5,354 research outputs found
Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of
the AdS_5 x S^5 superstring world-sheet theory in terms of physical degrees of
freedom we construct the Pohlmeyer-reduced version of the corresponding sigma
model. The Pohlmeyer reduction procedure involves several steps. Starting with
a coset space string sigma model in the conformal gauge and writing the
classical equations in terms of currents one can fix the residual conformal
diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables
(related locally to currents but non-locally to the original string coordinate
fields) so that the Virasoro constraints are automatically satisfied. The
resulting gauge-fixed equations can be obtained from a Lagrangian of a
non-abelian Toda type: a gauged WZW model with an integrable potential coupled
also to a set of 2d fermionic fields. A gauge-fixed form of the
Pohlmeyer-reduced theory can be found by integrating out the 2d gauge field of
the gauged WZW model. Its small-fluctuation spectrum contains 8 bosonic and 8
fermionic degrees of freedom with equal masses. We conjecture that the reduced
model has world-sheet supersymmetry and is ultraviolet-finite. We show that in
the special case of the AdS_2 x S^2 superstring model the reduced theory is
indeed supersymmetric: it is equivalent to the N=2 supersymmetric extension of
the sine-Gordon model.Comment: 56 pages. v2: section 6.4 expanded with comments on mass spectrum and
the corresponding S-matrix; v3,v4: minor corrections and clarifications adde
On conformal higher spins in curved background
We address the question of how to represent an interacting action for the
tower of conformal higher spin fields in a form covariant with respect to a
background metric. We use a background metric to define a star product which
plays a central role in the definition of the corresponding gauge
transformations. By an analogy with the kinetic term in the 4-derivative Weyl
gravity action expanded near an on-shell background one expects that the
kinetic term in such an action should be gauge-invariant in a Bach-flat metric.
We demonstrate this fact to first order in expansion in powers of the curvature
of the background metric. This generalizes the result of arXiv:1404.7452 for
spin 3 case to all conformal higher spins. We also comment on a possibility of
extending this claim to terms quadratic in the curvature and discuss the
appearance of background-dependent mixing terms in the quadratic part of the
conformal higher spin action.Comment: 24 pages. v2,v3: minor corrections and remarks adde
Dynamics of Coupled Maps with a Conservation Law
A particularly simple model belonging to a wide class of coupled maps which
obey a local conservation law is studied. The phase structure of the system and
the types of the phase transitions are determined. It is argued that the
structure of the phase diagram is robust with respect to mild violations of the
conservation law. Critical exponents possibly determining a new universality
class are calculated for a set of independent order parameters. Numerical
evidence is produced suggesting that the singularity in the density of Lyapunov
exponents at is a reflection of the singularity in the density of
Fourier modes (a ``Van Hove'' singularity) and disappears if the conservation
law is broken. Applicability of the Lyapunov dimension to the description of
spatiotemporal chaos in a system with a conservation law is discussed.Comment: To be published in CHAOS #7 (31 page, 16 figures
From BRST to light-cone description of higher spin gauge fields
In this short note we show, at the level of action principles, how the
light-cone action of higher spin gauge fields can easily be obtained from the
BRST formulation through the elimination of quartets. We analyze how the
algebra of cohomology classes is affected by such a reduction. By applying the
reduction to the Poincare generators, we give an alternative way of analyzing
the physical spectrum of the Fronsdal type actions, with or without trace
condition.Comment: 13 pages Latex file, Proceedings of the Workshop "Quantum Field
Theory and Hamiltonian Systems'', Caciulata, Romania, 16 - 21 Oct, 2004; more
references added, acknowledgments correcte
BRST-anti-BRST Symmetric Conversion of Second-Class Constraints
A general method of the BRST--anti-BRST symmetric conversion of second-class
constraints is presented. It yields a pair of commuting and nilpotent BRST-type
charges that can be naturally regarded as BRST and anti-BRST ones.
Interchanging the BRST and anti-BRST generators corresponds to a symmetry
between the original second-class constraints and the conversion variables,
which enter the formalism on equal footing.Comment: 12 pages, misprints correcte
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