19 research outputs found
New hydrogen-like potentials
Using the modified factorization method introduced by Mielnik, we construct a
new class of radial potentials whose spectrum for l=0 coincides exactly with
that of the hydrogen atom. A limiting case of our family coincides with the
potentials previously derived by Abraham and MosesComment: 6 pages, latex, 2 Postscript figure
Bi-Hamiltonian representation, symmetries and integrals of mixed heavenly and Husain systems
In the recent paper by one of the authors (MBS) and A. A. Malykh on the
classification of second-order PDEs with four independent variables that
possess partner symmetries (J. Phys. A: Math. Theor. Vol. 42 (2009) 395202
(20pp)), mixed heavenly equation and Husain equation appear as closely related
canonical equations admitting partner symmetries. Here for the mixed heavenly
equation and Husain equation, formulated in a two-component form, we present
recursion operators, Lax pairs of Olver-Ibragimov-Shabat type and discover
their Lagrangians, symplectic and bi-Hamiltonian structure. We obtain all point
and second-order symmetries, integrals and bi-Hamiltonian representations of
these systems and their symmetry flows together with infinite hierarchies of
nonlocal higher symmetries.Comment: LaTeX2e source, 43 pages, 23 references, title modified, errors
corrected, study of recursions of symmetries and integrals adde
Partner symmetries and non-invariant solutions of four-dimensional heavenly equations
We extend our method of partner symmetries to the hyperbolic complex
Monge-Amp\`ere equation and the second heavenly equation of Pleba\~nski. We
show the existence of partner symmetries and derive the relations between them
for both equations. For certain simple choices of partner symmetries the
resulting differential constraints together with the original heavenly
equations are transformed to systems of linear equations by an appropriate
Legendre transformation. The solutions of these linear equations are
generically non-invariant. As a consequence we obtain explicitly new classes of
heavenly metrics without Killing vectors.Comment: 20 pages, 1 table, corrected typo
On Self-Dual Gravity I
(One typo corrected and one incorrect statement removed. Extra details on
conserved quantities and symmetry algebras added).Comment: 17 pages, Latex, DAMTP-R92/4
The N=4 string is the same as the N=2 string
We redo the quantization of the N=4 string, taking into account the
reducibility of the constraints. The result is equivalent to the N=2 string,
with critical dimension D=4 and signature (++--). The N=4 formulation has
several advantages: the sigma-model field equations are implied classically,
rather than by quantum/beta-function calculations; self-duality/chirality is
one of the super-Virasoro constraints; SO(2,2) covariance is manifest. This
reveals that the theory includes fermions, and is apparently spacetime
supersymmetric.Comment: 7 pg (uuencoded dvi file; otherwise same as original
A spinor approach to Walker geometry
A four-dimensional Walker geometry is a four-dimensional manifold M with a
neutral metric g and a parallel distribution of totally null two-planes. This
distribution has a natural characterization as a projective spinor field
subject to a certain constraint. Spinors therefore provide a natural tool for
studying Walker geometry, which we exploit to draw together several themes in
recent explicit studies of Walker geometry and in other work of Dunajski (2002)
and Plebanski (1975) in which Walker geometry is implicit. In addition to
studying local Walker geometry, we address a global question raised by the use
of spinors.Comment: 41 pages. Typos which persisted into published version corrected,
notably at (2.15
The N=2(4) string is self-dual N=4 Yang-Mills
N=2 string amplitudes, when required to have the Lorentz covariance of the
equivalent N=4 string, describe a self-dual form of N=4 super Yang-Mills in 2+2
dimensions. Spin-independent couplings and the ghost nature of SO(2,2)
spacetime make it a topological-like theory with vanishing loop corrections.Comment: 7 pg., ITP-SB-92-24 (uuencoded dvi file; otherwise same as original
Born-Infeld Theory and Stringy Causality
Fluctuations around a non-trivial solution of Born-Infeld theory have a
limiting speed given not by the Einstein metric but the Boillat metric. The
Boillat metric is S-duality invariant and conformal to the open string metric.
It also governs the propagation of scalars and spinors in Born-Infeld theory.
We discuss the potential clash between causality determined by the closed
string and open string light cones and find that the latter never lie outside
the former. Both cones touch along the principal null directions of the
background Born-Infeld field. We consider black hole solutions in situations in
which the distinction between bulk and brane is not sharp such as space filling
branes and find that the location of the event horizon and the thermodynamic
properties do not depend on whether one uses the closed or open string metric.
Analogous statements hold in the more general context of non-linear
electrodynamics or effective quantum-corrected metrics. We show how Born-Infeld
action to second order might be obtained from higher-curvature gravity in
Kaluza-Klein theory. Finally we point out some intriguing analogies with
Einstein-Schr\"odinger theory.Comment: 31 pages, 4 figures, LaTex; Some comments and references adde
Noncommutative Electromagnetism As A Large N Gauge Theory
We map noncommutative (NC) U(1) gauge theory on R^d_C X R^{2n}_{NC} to U(N ->
\infty) Yang-Mills theory on R^d_C, where R^d_C is a d-dimensional commutative
spacetime while R^{2n}_{NC} is a 2n-dimensional NC space. The resulting U(N)
Yang-Mills theory on R^d_C is equivalent to that obtained by the dimensional
reduction of (d+2n)-dimensional U(N) Yang-Mills theory onto R^d_C. We show that
the gauge-Higgs system (A_\mu,\Phi^a) in the U(N -> \infty) Yang-Mills theory
on R^d_C leads to an emergent geometry in the (d+2n)-dimensional spacetime
whose metric was determined by Ward a long time ago. In particular, the
10-dimensional gravity for d=4 and n=3 corresponds to the emergent geometry
arising from the 4-dimensional N=4 vector multiplet in the AdS/CFT duality. We
further elucidate the emergent gravity by showing that the gauge-Higgs system
(A_\mu,\Phi^a) in half-BPS configurations describes self-dual Einstein gravity.Comment: 25 pages; More clarifications, to appear in Eur. Phys. J.
Analog gravity from field theory normal modes?
We demonstrate that the emergence of a curved spacetime ``effective
Lorentzian geometry'' is a common and generic result of linearizing a field
theory around some non-trivial background. This investigation is motivated by
considering the large number of ``analog models'' of general relativity that
have recently been developed based on condensed matter physics, and asking
whether there is something more fundamental going on. Indeed, linearization of
a classical field theory (a field theoretic ``normal mode analysis'') results
in fluctuations whose propagation is governed by a Lorentzian-signature curved
spacetime ``effective metric''. For a single scalar field, this procedure
results in a unique effective metric, which is quite sufficient for simulating
kinematic aspects of general relativity (up to and including Hawking
radiation). Quantizing the linearized fluctuations, the one-loop effective
action contains a term proportional to the Einstein--Hilbert action, suggesting
that while classical physics is responsible for generating an ``effective
geometry'', quantum physics can be argued to induce an ``effective dynamics''.
The situation is strongly reminiscent of Sakharov's ``induced gravity''
scenario, and suggests that Einstein gravity is an emergent low-energy
long-distance phenomenon that is insensitive to the details of the high-energy
short-distance physics. (We mean this in the same sense that hydrodynamics is a
long-distance emergent phenomenon, many of whose predictions are insensitive to
the short-distance cutoff implicit in molecular dynamics.)Comment: Revtex 4 (beta 5); 12 pages in single-column forma