297 research outputs found
Consistent gravitational anomalies for chiral bosons
Exact consistent gravitational anomalies for chiral bosons in two dimensions
are treated both with the Schwinger-DeWitt regularization and independently
through a cohomological procedure. The diffeomorphism transformations are
described by a single ghost which allows to climb the cohomological chain in a
unique way.Comment: 20 pages, 3 figures; v3: reference adde
Algebraic Classification of Weyl Anomalies in Arbitrary Dimensions
Conformally invariant massless field systems involving only dimensionless
parameters are known to describe particle physics at very high energy. In the
presence of an external gravitational field, the conformal symmetry may
generalize to Weyl invariance. However, the latter symmetry no longer survives
after quantization: A Weyl anomaly appears. In this Letter, a purely algebraic
understanding of the universal structure of the Weyl anomalies is presented.
The results hold in arbitrary dimensions and independently of any
regularization scheme.Comment: 4 pages - accepted for publication in Physical Review Letter
Algebraic Properties of BRST Coupled Doublets
We characterize the dependence on doublets of the cohomology of an arbitrary
nilpotent differential s (including BRST differentials and classical linearized
Slavnov-Taylor (ST) operators) in terms of the cohomology of the
doublets-independent component of s. All cohomologies are computed in the space
of local integrated formal power series. We drop the usual assumption that the
counting operator for the doublets commutes with s (decoupled doublets) and
discuss the general case where the counting operator does not commute with s
(coupled doublets). The results are purely algebraic and do not rely on
power-counting arguments.Comment: Some explanations enlarged, references adde
General solutions of the Wess-Zumino consistency condition for the Weyl anomalies
The general solutions of the Wess-Zumino consistency condition for the
conformal (or Weyl, or trace) anomalies are derived. The solutions are
obtained, in arbitrary dimensions, by explicitly computing the cohomology of
the corresponding Becchi-Rouet-Stora-Tyutin differential in the space of
integrated local functions at ghost number unity. This provides a purely
algebraic, regularization-independent classification of the Weyl anomalies in
arbitrary dimensions. The so-called type-A anomaly is shown to satisfy a
non-trivial descent of equations, similarly to the non-Abelian chiral anomaly
in Yang-Mills theory.Comment: 9 pages. RevTeX fil
Graded Majorana spinors
In many mathematical and physical contexts spinors are treated as Grassmann
odd valued fields. We show that it is possible to extend the classification of
reality conditions on such spinors by a new type of Majorana condition. In
order to define this graded Majorana condition we make use of
pseudo-conjugation, a rather unfamiliar extension of complex conjugation to
supernumbers. Like the symplectic Majorana condition, the graded Majorana
condition may be imposed, for example, in spacetimes in which the standard
Majorana condition is inconsistent. However, in contrast to the symplectic
condition, which requires duplicating the number of spinor fields, the graded
condition can be imposed on a single Dirac spinor. We illustrate how graded
Majorana spinors can be applied to supersymmetry by constructing a globally
supersymmetric field theory in three-dimensional Euclidean space, an example of
a spacetime where standard Majorana spinors do not exist.Comment: 16 pages, version to appear in J. Phys. A; AFK previously published
under the name A. F. Schunc
Two-Center Black Holes Duality-Invariants for stu Model and its lower-rank Descendants
We classify 2-center extremal black hole charge configurations through
duality-invariant homogeneous polynomials, which are the generalization of the
unique invariant quartic polynomial for single-center black holes based on
homogeneous symmetric cubic special Kaehler geometries. A crucial role is
played by an horizontal SL(p,R) symmetry group, which classifies invariants for
p-center black holes. For p = 2, a (spin 2) quintet of quartic invariants
emerge. We provide the minimal set of independent invariants for the rank-3 N =
2, d = 4 stu model, and for its lower-rank descendants, namely the rank-2 st^2
and rank-1 t^3 models; these models respectively exhibit seven, six and five
independent invariants. We also derive the polynomial relations among these and
other duality invariants. In particular, the symplectic product of two charge
vectors is not independent from the quartic quintet in the t^3 model, but
rather it satisfies a degree-16 relation, corresponding to a quartic equation
for the square of the symplectic product itself.Comment: 1+31 pages; v2: amendments in Sec. 9, App. C added, other minor
refinements, Refs. added; v3: Ref. added, typos fixed. To appear on
J.Math.Phy
Non-perturbative phenomena in the three-dimensional random field Ising model
The systematic approach for the calculations of the non-perturbative
contributions to the free energy in the ferromagnetic phase of the random field
Ising model is developed. It is demonstrated that such contributions appear due
to localized in space instanton-like excitations. It is shown that away from
the critical region such instanton solutions are described by the set of the
mean-field saddle-point equations for the replica vector order parameter, and
these equations can be formally reduced to the only saddle-point equation of
the pure system in dimensions (D-2). In the marginal case, D=3, the
corresponding non-analytic contribution is computed explicitly. Nature of the
phase transition in the three-dimensional random field Ising model is
discussed.Comment: 12 page
Algebraic characterization of the Wess-Zumino consistency conditions in gauge theories
A new way of solving the descent equations corresponding to the Wess-Zumino
consistency conditions is presented. The method relies on the introduction of
an operator which allows to decompose the exterior space-time
derivative as a commutator. The case of the Yang-Mills theories is
treated in detail.Comment: 16 pages, UGVA-DPT 1992/08-781 to appear in Comm. Math. Phy
A systematic method for constructing time discretizations of integrable lattice systems: local equations of motion
We propose a new method for discretizing the time variable in integrable
lattice systems while maintaining the locality of the equations of motion. The
method is based on the zero-curvature (Lax pair) representation and the
lowest-order "conservation laws". In contrast to the pioneering work of
Ablowitz and Ladik, our method allows the auxiliary dependent variables
appearing in the stage of time discretization to be expressed locally in terms
of the original dependent variables. The time-discretized lattice systems have
the same set of conserved quantities and the same structures of the solutions
as the continuous-time lattice systems; only the time evolution of the
parameters in the solutions that correspond to the angle variables is
discretized. The effectiveness of our method is illustrated using examples such
as the Toda lattice, the Volterra lattice, the modified Volterra lattice, the
Ablowitz-Ladik lattice (an integrable semi-discrete nonlinear Schroedinger
system), and the lattice Heisenberg ferromagnet model. For the Volterra lattice
and modified Volterra lattice, we also present their ultradiscrete analogues.Comment: 61 pages; (v2)(v3) many minor correction
Supersymmetric structure of the induced W gravities
We derive the supersymmetric structure present in W-gravities which has been
already observed in various contexts as Yang-Mills theory, topological field
theories, bosonic string and chiral W_{3}-gravity. This derivation which is
made in the geometrical framework of Zucchini, necessitates the introduction of
an appropriate new basis of variables which replace the canonical fields and
their derivatives. This construction is used, in the W_{2}-case, to deduce from
the Chern-Simons action the Wess-Zumino-Polyakov action.Comment: 17 pages, Latex. To appear in Class. Quantum. Gravit
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