59,523 research outputs found
Knot Invariants and New Weight Systems from General 3D TFTs
We introduce and study the Wilson loops in a general 3D topological field
theories (TFTs), and show that the expectation value of Wilson loops also gives
knot invariants as in Chern-Simons theory. We study the TFTs within the
Batalin-Vilkovisky (BV) and Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ)
framework, and the Ward identities of these theories imply that the expectation
value of the Wilson loop is a pairing of two dual constructions of (co)cycles
of certain extended graph complex (extended from Kontsevich's graph complex to
accommodate the Wilson loop). We also prove that there is an isomorphism
between the same complex and certain extended Chevalley-Eilenberg complex of
Hamiltonian vector fields. This isomorphism allows us to generalize the Lie
algebra weight system for knots to weight systems associated with any
homological vector field and its representations. As an example we construct
knot invariants using holomorphic vector bundle over hyperKahler manifolds.Comment: 55 pages, typos correcte
The Virtue of Defects in 4D Gauge Theories and 2D CFTs
We advance a correspondence between the topological defect operators in
Liouville and Toda conformal field theories - which we construct - and loop
operators and domain wall operators in four dimensional N=2 supersymmetric
gauge theories on S^4. Our computation of the correlation functions in
Liouville/Toda theory in the presence of topological defect operators, which
are supported on curves on the Riemann surface, yields the exact answer for the
partition function of four dimensional gauge theories in the presence of
various walls and loop operators; results which we can quantitatively
substantiate with an independent gauge theory analysis. As an interesting
outcome of this work for two dimensional conformal field theories, we prove
that topological defect operators and the Verlinde loop operators are different
descriptions of the same operators.Comment: 59 pages, latex; v2 corrections to some formula
The universal C*-algebra of the electromagnetic field II. Topological charges and spacelike linear fields
Conditions for the appearance of topological charges are studied in the
framework of the universal C*-algebra of the electromagnetic field, which is
represented in any theory describing electromagnetism. It is shown that
non-trivial topological charges, described by pairs of fields localised in
certain topologically non-trivial spacelike separated regions, can appear in
regular representations of the algebra only if the fields depend non-linearly
on the mollifying test functions. On the other hand, examples of regular vacuum
representations with non-trivial topological charges are constructed, where the
underlying field still satisfies a weakened form of "spacelike linearity". Such
representations also appear in the presence of electric currents. The status of
topological charges in theories with several types of electromagnetic fields,
which appear in the short distance (scaling) limit of asymptotically free
non-abelian gauge theories, is also briefly discussed.Comment: 24 pages, 2 figure
Gauge fields as composite boundary excitations
We investigate representations of the conformal group that describe
"massless" particles in the interior and at the boundary of anti-de Sitter
space. It turns out that massless gauge excitations in anti-de Sitter are gauge
"current" operators at the boundary. Conversely, massless excitations at the
boundary are topological singletons in the interior. These representations lie
at the threshold of two "unitary bounds" that apply to any conformally
invariant field theory. Gravity and Yang-Mills gauge symmetry in anti-De Sitter
is translated to global translational symmetry and continuous -symmetry of
the boundary superconformal field theory.Comment: Latex 2 figures in one eps fil
Twisted Supersymmetric Gauge Theories and Orbifold Lattices
We examine the relation between twisted versions of the extended
supersymmetric gauge theories and supersymmetric orbifold lattices. In
particular, for the SYM in , we show that the continuum
limit of orbifold lattice reproduces the twist introduced by Marcus, and the
examples at lower dimensions are usually Blau-Thompson type. The orbifold
lattice point group symmetry is a subgroup of the twisted Lorentz group, and
the exact supersymmetry of the lattice is indeed the nilpotent scalar
supersymmetry of the twisted versions. We also introduce twisting in terms of
spin groups of finite point subgroups of -symmetry and spacetime symmetry.Comment: 32 page
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