11 research outputs found
Fundamentals on the Noncommutative Plane
We consider the addition of charged matter (``fundametals'') to
noncommutative Yang-Mills theory and noncommutative QED, derive Feynman rules
and tree-level potentials for them, and study the divergence structure of the
theory. These particles behave very much as they do in the commutative theory,
except that (1) they occupy bound-state wavefunctions which are essentially
those of charged particles in magnetic fields, and (2) there is slight momentum
nonconservation at vertices. There is no reduction in the degree of divergence
of charged fermion loops like that which affects nonplanar noncommutative
Yang-Mills diagrams.Comment: LaTeX, 25 pages, 8 figures; revised versio
A Simple Particle Action from a Twistor Parametrization of AdS_5
The SO(4,2) isometries of AdS_5 are realized non-linearly on its
horospherical coordinates (x^m,\rho). On the other hand, Penrose twistors have
long been known to linearly realize these symmetries on 4-dimensional Minkowski
space, the boundary of AdS_5, parametrized by x^m. Here we extend the twistor
construction and define a pair of twistors, allowing us to include a radial
coordinate in the construction. The linear action of SO(4,2) on the twistors
induces the correct isometries of AdS_5. We apply this new construction to the
study of the dynamics of a massive particle in AdS_5. We show that in terms of
the twistor variables the action takes a simple form of a 1-dimensional gauge
theory. Our result might open up the possibility to find a simple worldvolume
action also for the string propagating on AdS_5.Comment: 11 pages, LaTe
Supertwistors as Quarks of SU(2,2|4)
The GS superstring on AdS_5 x S^5 has a nonlinearly realized, spontaneously
broken SU(2,2|4) symmetry. Here we introduce a two-dimensional model in which
the unbroken SU(2,2|4) symmetry is linearly realized. The basic variables are
supertwistors, which transform in the fundamental representation of this
supergroup.
The quantization of this supertwistor model leads to the complete oscillator
construction of the unitary irreducible representations of the centrally
extended SU(2,2|4). They include the states of d=4 SYM theory, massless and KK
states of AdS_5 supergravity, and the descendants on AdS_5 of the standard
massive string states, which form intermediate and long supermultiplets. We
present examples of such multiplets and discuss possible states of solitonic
and (p,q) strings.Comment: 12 pages, LaTeX, 1 EPS figur
Why Matrix theory works for oddly shaped membranes
We give a simple proof of why there is a Matrix theory approximation for a
membrane shaped like an arbitrary Riemann surface. As corollaries, we show that
noncompact membranes cannot be approximated by matrices and that the Poisson
algebra on any compact phase space is U(infinity). The matrix approximation
does not appear to work properly in theories such as IIB string theory or
bosonic membrane theory where there is no conserved 3-form charge to which the
membranes couple.Comment: 8 pages, 4 figures, revtex; references adde