95 research outputs found
Seiberg-Witten theory for a non-trivial compactification from five to four dimensions
The prepotential and spectral curve are described for a smooth interpolation
between an enlarged N=4 SUSY and ordinary N=2 SUSY Yang-Mills theory in four
dimensions, obtained by compactification from five dimensions with non-trivial
(periodic and antiperiodic) boundary conditions. This system provides a new
solution to the generalized WDVV equations. We show that this exhausts all
possible solutions of a given functional form.Comment: 10 pages, LaTeX, 2 figures using emlines.st
An Extended Abel-Jacobi Map
We solve the problem of inversion of an extended Abel-Jacobi map where are (normalised) abelian
differentials of the third kind. In contrast to the extensions already studied,
this one contains meromorphic differentials having a common pole . This
inversion problem arises in algebraic geometric description of monopoles, as
well as in the linearization of integrable systems on finite-dimensional
unreduced coadjoint orbits on loop algebras.Comment: 11 page
QCD, Wick's Theorem for KdV -functions and the String Equation
Two consistency conditions for partition functions established by Akemann and
Dam-gaard in their studies of the fermionic mass dependence of the QCD
partition function at low energy ({\it a la} Leutwiller-Smilga-Verbaarschot)
are interpreted in terms of integrable hierarchies. Their algebraic relation is
shown to be a consequence of Wick's theorem for 2d fermionic correlators
(Hirota identities) in the special case of the 2-reductions of the KP hierarchy
(that is KdV/mKdV). The consistency condition involving derivatives is an
incarnation of the string equation associated with the particular matrix model
(the particular kind of the Kac-Schwarz operator).Comment: 7 pages LaTex. Corrections to grant numbers only for administering
bureaucrat
Bring's Curve: its Period Matrix and the Vector of Riemann Constants
Bring's curve is the genus 4 Riemann surface with automorphism group of maximal size, S₅. Riera and Rodríguez have provided the most detailed study of the curve thus far via a hyperbolic model. We will recover and extend their results via an algebraic model based on a sextic curve given by both Hulek and Craig and implicit in work of Ramanujan. In particular we recover their period matrix; further, the vector of Riemann constants will be identified
The Construction of Monopoles
We show that the Higgs and gauge fields for a BPS monopole may be constructed
directly from the spectral curve without having to solve the gauge constraint
needed to obtain the Nahm data. The result is the analogue of the instanton
result: given ADHM data one can reconstruct the gauge fields algebraically
together with differentiation. Here, given the spectral curve, one can
similarly reconstruct the Higgs and gauge fields. This answers a problem that
has remained open since the discovery of monopoles.Comment: 21 pages, revise
WDVV Equations as Functional Relations
We discuss the associativity or WDVV equations and demonstrate that they can
be rewritten as certain functional relations between the {\it second}
derivatives of a single function, similar to the dispersionless Hirota
equations. The properties of these functional relations are further discussed.Comment: 9 pages LaTex. Typos in equations (33) and (38) correcte
Yangians, Integrable Quantum Systems and Dorey's rule
We study tensor products of fundamental representations of Yangians and show
that the fundamental quotients of such tensor products are given by Dorey's
rule.Comment: We have made corrections to the results for the Yangians associated
to the non--simply laced algebra
The Curve of Compactified 6D Gauge Theories and Integrable Systems
We analyze the Seiberg-Witten curve of the six-dimensional N=(1,1) gauge
theory compactified on a torus to four dimensions. The effective theory in four
dimensions is a deformation of the N=2* theory. The curve is naturally
holomorphically embedding in a slanted four-torus--actually an abelian
surface--a set-up that is natural in Witten's M-theory construction of N=2
theories. We then show that the curve can be interpreted as the spectral curve
of an integrable system which generalizes the N-body elliptic Calogero-Moser
and Ruijsenaars-Schneider systems in that both the positions and momenta take
values in compact spaces. It turns out that the resulting system is not simply
doubly elliptic, rather the positions and momenta, as two-vectors, take values
in the ambient abelian surface. We analyze the two-body system in some detail.
The system we uncover provides a concrete realization of a Beauville-Mukai
system based on an abelian surface rather than a K3 surface.Comment: 22 pages, JHEP3, 4 figures, improved readility of figures, added
reference
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
Dilaton black holes in grand canonical ensemble near the extreme state
Dilaton black holes with a pure electric charge are considered in a framework
of a grand canonical ensemble near the extreme state. It is shown that there
exists such a subset of boundary data that the Hawking temperature smoothly
goes to zero to an infinite value of a horizon radius but the horizon area and
entropy are finite and differ from zero. In string theory the existence of a
horizon in the extreme limit is due to the finiteness of a system only.Comment: 8 pages, RevTex 3.0. Presentation improved, discussion on metrics in
string theory simplified. To be published in Phys.Rev.
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