Research Interest of Dmitriy Belov

      Publication 1: D.Belov and G.Moore, "Holographic approach to action for self-dual fields" (URL)
      Publication 2: D.Belov and G.Moore, "Classification of spin abelian Chern-Simons theories" (URL)
      Publication 3: D.Belov and G.Moore, "Conformal blocks for AdS5 singletons" (URL)

    URL of Research: 

Statement of Interest:


  Currently I'm working on the following two projects:  1. about
geometry of RR fields in type II supergravity. In the paper
"Holographic approach to actions for self- dual fields" we
constructed a classical action which reproduces classical equations
of motion, yields correct Dirac quantization condition and yields
correct quantum field theory. The approach is based on the fact
that a self-dual field in 4k+2 dimensions is related to certain
generalized spin abelian Chern-Simons theory in 4k+3 dimensions.
Similarly RR fields of type IIA and IIB supergravity are related to
generalized spin abelian Chern-Simons theories in 11 dimensions. We
called these theories Chern-Simons A and Chern-Simons B
respectively. The holographic approach for RR fields yields Dirac
quantization conditions, and in particular generalizes the
Freed-Witten effect. In particular, Chern-Simons-B theory yields
action for the IIB supergravity.  2. about classification of
abelian quantum Hall fluids. It is well known that the effective
field theory which describes abelian quantum Hall fluid is a
Maxwell-Chern-Simons theory with the gauge group U(1)^N. Classical
spin abelian Chern-Simons theories are classified by integral
lattices of rank N. In the paper [2] we showed that quantum spin
abelian Chern-Simons theories are classified differently: they
depend only on the certain invariants of the lattice. Actually all
these invariants can be classified. The classification is based on
the classification of stable equivalence classes of integral
lattices [V. Nikulin]. One the implications of the classification
is prediction of *all* Hall conductivities one can obtain for
abelian Hall fluid.