19,607 research outputs found
Functional integration and abelian link invariants
The functional integral computation of the various topological invariants,
which are associated with the Chern-Simons field theory, is considered. The
standard perturbative setting in quantum field theory is rewieved and new
developments in the path-integral approach, based on the Deligne-Beilinson
cohomology, are described in the case of the abelian U(1) Chern-Simons field
theory formulated in S^1 x S^2.Comment: 20 pages, 4 figures, Contribution to the Proceedings of the workshop
"Chern-Simons Gauge theory: 20 years after", Bonn, August 200
Nonlocally Regularized Antibracket-Antifield Formalism and Anomalies in Chiral Gravity
The nonlocal regularization method, recently proposed in
ref.\,\ct{emkw91,kw92,kw93}, is extended to general gauge theories by
reformulating it along the ideas of the antibracket-antifield formalism. From
the interplay of both frameworks a fully regularized version of the
field-antifield (FA) formalism arises, being able to deal with higher order
loop corrections and to describe higher order loop contributions to the BRST
anomaly. The quantum master equation, considered in the FA framework as the
quantity parametrizing BRST anomalies, is argued to be incomplete at two and
higher order loops and conjectured to reproduce only the one-loop corrections
to the anomaly generated by the addition of , ,
counterterms. Chiral gravity is used to exemplify the nonlocally
regularized FA formalism. First, the regularized one-loop quantum master
equation is used to compute the complete one-loop anomaly. Its two-loop order,
however, is shown to reproduce only the modification to the two-loop anomaly
produced by the addition of a suitable one-loop counterterm, thereby providing
an explicit verification of the previous statement for . The well-known
universal two-loop anomaly, instead, is alternatively obtained from the BRST
variation of the nonlocally regulated effective action. Incompleteness of the
quantum master equation is thus concluded to be a consequence of a naive
derivation of the FA BRST Ward identity.Comment: 32 pages, LaTeX (uses feynman), 3 figures (few typos corrected, 3
references added, final version to appear in Nucl.Phys.B
Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS_5 x S^5 superstring theory
We investigate the structure of the quantum S-matrix for perturbative
excitations of the Pohlmeyer reduced version of the AdS_5 x S^5 superstring
following arXiv:0912.2958. The reduced theory is a fermionic extension of a
gauged WZW model with an integrable potential. We use as an input the result of
the one-loop perturbative scattering amplitude computation and an analogy with
simpler reduced AdS_n x S^n theories with n=2,3. The n=2 theory is equivalent
to the N=2 2-d supersymmetric sine-Gordon model for which the exact quantum
S-matrix is known. In the n=3 case the one-loop perturbative S-matrix, improved
by a contribution of a local counterterm, satisfies the group factorization
property and the Yang-Baxter equation, and reveals the existence of a novel
quantum-deformed 2-d supersymmetry which is not manifest in the action. The
one-loop perturbative S-matrix of the reduced AdS_5 x S^5 theory has the group
factorisation property but does not satisfy the Yang-Baxter equation suggesting
some subtlety with the realisation of quantum integrability. As a possible
resolution, we propose that the S-matrix of this theory may be identified with
the quantum-deformed [psu(2|2)]^2 x R^2 symmetric R-matrix constructed in
arXiv:1002.1097. We conjecture the exact all-order form of this S-matrix and
discuss its possible relation to the perturbative S-matrix defined by the path
integral. As in the AdS_3 x S^3 case the symmetry of the S-matrix may be
interpreted as an extended quantum-deformed 2-d supersymmetry.Comment: 61 pages, 2 figures; v2: minor corrections and reference added; v3:
minor correction
Stability of Two-Dimensional Soft Quasicrystals
The relative stability of two-dimensional soft quasicrystals is examined
using a recently developed projection method which provides a unified numerical
framework to compute the free energy of periodic crystal and quasicrystals.
Accurate free energies of numerous ordered phases, including dodecagonal,
decagonal and octagonal quasicrystals, are obtained for a simple model, i.e.
the Lifshitz-Petrich free energy functional, of soft quasicrystals with two
length-scales. The availability of the free energy allows us to construct phase
diagrams of the system, demonstrating that, for the Lifshitz-Petrich model, the
dodecagonal and decagonal quasicrystals can become stable phases, whereas the
octagonal quasicrystal stays as a metastable phase.Comment: 11 pages, 7 figure
Symbolic computation of conservation laws for nonlinear partial differential equations in multiple space dimensions
A method for symbolically computing conservation laws of nonlinear partial
differential equations (PDEs) in multiple space dimensions is presented in the
language of variational calculus and linear algebra. The steps of the method
are illustrated using the Zakharov-Kuznetsov and Kadomtsev-Petviashvili
equations as examples. The method is algorithmic and has been implemented in
Mathematica. The software package, ConservationLawsMD.m, can be used to
symbolically compute and test conservation laws for polynomial PDEs that can be
written as nonlinear evolution equations. The code ConservationLawsMD.m has
been applied to (2+1)-dimensional versions of the Sawada-Kotera, Camassa-Holm,
and Gardner equations, and the multi-dimensional Khokhlov-Zabolotskaya
equation.Comment: 26 pages. Paper will appear in Journal of Symbolic Computation
(2011). Presented at the Special Session on Geometric Flows, Moving Frames
and Integrable Systems, 2010 Spring Central Sectional Meeting of the American
Mathematical Society, Macalester College, St. Paul, Minnesota, April 10, 201
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