3,716 research outputs found
Quantum Background Independence of Closed String Field Theory
We prove local background independence of the complete quantum closed string
field theory using the recursion relations for string vertices and the
existence of connections in CFT theory space. Indeed, with this data we
construct an antibracket preserving map between the state spaces of two nearby
conformal theories taking the corresponding string field measures into each other. A geometrical construction of the map is
achieved by introducing a Batalin-Vilkovisky (BV) algebra on spaces of Riemann
surfaces, together with a map to the BV algebra of string functionals. The
conditions of background independence show that the field independent terms of
the master action arise from vacuum vertices \V_{g,0}, and that the overall
-independent normalization of the string field measure involves the
theory space connection. Our result puts on firm ground the widely believed
statement that string theories built from nearby conformal theories are
different states of the same theory.Comment: 60 pages, phyzzx.tex, MIT-CTP-224
Direct data-driven control of constrained linear parameter-varying systems: A hierarchical approach
In many nonlinear control problems, the plant can be accurately described by
a linear model whose operating point depends on some measurable variables,
called scheduling signals. When such a linear parameter-varying (LPV) model of
the open-loop plant needs to be derived from a set of data, several issues
arise in terms of parameterization, estimation, and validation of the model
before designing the controller. Moreover, the way modeling errors affect the
closed-loop performance is still largely unknown in the LPV context. In this
paper, a direct data-driven control method is proposed to design LPV
controllers directly from data without deriving a model of the plant. The main
idea of the approach is to use a hierarchical control architecture, where the
inner controller is designed to match a simple and a-priori specified
closed-loop behavior. Then, an outer model predictive controller is synthesized
to handle input/output constraints and to enhance the performance of the inner
loop. The effectiveness of the approach is illustrated by means of a simulation
and an experimental example. Practical implementation issues are also
discussed.Comment: Preliminary version of the paper "Direct data-driven control of
constrained systems" published in the IEEE Transactions on Control Systems
Technolog
Quantum string integrability and AdS/CFT
Recent explorations of the AdS/CFT correspondence have unveiled integrable
structures underlying both planar N = 4 super-Yang-Mills theory and type IIB
string theory on AdS_5 x S^5. Integrability in the gauge theory emerges from
the fact that the dilatation generator can be identified with the Hamiltonian
of an integrable quantum spin chain, and the classical string theory has been
shown to contain infinite towers of hidden currents, a typical signature of
integrability. Efforts to match the integrable structures of various classical
string configurations to those of corresponding gauge theory quantum spin
chains have been largely successful. By studying a semiclassical expansion
about a class of point-like solitonic solutions to the classical string
equations of motion on AdS_5 x S^5, we take a step toward demonstrating that
integrability in the string theory survives quantum corrections beyond tree
level. Quantum fluctuations are chosen to align with background curvature
corrections to the pp-wave limit of AdS_5 x S^5, and we present evidence for an
infinite tower of local bosonic charges that are conserved by the quantum
theory to quartic order in the expansion. We explicitly compute several higher
charges based on a Lax representation of the worldsheet sigma model and provide
a prescription for matching the eigenvalue spectra of these charges with
corresponding quantities descending from the integrable structure of the gauge
theory.Comment: v2: references and typos corrected; v3: minor corrections and
comments, 23 page
Defect loops in gauged Wess-Zumino-Witten models
We consider loop observables in gauged Wess-Zumino-Witten models, and study
the action of renormalization group flows on them. In the WZW model based on a
compact Lie group G, we analyze at the classical level how the space of
renormalizable defects is reduced upon the imposition of global and affine
symmetries. We identify families of loop observables which are invariant with
respect to an affine symmetry corresponding to a subgroup H of G, and show that
they descend to gauge-invariant defects in the gauged model based on G/H. We
study the flows acting on these families perturbatively, and quantize the fixed
points of the flows exactly. From their action on boundary states, we present a
derivation of the "generalized Affleck-Ludwig rule, which describes a large
class of boundary renormalization group flows in rational conformal field
theories.Comment: 43 pages, 2 figures. v2: a few typos corrected, version to be
published in JHE
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