Trigonometric $\vee $-systems and solutions of WDVV equations
نویسندگان
چکیده
منابع مشابه
Trigonometric Solutions of the WDVV Equations from Root Systems
By introduction of an additional variable and addition of a Weyl invariant correction term to the perturbative prepotential in five-dimensional SeibergWitten theory we construct solutions of the WDVV equations of trigonometric type for all crystallographic root systems.
متن کاملTrigonometric solutions of WDVV equations and generalized Calogero-Moser-Sutherland systems
We consider trigonometric solutions of WDVV equations and derive geometric conditions when a collection of vectors with multiplicities determines such a solution. We incorporate these conditions into the notion of trigonometric Veselov system (∨-system) and we determine all trigonometric ∨-systems with up to five vectors. We show that generalized Calogero-Moser-Sutherland operator admits a fact...
متن کاملA note on the relationship between rational and trigonometric solutions of the WDVV equations
Legendre transformations provide a natural symmetry on the space of solutions to the WDVV equations, and more specifically, between different Frobenius manifolds. In this paper a twisted Legendre transformation is constructed between solutions which define the corresponding dual Frobenius manifolds. As an application it is shown that certain trigonometric and rational solutions of the WDVV equa...
متن کاملWeyl Groups and Elliptic Solutions of the Wdvv Equations
A functional ansatz is developed which gives certain elliptic solutions of the Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equation. This is based on the elliptic trilogarithm function introduced by Beilinson and Levin. For this to be a solution results in a number of purely algebraic conditions on the set of vectors that appear in the ansatz, this providing an elliptic version of the idea, in...
متن کاملDeformations of the root systems and new solutions to generalised WDVV equations
A special class of solutions to the generalised WDVV equations related to a finite set of covectors is investigated. Some geometric conditions on such a set which guarantee that the corresponding function satisfies WDVV equations are found (∨-conditions). These conditions are satisfied for all root systems and their special deformations discovered in the theory of the Calogero-Moser systems by ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2021
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8121/abccf8