9,784 research outputs found
Jordan-Schwinger Representations and Factorised Yang-Baxter Operators
The construction elements of the factorised form of the Yang-Baxter R
operator acting on generic representations of q-deformed sl(n+1) are studied.
We rely on the iterative construction of such representations by the restricted
class of Jordan-Schwinger representations. The latter are formulated
explicitly. On this basis the parameter exchange and intertwining operators are
derived.Comment: based on a contribution to ISQS200
The Ruijsenaars-Schneider Model in the Context of Seiberg-Witten Theory
The compactification of five dimensional N=2 SUSY Yang-Mills (YM) theory onto
a circle provides a four dimensional YM model with N=4 SUSY. This supersymmetry
can be broken down to N=2 if non-trivial boundary conditions in the compact
dimension, \phi(x_5 +R) = e^{2\pi i\epsilon}\phi(x_5), are imposed on half of
the fields. This two-parameter (R,\epsilon) family of compactifications
includes as particular limits most of the previously studied four dimensional
N=2 SUSY YM models with supermultiplets in the adjoint representation of the
gauge group. The finite-dimensional integrable system associated to these
theories via the Seiberg-Witten construction is the generic elliptic
Ruijsenaars-Schneider model. In particular the perturbative (weak coupling)
limit is described by the trigonometric Ruijsenaars-Schneider model.Comment: 18 pages, LaTe
All orders structure and efficient computation of linearly reducible elliptic Feynman integrals
We define linearly reducible elliptic Feynman integrals, and we show that
they can be algorithmically solved up to arbitrary order of the dimensional
regulator in terms of a 1-dimensional integral over a polylogarithmic
integrand, which we call the inner polylogarithmic part (IPP). The solution is
obtained by direct integration of the Feynman parametric representation. When
the IPP depends on one elliptic curve (and no other algebraic functions), this
class of Feynman integrals can be algorithmically solved in terms of elliptic
multiple polylogarithms (eMPLs) by using integration by parts identities. We
then elaborate on the differential equations method. Specifically, we show that
the IPP can be mapped to a generalized integral topology satisfying a set of
differential equations in -form. In the examples we consider the
canonical differential equations can be directly solved in terms of eMPLs up to
arbitrary order of the dimensional regulator. The remaining 1-dimensional
integral may be performed to express such integrals completely in terms of
eMPLs. We apply these methods to solve two- and three-points integrals in terms
of eMPLs. We analytically continue these integrals to the physical region by
using their 1-dimensional integral representation.Comment: The differential equations method is applied to linearly reducible
elliptic Feynman integrals, the solutions are in terms of elliptic
polylogarithms, JHEP version, 50 page
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