251,021 research outputs found
Superconformal Blocks: General Theory
In this work we launch a systematic theory of superconformal blocks for
four-point functions of arbitrary supermultiplets. Our results apply to a large
class of superconformal field theories including 4-dimensional models with any
number of supersymmetries. The central new ingredient is a
universal construction of the relevant Casimir differential equations. In order
to find these equations, we model superconformal blocks as functions on the
supergroup and pick a distinguished set of coordinates. The latter are chosen
so that the superconformal Casimir operator can be written as a perturbation of
the Casimir operator for spinning bosonic blocks by a fermionic (nilpotent)
term. Solutions to the associated eigenvalue problem can be obtained through a
quantum mechanical perturbation theory that truncates at some finite order so
that all results are exact. We illustrate the general theory at the example of
dimensional theories with supersymmetry for which we
recover known superblocks. The paper concludes with an outlook to 4-dimensional
blocks with supersymmetry.Comment: JHEP format, an appendix and remarks added, typos correcte
Principal infinity-bundles - General theory
The theory of principal bundles makes sense in any infinity-topos, such as
that of topological, of smooth, or of otherwise geometric
infinity-groupoids/infinity-stacks, and more generally in slices of these. It
provides a natural geometric model for structured higher nonabelian cohomology
and controls general fiber bundles in terms of associated bundles. For suitable
choices of structure infinity-group G these G-principal infinity-bundles
reproduce the theories of ordinary principal bundles, of bundle
gerbes/principal 2-bundles and of bundle 2-gerbes and generalize these to their
further higher and equivariant analogs. The induced associated infinity-bundles
subsume the notions of gerbes and higher gerbes in the literature.
We discuss here this general theory of principal infinity-bundles, intimately
related to the axioms of Giraud, Toen-Vezzosi, Rezk and Lurie that characterize
infinity-toposes. We show a natural equivalence between principal
infinity-bundles and intrinsic nonabelian cocycles, implying the classification
of principal infinity-bundles by nonabelian sheaf hyper-cohomology. We observe
that the theory of geometric fiber infinity-bundles associated to principal
infinity-bundles subsumes a theory of infinity-gerbes and of twisted
infinity-bundles, with twists deriving from local coefficient infinity-bundles,
which we define, relate to extensions of principal infinity-bundles and show to
be classified by a corresponding notion of twisted cohomology, identified with
the cohomology of a corresponding slice infinity-topos.
In a companion article [NSSb] we discuss explicit presentations of this
theory in categories of simplicial (pre)sheaves by hyper-Cech cohomology and by
simplicial weakly-principal bundles; and in [NSSc] we discuss various examples
and applications of the theory.Comment: 46 pages, published versio
Symmetry breaking boundaries I. General theory
We study conformally invariant boundary conditions that break part of the
bulk symmetries. A general theory is developped for those boundary conditions
for which the preserved subalgebra is the fixed algebra under an abelian
orbifold group. We explicitly construct the boundary states and reflection
coefficients as well as the annulus amplitudes. Integrality of the annulus
coefficients is proven in full generality.Comment: 60 pages, LaTeX2e; typos fixed and other minor correction
The Faraday effect revisited: General theory
This paper is the first in a series revisiting the Faraday effect, or more
generally, the theory of electronic quantum transport/optical response in bulk
media in the presence of a constant magnetic field. The independent electron
approximation is assumed. At zero temperature and zero frequency, if the Fermi
energy lies in a spectral gap, we rigorously prove the Widom-Streda formula.
For free electrons, the transverse conductivity can be explicitly computed and
coincides with the classical result. In the general case, using magnetic
perturbation theory, the conductivity tensor is expanded in powers of the
strength of the magnetic field . Then the linear term in of this
expansion is written down in terms of the zero magnetic field Green function
and the zero field current operator. In the periodic case, the linear term in
of the conductivity tensor is expressed in terms of zero magnetic field
Bloch functions and energies. No derivatives with respect to the quasi-momentum
appear and thereby all ambiguities are removed, in contrast to earlier work.Comment: Final version, accepted for publication in J. Math. Phy
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