Higher Order Deformations of Complex Structures

Abstract

Deformations of complex structures by finite Beltrami differentials are considered on general Riemann surfaces. Exact formulas to any fixed order are derived for the corresponding deformations of the period matrix, Green's functions, and correlation functions in conformal field theories with vanishing total central charge. The stress tensor is shown to give a simple representation of these deformations valid to all orders. Such deformation formulas naturally enter into the evaluation of superstring amplitudes at two-loop order with Ramond punctures, and at higher loop order, in the supergravity formulation of the RNS superstring.

References in corpus (8)

• Two-Loop Superstrings VI: Non-Renormalization Theorems and the 4-Point Function
• Two-Loop Superstrings I, Main Formulas
• Two-Loop Superstrings II, The Chiral Measure on Moduli Space
• Superstring Perturbation Theory Revisited
• Two-Loop Superstrings V: Gauge Slice Independence of the N-Point Function
• Lectures on Two-Loop Superstrings
• The Super Period Matrix With Ramond Punctures
• The Super Period Matrix with Ramond Punctures in the supergravity formulation

Cited by in corpus (7)

• Closed Superstring Field Theory and its Applications
• Highly Excited Strings I: Generating Function
• Deforming super Riemann surfaces with gravitinos and super Schottky groups
• Handle Operators in String Theory
• Analytic and Algebraic Deformations of Super Riemann Surfaces
• Derived brackets in bosonic string worldsheet sigma-model
• On the splitting of genus two supermoduli