20,596 research outputs found
Cubic interaction vertices for massive and massless higher spin fields
Using the light-cone formulation of relativistic dynamics, we develop various
methods for constructing cubic interaction vertices and apply these methods to
the study of higher spin fields propagating in flat space of dimension greater
than or equal to four. Generating functions of parity invariant cubic
interaction vertices for massive and massless higher spin fields of arbitrary
symmetry are obtained. We derive restrictions on the allowed values of spins
and the number of derivatives, which provide a classification of cubic
interaction vertices for totally symmetric fields. As an example of application
of the light-cone formalism, we obtain simple expressions for the minimal
Yang-Mills and gravitational interactions of massive totally symmetric
arbitrary spin fields. We give the complete list of parity invariant and parity
violating cubic interaction vertices that can be constructed for massless
fields in five and six-dimensional spaces.Comment: 55 pages, LaTeX-2e, v3: Equations (3.15),(3.16) added to Section 3.
Discussion of vertices for massless fields in d=4 and footnotes 16,17 added
to Section 5.1. New vertices added to Table I. Misprints in equations (7.4),
(C.5), and (D.58) correcte
Conifold geometries, matrix models and quantum solutions
This paper is a continuation of hepth/0507224 where open topological B-models
describing D-branes on 2-cycles of local Calabi--Yau geometries with conical
singularities were studied. After a short review, the paper expands in
particular on two aspects: the gauge fixing problem in the reduction to two
dimensions and the quantum matrix model solutions.Comment: 17 p. To appear in proc. Symposium QTS-4, Varna (Bulgaria), August
200
Scattering of Massless Particles: Scalars, Gluons and Gravitons
In a recent note we presented a compact formula for the complete tree-level
S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime
dimension. In this paper we show that a natural formulation also exists for a
massless colored cubic scalar theory. In Yang-Mills, the formula is an integral
over the space of n marked points on a sphere and has as integrand two factors.
The first factor is a combination of Parke-Taylor-like terms dressed with U(N)
color structures while the second is a Pfaffian. The S-matrix of a U(N)xU(N')
cubic scalar theory is obtained by simply replacing the Pfaffian with a U(N')
version of the previous U(N) factor. Given that gravity amplitudes are obtained
by replacing the U(N) factor in Yang-Mills by a second Pfaffian, we are led to
a natural color-kinematics correspondence. An expansion of the integrand of the
scalar theory leads to sums over trivalent graphs and are directly related to
the KLT matrix. We find a connection to the BCJ color-kinematics duality as
well as a new proof of the BCJ doubling property that gives rise to gravity
amplitudes. We end by considering a special kinematic point where the partial
amplitude simply counts the number of color-ordered planar trivalent trees,
which equals a Catalan number. The scattering equations simplify dramatically
and are equivalent to a special Y-system with solutions related to roots of
Chebyshev polynomials.Comment: 31 page
On the solution of the initial value constraints for general relativity coupled to matter in terms of Ashtekar's variables
The method of solution of the initial value constraints for pure canonical
gravity in terms of Ashtekar's new canonical variables due to CDJ is further
developed in the present paper. There are 2 new main results : 1) We extend the
method of CDJ to arbitrary matter-coupling again for non-degenerate metrics :
the new feature is that the 'CDJ-matrix' adopts a nontrivial antisymmetric part
when solving the vector constraint and that the Klein-Gordon-field is used,
instead of the symmetric part of the CDJ-matrix, in order to satisfy the scalar
constraint. 2) The 2nd result is that one can solve the general initial value
constraints for arbitrary matter coupling by a method which is completely
independent of that of CDJ. It is shown how the Yang-Mills and gravitational
Gauss constraints can be solved explicitely for the corresponding electric
fields. The rest of the constraints can then be satisfied by using either
scalar or spinor field momenta. This new trick might be of interest also for
Yang-Mills theories on curved backgrounds.Comment: Latex, 15 pages, PITHA93-1, January 9
Anomalous reparametrizations and butterfly states in string field theory
The reparametrization symmetries of Witten's vertex in ordinary or vacuum
string field theories can be used to extract useful information about classical
solutions of the equations of motion corresponding to D-branes. It follows,
that the vacuum string field theory in general has to be regularized. For the
regularization recently considered by Gaiotto et al., we show that the
identities we derive, are so constraining, that among all surface states they
uniquely select the simplest butterfly projector discovered numerically by
those authors. The reparametrization symmetries are also used to give a simple
proof that the butterfly states and their generalizations are indeed
projectors.Comment: 37 pages, 4 figures, v2: numerical factors in section 2.3 and
Appendix C corrected, report number correcte
The inverse spectral problem for the discrete cubic string
Given a measure on the real line or a finite interval, the "cubic string"
is the third order ODE where is a spectral parameter. If
equipped with Dirichlet-like boundary conditions this is a nonselfadjoint
boundary value problem which has recently been shown to have a connection to
the Degasperis-Procesi nonlinear water wave equation. In this paper we study
the spectral and inverse spectral problem for the case of Neumann-like boundary
conditions which appear in a high-frequency limit of the Degasperis--Procesi
equation. We solve the spectral and inverse spectral problem for the case of
being a finite positive discrete measure. In particular, explicit
determinantal formulas for the measure are given. These formulas generalize
Stieltjes' formulas used by Krein in his study of the corresponding second
order ODE .Comment: 24 pages. LaTeX + iopart, xypic, amsthm. To appear in Inverse
Problems (http://www.iop.org/EJ/journal/IP
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