31 research outputs found
The chiral supereigenvalue model
A supereigenvalue model with purely positive bosonic eigenvalues is presented and solved by considering its superloop equations. This model represents the supersymmetric generalization of the complex one-matrix model, in analogy to the relation between the supereigenvalue and the Hermitian one-matrix model. Closed expressions for all planar multi-superloop correlation functions are found. Moreover an iterative scheme allows the calculation of higher genus contributions to the free energy and the correlators. Explicit results for genus one are given
The Supereigenvalue Model in the Double-Scaling Limit
The double-scaling limit of the supereigenvalue model is performed in the
moment description. This description proves extremely useful for the
identification of the multi-critical points in the space of bosonic and
fermionic coupling constants. An iterative procedure for the calculation of
higher-genus contributions to the free energy and to the multi-loop correlators
in the double-scaling limit is developed. We present the general structure of
these quantities at genus g and give explicit results up to and including genus
two.Comment: 19 pages, LaTe
Iterative Solution of the Supereigenvalue Model
An integral form of the discrete superloop equations for the supereigenvalue
model of Alvarez-Gaume, Itoyama, Manes and Zadra is given. By a change of
variables from coupling constants to moments we find a compact form of the
planar solution for general potentials. In this framework an iterative scheme
for the calculation of higher genera contributions to the free energy and the
multi-loop correlators is developed. We present explicit results for genus one.Comment: 21 pages, LaTeX, no figure
On the Hopf algebra structure of the AdS/CFT S-matrix
We formulate the Hopf algebra underlying the su(2|2) worldsheet S-matrix of
the AdS_5 x S^5 string in the AdS/CFT correspondence. For this we extend the
previous construction in the su(1|2) subsector due to Janik to the full algebra
by specifying the action of the coproduct and the antipode on the remaining
generators. The nontriviality of the coproduct is determined by length-changing
effects and results in an unusual central braiding. As an application we
explicitly determine the antiparticle representation by means of the
established antipode.Comment: 12 pages, no figures, minor changes, typos corrected, comments and
references added, v3: three references adde
The Matrix Theory S-Matrix
The technology required for eikonal scattering amplitude calculations in
Matrix theory is developed. Using the entire supersymmetric completion of the
v^4/r^7 Matrix theory potential we compute the graviton-graviton scattering
amplitude and find agreement with eleven dimensional supergravity at tree
level.Comment: 10 pages, RevTeX, no figure
Coordinate representation of particle dynamics in AdS and in generic static spacetimes
We discuss the quantum dynamics of a particle in static curved spacetimes in
a coordinate representation. The scheme is based on the analysis of the squared
energy operator E^2, which is quadratic in momenta and contains a scalar
curvature term. Our main emphasis is on AdS spaces, where this term is fixed by
the isometry group. As a byproduct the isometry generators are constructed and
the energy spectrum is reproduced. In the massless case the conformal symmetry
is realized as well. We show the equivalence between this quantization and the
covariant quantization, based on the Klein-Gordon type equation in AdS. We
further demonstrate that the two quantization methods in an arbitrary
(N+1)-dimensional static spacetime are equivalent to each other if the scalar
curvature terms both in the operator E^2 and in the Klein-Gordon type equation
have the same coefficient equal to (N-1)/(4N).Comment: 14 pages, no figures, typos correcte
Open and Closed Supermembranes with Winding
Motivated by manifest Lorentz symmetry and a well-defined large-N limit
prescription, we study the supersymmetric quantum mechanics proposed as a model
for the collective dynamics of D0-branes from the point of view of the
11-dimensional supermembrane. We argue that the continuity of the spectrum
persists irrespective of the presence of winding around compact target-space
directions and discuss the central charges in the superalgebra arising from
winding membrane configurations. Along the way we comment on the structure of
open supermembranes.Comment: Contribution to the proc. Strings '97, 10 pages, LaTeX, uses espcrc
Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
Tree-level scattering amplitudes in N=4 super Yang-Mills theory have recently
been shown to transform covariantly with respect to a 'dual' superconformal
symmetry algebra, thus extending the conventional superconformal symmetry
algebra psu(2,2|4) of the theory. In this paper we derive the action of the
dual superconformal generators in on-shell superspace and extend the dual
generators suitably to leave scattering amplitudes invariant. We then study the
algebra of standard and dual symmetry generators and show that the inclusion of
the dual superconformal generators lifts the psu(2,2|4) symmetry algebra to a
Yangian. The non-local Yangian generators acting on amplitudes turn out to be
cyclically invariant due to special properties of psu(2,2|4). The
representation of the Yangian generators takes the same form as in the case of
local operators, suggesting that the Yangian symmetry is an intrinsic property
of planar N=4 super Yang-Mills, at least at tree level.Comment: 23 pages, no figures; v2: typos corrected, references added; v3:
minor changes, references adde
Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory
49 pages, 20 figures; v2: typos fixedPlanar N=4 Super Yang-Mills theory appears to be a quantum integrable four-dimensional conformal theory. This has been used to find equations believed to describe its exact spectrum of anomalous dimensions. Integrability seemingly also extends to the planar space-time scattering amplitudes of the N=4 model, which show strong signs of Yangian invariance. However, in contradistinction to the spectral problem, this has not yet led to equations determining the exact amplitudes. We propose that the missing element is the spectral parameter, ubiquitous in integrable models. We show that it may indeed be included into recent on-shell approaches to scattering amplitude integrands, providing a natural deformation of the latter. Under some constraints, Yangian symmetry is preserved. Finally we speculate that the spectral parameter might also be the regulator of choice for controlling the infrared divergences appearing when integrating the integrands in exactly four dimensions.Peer reviewe