Logarithmic Conformal Field Theory and Seiberg-Witten Models

Abstract

The periods of arbitrary abelian forms on hyperelliptic Riemann surfaces, in particular the periods of the meromorphic Seiberg-Witten differential, are shown to be in one-to-one correspondence with the conformal blocks of correlation functions of the rational logarithmic conformal field theory with central charge c=c(2,1)=-2. The fields of this theory precisely simulate the branched double covering picture of a hyperelliptic curve, such that generic periods can be expressed in terms of certain generalised hypergeometric functions, namely the Lauricella functions of type F_D.

LaTeX 13+1 pages; some typos corrected, references added

References in corpus (7)

• A Local Logarithmic Conformal Field Theory
• Matrix D-brane Dynamics, Logarithmic Operators and Quantization of Noncommutative Spacetime
• Origin of Logarithmic Operators in Conformal Field Theories
• Logarithmic conformal field theories and AdS correspondence
• Exact Multifractality for Disordered N-Flavour Dirac Fermions in Two Dimensions
• Isomonodromic Properties of the Seiberg-Witten Solution
• Logarithmic Conformal Field Theory Solutions of Two Dimensional Magnetohydrodynamics

Cited by in corpus (25)

• Bits and Pieces in Logarithmic Conformal Field Theory
• Logarithmic torus amplitudes
• Singletons and Logarithmic CFT in ADS/CFT correspondence
• Boundary Logarithmic Conformal Field Theory
• Operator Product Expansion in Logarithmic Conformal Field Theory
• Boundary states in boundary logarithmic CFT
• Logarithmic operators in the SL(2,R) WZNW model
• Disordered Systems and Logarithmic Conformal Field Theory
• Universality in Quantum Hall Systems: Coset Construction of Incompressible States
• Legendre's Relation and the Quantum Equivalence osp(4|4)_(1) = osp(2|2)_(-2) + su(2)_(0)
• Logarithmic Currents in the SU(2)_0 WZNW model
• Ghost Systems Revisited: Modified Virasoro Generators and Logarithmic Conformal Field Theories
• Extended chiral algebras in the SU(2)_0 WZNW model
• The O(n) Model in the $n\to 0$ Limit (self-avoiding-walks) and Logarithmic Conformal Field Theory
• Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas
• Extended multiplet structure in Logarithmic Conformal Field Theories
• Logarithmic Correlation Functions in Liouville Field Theory
• Stress Energy tensor in LCFT and the Logarithmic Sugawara construction
• Operator Product Expansion and Zero Mode Structure in Logarithmic CFT
• Two-Point Functions and Boundary States in Boundary Logarithmic Conformal Field Theories
• Two-Point Functions and Logarithmic Boundary Operators in Boundary Logarithmic Conformal Field Theories
• A Note on Four-Point Functions in Logarithmic Conformal Field Theory
• Logarithmic operators in SL(2, R) WZNW model, Singletons and AdS_3/(L)CFT_2 correspondence
• Indecomposable Representations in Z_n Symmetric b,c Ghost Systems via Deformations of the Virasoro Field
• Pure Gauge SU(2) Seiberg-Witten Theory and Modular Forms