scholarly journals WDVV Equations from Algebra of Forms

1997 ◽  
Vol 12 (11) ◽  
pp. 773-787 ◽  
Author(s):  
A. Marshakov ◽  
A. Mironov ◽  
A. Morozov
Keyword(s):  
Riemann Surfaces ◽  
Algebraic Structures ◽  
Wdvv Equations ◽  
Hyperelliptic Riemann Surfaces ◽  
Direct Generalization ◽  
Witten Theory ◽  
Ring Of Polynomials ◽  
String Models

A class of solutions to the WDVV equations is provided by period matrices of hyperelliptic Riemann surfaces, with or without punctures. The equations themselves reflect associativity of explicitly described multiplicative algebra of (possibly meromorphic) one-differentials, which holds at least in the hyperelliptic case. This construction is direct generalization of the old one, involving the ring of polynomials factorized over an ideal, and is inspired by the study of the Seiberg–Witten theory. It has potential to be further extended to reveal algebraic structures underlying the theory of quantum cohomologies and the prepotentials in string models with N=2 supersymmetry.

scholarly journals A remark on the η-invariant for automorphisms of hyperelliptic Riemann surfaces

2000 ◽  
Vol 62 (2) ◽  
pp. 177-182 ◽  
Author(s):  
Takayuki Morifuji
Keyword(s):  
Finite Order ◽  
Riemann Surfaces ◽  
Prime Order ◽  
Mapping Torus ◽  
Hyperelliptic Riemann Surfaces ◽  
Order Surface

We give a characterisation for the vanishing of the η-invariant of prime order automorphisms of hyperelliptic Riemann surfaces through the mapping torus construction. To this end, we introduce a notion of s-symmetry for finite order surface automorphisms.

The full automorphism groups of hyperelliptic Riemann surfaces

1993 ◽  
Vol 79 (1) ◽  
pp. 267-282 ◽  
Author(s):  
E. Bujalance ◽  
J. M. Gamboa ◽  
G. Gromadzki
Keyword(s):  
Riemann Surfaces ◽  
Automorphism Groups ◽  
Hyperelliptic Riemann Surfaces

scholarly journals MORE EVIDENCE FOR THE WDVV EQUATIONS IN ${\mathcal N} = 2$ SUSY YANG–MILLS THEORIES

2000 ◽  
Vol 15 (08) ◽  
pp. 1157-1206 ◽  
Author(s):  
A. MARSHAKOV ◽  
A. MIRONOV ◽  
A. MOROZOV
Keyword(s):  
Field Theory ◽  
Adjoint Representation ◽  
Hyperelliptic Curves ◽  
Fundamental Representation ◽  
Wdvv Equations ◽  
Yang Mills ◽  
Perturbative Regime ◽  
String Models ◽  
Supersymmetric Theories ◽  
Moser System

We consider 4D and 5D [Formula: see text] supersymmetric theories and demonstrate that in general their Seiberg–Witten prepotentials satisfy the Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations. General proof for the Yang–Mills models (with matter in the first fundamental representation) makes use of the hyperelliptic curves and underlying integrable systems. A wide class of examples is discussed; it contains few understandable exceptions. In particular, in the perturbative regime of 5D theories, in addition to naive field theory expectations some extra terms appear, as happens in heterotic string models. We consider also the example of the Yang–Mills theory with matter hypermultiplet in the adjoint representation (related to the elliptic Calogero–Moser system) when the standard WDVV equations do not hold.

scholarly journals Topological Classification of Conformal Actions onpq-Hyperelliptic Riemann Surfaces

2007 ◽  
Vol 2007 ◽  
pp. 1-29 ◽  
Author(s):  
Ewa Tyszkowska
Keyword(s):  
Riemann Surface ◽  
Riemann Surfaces ◽  
Compact Riemann Surface ◽  
Topological Classification ◽  
Hyperelliptic Riemann Surfaces

A compact Riemann surfaceXof genusg>1is said to bep-hyperellipticifXadmits a conformal involutionρ, for whichX/ρis an orbifold of genusp. If in additionXisq-hyperelliptic, then we say thatXispq-hyperelliptic. Here we study conformal actions onpq-hyperelliptic Riemann surfaces with centralp- andq-hyperelliptic involutions.

On symmetries of p-hyperelliptic Riemann surfaces

1997 ◽  
Vol 308 (1) ◽  
pp. 31-45 ◽  
Author(s):  
E. Bujalance ◽  
A. F. Costa
Keyword(s):  
Riemann Surfaces ◽  
Hyperelliptic Riemann Surfaces
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