177,505 research outputs found
E-strings, , and triality
We study the E-string theory on with Wilson lines.
We consider two examples where interesting automorphisms arise. In the first
example, the spectrum is invariant under the Weyl group acting on the
Wilson line parameters. We obtain the Seiberg-Witten curve expressed in terms
of Weyl invariant Jacobi forms. We also clarify how it is related to the
thermodynamic limit of the Nekrasov-type formula. In the second example, the
spectrum is invariant under the triality combined with modular
transformations, the automorphism originally found in the 4d
supersymmetric gauge theory with four massive flavors. We
introduce the notion of triality invariant Jacobi forms and present the
Seiberg-Witten curve in terms of them. We show that this Seiberg-Witten curve
reduces precisely to that of the 4d theory with four flavors in the limit of
shrinking to zero size.Comment: 39 page
Symmetry group analysis of an ideal plastic flow
In this paper, we study the Lie point symmetry group of a system describing
an ideal plastic plane flow in two dimensions in order to find analytical
solutions. The infinitesimal generators that span the Lie algebra for this
system are obtained. We completely classify the subalgebras of up to
codimension two in conjugacy classes under the action of the symmetry group.
Based on invariant forms, we use Ansatzes to compute symmetry reductions in
such a way that the obtained solutions cover simultaneously many invariant and
partially invariant solutions. We calculate solutions of the algebraic,
trigonometric, inverse trigonometric and elliptic type. Some solutions
depending on one or two arbitrary functions of one variable have also been
found. In some cases, the shape of a potentially feasible extrusion die
corresponding to the solution is deduced. These tools could be used to thin,
curve, undulate or shape a ring in an ideal plastic material
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