920 research outputs found
The AdS(5)xS(5) Semi-Symmetric Space Sine-Gordon Theory
The generalized symmetric space sine-Gordon theories are a series of
1+1-integrable field theories that are classically equivalent to superstrings
on symmetric space spacetimes F/G. They are formulated in terms of a
semi-symmetric space as a gauged WZW model with fermions and a potential term
to deform it away from the conformal fixed point. We consider in particular the
case of PSU(2,2|4)/Sp(2,2)xSp(4) which corresponds to AdS(5)xS(5). We argue
that the infinite tower of conserved charges of these theories includes an
exotic N=(8,8) supersymmetry that is realized in a mildy non-local way at the
Lagrangian level. The supersymmetry is associated to a double central extension
of the superalgebra psu(2|2)+psu(2|2) and includes a non-trivial R symmetry
algebra corresponding to global gauge transformations, as well as 2-dimensional
spacetime translations. We then explicitly construct soliton solutions and show
that they carry an internal moduli superspace CP(2|1)xCP(2|1) with both bosonic
and Grassmann collective coordinates. We show how to semi-classical quantize
the solitons by writing an effective quantum mechanical system on the moduli
space which takes the form of a co-adjoint orbit of SU(2|2)xSU(2|2). The
spectrum consists of a tower of massive states in the short, or atypical,
symmetric representations, just as the giant magnon states of the string world
sheet theory, although here the tower is truncated.Comment: 39 pages, references adde
Supersymmetric Reflection Matrices
We briefly review the general structure of integrable particle theories in
1+1 dimensions having N=1 supersymmetry. Examples are specific perturbed
superconformal field theories (of Yang-Lee type) and the N=1 supersymmetric
sine-Gordon theory. We comment on the modifications that are required when the
N=1 supersymmetry algebra contains non-trivial topological charges.Comment: 7 pages, Revtex, 2 figures, talk given at the International Seminar
on Supersymmetry and Quantum Field Theory, dedicated to the memory of
D.V.Volkov, Kharkov (Ukraine), January 5-7, 199
Calculating the Prepotential by Localization on the Moduli Space of Instantons
We describe a new technique for calculating instanton effects in
supersymmetric gauge theories applicable on the Higgs or Coulomb branches. In
these situations the instantons are constrained and a potential is generated on
the instanton moduli space. Due to existence of a nilpotent fermionic symmetry
the resulting integral over the instanton moduli space localizes on the
critical points of the potential. Using this technology we calculate the one-
and two-instanton contributions to the prepotential of SU(N) gauge theory with
N=2 supersymmetry and show how the localization approach yields the prediction
extracted from the Seiberg-Witten curve. The technique appears to extend to
arbitrary instanton number in a tractable way.Comment: 24 pages, JHEP.cls, more references and extra discussion on N_F=2N
cas
An integrable deformation of the AdS5Ă—S5superstring
The S-matrix on the world-sheet theory of the string in AdS5 x S5 has
previously been shown to admit a deformation where the symmetry algebra is
replaced by the associated quantum group. The case where q is real has been
identified as a particular deformation of the Green-Schwarz sigma model. An
interpretation of the case with q a root of unity has, until now, been lacking.
We show that the Green-Schwarz sigma model admits a discrete deformation which
can be viewed as a rather simple deformation of the F/F_V gauged WZW model,
where F=PSU(2,2|4). The deformation parameter q is then a k-th root of unity
where k is the level. The deformed theory has the same equations-of-motion as
the Green-Schwarz sigma model but has a different symplectic structure. We show
that the resulting theory is integrable and has just the right amount of
kappa-symmetries that appear as a remnant of the fermionic part of the original
gauge symmetry. This points to the existence of a fully consistent deformed
string background.Comment: 23 pages, improved and expanded discussion of metric and B fiel
Classical and Quantum Solitons in the Symmetric Space Sine-Gordon Theories
We construct the soliton solutions in the symmetric space sine-Gordon
theories. The latter are a series of integrable field theories in
1+1-dimensions which are associated to a symmetric space F/G, and are related
via the Pohlmeyer reduction to theories of strings moving on symmetric spaces.
We show that the solitons are kinks that carry an internal moduli space that
can be identified with a particular co-adjoint orbit of the unbroken subgroup H
of G. Classically the solitons come in a continuous spectrum which encompasses
the perturbative fluctuations of the theory as the kink charge becomes small.
We show that the solitons can be quantized by allowing the collective
coordinates to be time-dependent to yield a form of quantum mechanics on the
co-adjoint orbit. The quantum states correspond to symmetric tensor
representations of the symmetry group H and have the interpretation of a fuzzy
geometric version of the co-adjoint orbit. The quantized finite tower of
soliton states includes the perturbative modes at the base.Comment: 53 pages, additional comments and small errors corrected, final
journal versio
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
On the Chiral Ring of N=1 Supersymmetric Gauge Theories
We consider the chiral ring of the pure N=1 supersymmetric gauge theory with
SU(N) gauge group and show that the classical relation S^{N^2}=0 is modified to
the exact quantum relation (S^N-\Lambda^{3N})^N=0.Comment: 5 pages. Comments and references adde
Giant magnons of string theory in the lambda background
The analogues of giant magnon configurations are studied on the string world
sheet in the lambda background. This is a discrete deformation of the
AdS(5)xS(5) background that preserves the integrability of the world sheet
theory. Giant magnon solutions are generated using the dressing method and
their dispersion relation is found. This reduces to the usual dyonic giant
magnon dispersion relation in the appropriate limit and becomes relativistic in
another limit where the lambda model becomes the generalized sine-Gordon theory
of the Pohlmeyer reduction. The scattering of giant magnons is then shown in
the semi-classical limit to be described by the quantum S-matrix that is a
quantum group deformation of the conventional giant magnon S-matrix. It is
further shown that in the small g limit, a sector of the S-matrix is related to
the XXZ spin chain whose spectrum matches the spectrum of magnon bound states.Comment: 53 pages, 6 figures, final version to appear in JHE
Matrix Models, Geometric Engineering and Elliptic Genera
We compute the prepotential of N=2 supersymmetric gauge theories in four
dimensions obtained by toroidal compactifications of gauge theories from 6
dimensions, as a function of Kahler and complex moduli of T^2. We use three
different methods to obtain this: matrix models, geometric engineering and
instanton calculus. Matrix model approach involves summing up planar diagrams
of an associated gauge theory on T^2. Geometric engineering involves
considering F-theory on elliptic threefolds, and using topological vertex to
sum up worldsheet instantons. Instanton calculus involves computation of
elliptic genera of instanton moduli spaces on R^4. We study the
compactifications of N=2* theory in detail and establish equivalence of all
these three approaches in this case. As a byproduct we geometrically engineer
theories with massive adjoint fields. As one application, we show that the
moduli space of mass deformed M5-branes wrapped on T^2 combines the Kahler and
complex moduli of T^2 and the mass parameter into the period matrix of a genus
2 curve.Comment: 90 pages, Late
Superpotentials from flux compactifications of M-theory
In flux compactifications of M-theory a superpotential is generated whose
explicit form depends on the structure group of the 7-dimensional internal
manifold. In this note, we discuss superpotentials for the structure groups:
G_2, SU(3) or SU(2). For the G_2 case all internal fluxes have to vanish. For
SU(3) structures, the non-zero flux components entering the superpotential
describe an effective 1-dimensional model and a Chern-Simons model if there are
SU(2) structures.Comment: 10 page
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