40,442 research outputs found
Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
We discuss 2d duality transformations in the classical AdS5 x S5 superstring
and their effect on the integrable structure. T-duality along four directions
in Poincare parametrization of AdS5 maps the bosonic part of the superstring
action into itself. On bosonic level, this duality may be understood as a
symmetry of the first-order (phase space) system of equations for the coset
components of the current. The associated Lax connection is invariant modulo
the action of an so(2,4)-automorphism. We then show that this symmetry extends
to the full superstring, provided one supplements the transformation of the
bosonic components of the current with a transformation on the fermionic ones.
At the level of the action, this symmetry can be seen by combining the bosonic
duality transformation with a similar one applied to part of the fermionic
superstring coordinates. As a result, the full superstring action is mapped
into itself, albeit in a different kappa-symmetry gauge. One implication is
that the dual model has the same superconformal symmetry group as the original
one, and this may be seen as a consequence of the integrability of the
superstring. The invariance of the Lax connection under the duality implies a
map on the full set of conserved charges that should interchange some of the
Noether (local) charges with hidden (non-local) ones and vice versa.Comment: V2: 33 pages, clarifications added and minor corrections, replaced
with version to appear in PR
Hamiltonian cycles in Cayley graphs of imprimitive complex reflection groups
Generalizing a result of Conway, Sloane, and Wilkes for real reflection
groups, we show the Cayley graph of an imprimitive complex reflection group
with respect to standard generating reflections has a Hamiltonian cycle. This
is consistent with the long-standing conjecture that for every finite group, G,
and every set of generators, S, of G the undirected Cayley graph of G with
respect to S has a Hamiltonian cycle.Comment: 15 pages, 4 figures; minor revisions according to referee comments,
to appear in Discrete Mathematic
Chern-Simons Supergravities with Off-Shell Local Superalgebras
A new family of supergravity theories in odd dimensions is presented. The
Lagrangian densities are Chern-Simons forms for the connection of a
supersymmetric extension of the anti-de Sitter algebra. The superalgebras are
the supersymmetric extensions of the AdS algebra for each dimension, thus
completing the analysis of van Holten and Van Proeyen, which was valid for N=1
and for D=2,3,4,mod 8. The Chern-Simons form of the Lagrangian ensures
invariance under the gauge supergroup by construction and, in particular, under
local supersymmetry. Thus, unlike standard supergravity, the local
supersymmetry algebra closes off-shell and without requiring auxiliary fields.
The Lagrangian is explicitly given for D=5, 7 and 11. In all cases the
dynamical field content includes the vielbein, the spin connection, N
gravitini, and some extra bosonic ``matter'' fields which vary from one
dimension to another. The superalgebras fall into three families: osp(m|N) for
D=2,3,4, mod 8, osp(N|m) for D=6,7,8, mod 8, and su(m-2,2|N) for D=5 mod 4,
with m=2^{[D/2]}. The possible connection between the D=11 case and M-Theory is
also discussed.Comment: 13pages, RevTeX, no figures, two column
Blowing-Up the Four-Dimensional Z_3 Orientifold
We study the blowing-up of the four-dimensional Z_3 orientifold of
Angelantonj, Bianchi, Pradisi, Sagnotti and Stanev (ABPSS) by giving nonzero
vacuum expectation values (VEV's) to the twisted sector moduli blowing-up
modes. The blowing-up procedure induces a Fayet-Iliopoulos (FI) term for the
``anomalous'' U(1), whose magnitude depends linearly on the VEV's of the
blowing-up modes. To preserve the N=1 supersymmetry, non-Abelian matter fields
are forced to acquire nonzero VEV's, thus breaking (some of) the non-Abelian
gauge structure and decoupling some of the matter fields. We determine the form
of the FI term, construct explicit examples of (non-Abelian) D and F flat
directions, and determine the surviving gauge groups of the restabilized vacua.
We also determine the mass spectra, for which the restabilization reduces the
number of families.Comment: 19 pages, Late
Quantum matter in quantum space-time
Quantum matter in quantum space-time is discussed using general properties of
energy-conservation laws. As a rather radical conclusion, it is found that
standard methods of differential geometry and quantum field theory on curved
space-time are inapplicable in canonical quantum gravity, even at the level of
effective equations.Comment: 17 pages, v2: further references and more detailed conclusion
Semiclassical Trace Formulas for Noninteracting Identical Particles
We extend the Gutzwiller trace formula to systems of noninteracting identical
particles. The standard relation for isolated orbits does not apply since the
energy of each particle is separately conserved causing the periodic orbits to
occur in continuous families. The identical nature of the particles also
introduces discrete permutational symmetries. We exploit the formalism of
Creagh and Littlejohn [Phys. Rev. A 44, 836 (1991)], who have studied
semiclassical dynamics in the presence of continuous symmetries, to derive
many-body trace formulas for the full and symmetry-reduced densities of states.
Numerical studies of the three-particle cardioid billiard are used to
explicitly illustrate and test the results of the theory.Comment: 29 pages, 11 figures, submitted to PR
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