266 research outputs found
Supergravity Solution for Three-String Junction in M-Theory
Three-String junctions are allowed configurations in II B string theory which
preserve one-fourth supersymmetry. We obtain the 11-dimensional supergravity
solution for curved membranes corresponding to these three-string junctions.Comment: Latex file, 14 pages, minor modifications, version to appear in JHE
Is toric duality a Seiberg-like duality in (2+1)-d ?
We show that not all dimensional toric phases are Seiberg-like duals.
Particularly, we work out superconformal indices for the toric phases of Fanos
, and . We find that the indices for
the two toric phases of Fano do not match, which implies that
they are not Seiberg-like duals. We also take the route of acting Seiberg-like
duality transformation on toric quiver Chern-Simons theories to obtain dual
quivers. We study two examples and show that Seiberg-like dual quivers are not
always toric quivers.Comment: 21 pages, 7 figures, to be published in JHE
Effective SO Superpotential for N=1 Theory with N_f Fundamental Matter
Motivated by the duality conjecture of Dijkgraaf and Vafa between
supersymmetric gauge theories and matrix models, we derive the effective
superpotential of N=1 supersymmetric gauge theory with gauge group SO(N_c) and
arbitrary tree level polynomial superpotential of one chiral superfield in the
adjoint representation and N_f fundamental matter multiplets. For a special
point in the classical vacuum where the gauge group is unbroken, we show that
the effective superpotential matches with that obtained from the geometric
engineering approach.Comment: LaTeX, 1+19 pages, To appear in Nucl.Phys.
Partial resolution of complex cones over Fano
In our recent paper arXiv:1108.2387, we systematized inverse algorithm to
obtain quiver gauge theory living on the M2-branes probing the singularities of
special kind of Calabi-Yau four-folds which were complex cones over toric Fano
, , , . These quiver gauge
theories cannot be given a dimer tiling presentation. We use the method of
partial resolution to show that the toric data of and Fano
can be embedded inside the toric data of Fano
theories. This method indirectly justfies that the two node quiver Chern-Simons
theories corresponding to , Fano and their
orbifolds can be obtained by higgsing matter fields of the three node parent
quiver corresponding to Fano , , ,
three-folds.Comment: 22 pages, 8 figure
Computation of Lickorish's Three Manifold Invariants using Chern-Simons Theory
It is well known that any three-manifold can be obtained by surgery on a
framed link in . Lickorish gave an elementary proof for the existence of
the three-manifold invariants of Witten using a framed link description of the
manifold and the formalisation of the bracket polynomial as the Temperley-Lieb
Algebra. Kaul determined three-manifold invariants from link polynomials in
SU(2) Chern-Simons theory. Lickorish's formula for the invariant involves
computation of bracket polynomials of several cables of the link. We describe
an easier way of obtaining the bracket polynomial of a cable using
representation theory of composite braiding in SU(2) Chern-Simons theory. We
prove that the cabling corresponds to taking tensor products of fundamental
representations of SU(2). This enables us to verify that the two apparently
distinct three-manifold invariants are equivalent for a specific relation of
the polynomial variables.Comment: 25 pages, 11 eps figures, harvmac file (big mode
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
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
- …