1,460 research outputs found
Theory of higher spin tensor currents and central charges
We study higher spin tensor currents in quantum field theory. Scalar, spinor
and vector fields admit unique "improved" currents of arbitrary spin, traceless
and conserved. Off-criticality as well as at interacting fixed points
conservation is violated and the dimension of the current is anomalous. In
particular, currents J^(s,I) with spin s between 0 and 5 (and a second label I)
appear in the operator product expansion of the stress tensor. The TT OPE is
worked out in detail for free fields; projectors and invariants encoding the
space-time structure are classified. The result is used to write and discuss
the most general OPE for interacting conformal field theories and
off-criticality. Higher spin central charges c_(s,I) with arbitrary s are
defined by higher spin channels of the many-point T-correlators and central
functions interpolating between the UV and IR limits are constructed. We
compute the one-loop values of all c_(s,I) and investigate the RG trajectories
of quantum field theories in the conformal window following our approach. In
particular, we discuss certain phenomena (perturbative and nonperturbative)
that appear to be of interest, like the dynamical removal of the I-degeneracy.
Finally, we address the problem of formulating an action principle for the RG
trajectory connecting pairs of CFT's as a way to go beyond perturbation theory.Comment: Latex, 46 pages, 4 figures. Final version, to appear in NPB. (v2:
added two terms in vector OPE
An Exceptional Collection For Khovanov Homology
The Temperley-Lieb algebra is a fundamental component of SU(2) topological
quantum field theories. We construct chain complexes corresponding to minimal
idempotents in the Temperley-Lieb algebra. Our results apply to the framework
which determines Khovanov homology. Consequences of our work include
semi-orthogonal decompositions of categorifications of Temperley-Lieb algebras
and Postnikov decompositions of all Khovanov tangle invariants
On linear combinations of generalized involutive matrices
Let X(dagger) denotes the Moore-Penrose pseudoinverse of a matrix X. We study a number of situations when (aA + bB)(dagger) = aA + bB provided a, b is an element of C\{0} and A, B are n x n complex matrices such that A(dagger) = A and B(dagger) = B. (C) 2011 Taylor & FrancisLiu, X.; Wu, L.; Benítez López, J. (2011). On linear combinations of generalized involutive matrices. Linear and Multilinear Algebra. 59(11):1221-1236. doi:10.1080/03081087.2010.496111S12211236591
Measurements design and phenomena discrimination
The construction of measurements suitable for discriminating signal
components produced by phenomena of different types is considered. The required
measurements should be capable of cancelling out those signal components which
are to be ignored when focusing on a phenomenon of interest. Under the
hypothesis that the subspaces hosting the signal components produced by each
phenomenon are complementary, their discrimination is accomplished by
measurements giving rise to the appropriate oblique projector operator. The
subspace onto which the operator should project is selected by nonlinear
techniques in line with adaptive pursuit strategies
Rayleigh-Ritz majorization error bounds of the mixed type
The absolute change in the Rayleigh quotient (RQ) for a Hermitian matrix with
respect to vectors is bounded in terms of the norms of the residual vectors and
the angle between vectors in [\doi{10.1137/120884468}]. We substitute
multidimensional subspaces for the vectors and derive new bounds of absolute
changes of eigenvalues of the matrix RQ in terms of singular values of residual
matrices and principal angles between subspaces, using majorization. We show
how our results relate to bounds for eigenvalues after discarding off-diagonal
blocks or additive perturbations.Comment: 20 pages, 1 figure. Accepted to SIAM Journal on Matrix Analysis and
Application
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