34 research outputs found
Trivalent graphs, volume conjectures and character varieties
The generalized volume conjecture and the AJ conjecture (a.k.a. the quantum
volume conjecture) are extended to U_q(\fraksl_2) colored quantum invariants
of the theta and tetrahedron graph. The \SL(2,\bC) character variety of the
fundamental group of the complement of a trivalent graph with edges in
is a Lagrangian subvariety of the Hitchin moduli space over the Riemann
surface of genus . For the theta and tetrahedron graph, we conjecture
that the configuration of the character variety is locally determined by large
color asymptotics of the quantum invariants of the trivalent graph in terms of
complex Fenchel-Nielsen coordinates. Moreover, the -holonomic difference
equation of the quantum invariants provides the quantization of the character
variety.Comment: 11 pages, 2 figure
Multiplicity-free quantum 6j-symbols for U_q(sl_N)
We conjecture a closed form expression for the simplest class of
multiplicity-free quantum 6j-symbols for U_q(sl_N). The expression is a natural
generalization of the quantum 6j-symbols for U_q(sl_2) obtained by Kirillov and
Reshetikhin. Our conjectured form enables computation of colored HOMFLY
polynomials for various knots and links carrying arbitrary symmetric
representations.Comment: 8 pages; v2 typos corrected; v3 minor corrections and reference adde
Colored HOMFLY polynomials from Chern-Simons theory
We elaborate the Chern-Simons field theoretic method to obtain colored HOMFLY
invariants of knots and links. Using multiplicity-free quantum 6j-symbols for
U_q(sl_N), we present explicit evaluations of the HOMFLY invariants colored by
symmetric representations for a variety of knots, two-component links and
three-component links.Comment: 40 pages, 23 figures, a Mathematica notebook linked on the right as
an ancillary file; v2 typos corrected; v3 corrections in section 4.2 and
cosmetic changes; v4 corrections in two-component link
Supersymmetric Galilean conformal blocks
We set up the bootstrap procedure for supersymmetric Galilean Conformal (SGC)
field theories in two dimensions by constructing the SGC blocks in the
and two possible extensions of the Galilean
conformal algebra. In all analyzed cases, we present the bootstrap equations by
crossing symmetry of the four point function. In addition, we compute the
global SGC blocks analytically by solving the differential equations obtained
by acting with the Casimirs of the global subalgebras inside the four point
function. These global blocks agree with the general SGC blocks in the limit of
large central charge. We comment on possible applications to supersymmetric
BMS invariant field theories and flat holography.Comment: 43 pages, v2: references added and typos fixed, v3: refs added, minor
errors in the expression for the despotic blocks fixed. Matches published
versio