{R}^4$ genus-two string invariant
• Higher Order Deformations of Complex Structures
• Hierarchy of Modular Graph Identities
• NSR superstring measures in genus 5
• On the Super Mumford Form in the Presence of Ramond and Neveu-Schwarz Punctures
• Deforming super Riemann surfaces with gravitinos and super Schottky groups
• Identities among higher genus modular graph tensors
• Notes on reductions of superstring theory to bosonic string theory
• Two-loop superstring five-point amplitudes I: Construction via chiral splitting and pure spinors
• Analytic and Algebraic Deformations of Super Riemann Surfaces
• On the splitting of genus two supermoduli
• Superstrings beyond one loop
• Lectures on Scattering Amplitudes in String Theory