1,089 research outputs found
The Bethe ansatz for superconformal Chern-Simons
We study the anomalous dimensions for scalar operators for a
three-dimensional Chern-Simons theory recently proposed in arXiv:0806.1218. We
show that the mixing matrix at two-loop order is that for an integrable
Hamiltonian of an SU(4) spin chain with sites alternating between the
fundamental and the anti-fundamental representations. We find a set of Bethe
equations from which the anomalous dimensions can be determined and give a
proposal for the Bethe equations to the full superconformal group of
OSp(2,2|6).Comment: 22 pages, 9 figures; v2 Overall normalization of the Hamiltonian
corrected and missing diagram contributing to two-site interactions included.
Typos fixed; v3 Figure 8 corrected; v4 Misprints corrected; v5 Correct
figures recovered. Published version; v6: misprints in (3.15), (3.16), (3.17)
correcte
Classical Solutions for Two Dimensional QCD on the Sphere
We consider and gauge theory on the sphere. We express the
problem in terms of a matrix element of free fermions on a circle. This
allows us to find an alternative way to show Witten's result that the partition
function is a sum over classical saddle points. We then show how the phase
transition of Douglas and Kazakov occurs from this point of view. By
generalizing the work of Douglas and Kazakov, we find other `stringy' solutions
for the case in the large limit. Each solution is described by a net
charge. We derive a relation for the maximum charge for a given area and
we also describe the critical behavior for these new solutions. Finally, we
describe solutions for lattice which are in a sense dual to the
continuum solutions. (Parts of this paper were presented at the Strings
'93 Workshop, Berkeley, May 1993.)Comment: 26 pages, CERN-TH-7016, UVA-HET-93-0
Quark Potentials in the Higgs Phase of Large N Supersymmetric Yang-Mills Theories
We compute, in the large N limit, the quark potential for
supersymmetric SU(N) Yang-Mills theory broken to . At
short distances the quarks see only the unbroken gauge symmetry and have an
attractive potential that falls off as 1/L. At longer distances the interquark
interaction is sensitive to the symmetry breaking, and other QCD states appear.
These states correspond to combinations of the quark-antiquark pair with some
number of W-particles. If there is one or more W-particles then this state is
unstable because of the coulomb interaction between the W-particles and between
the W's and the quarks. As L is decreased the W-particles delocalize and these
coulomb branches merge onto a branch with a linear potential. The quarks on
this branch see the unbroken gauge group, but the flux tube is unstable to the
production of W-particles.Comment: 23 pages, 7 figures, harvmac (b
Simple Calculation of Instanton Corrections in Massive N=2 SU(3) SYM
We give an explicit derivation of the Picard-Fuchs equations for N=2
supersymmetric SU(3) Yang-Mills theory with massive hypermultiplets in
the fundamental representation. We determine the instanton corrections to the
prepotential in the weak coupling region using the relation between
\tr and the prepotential. This method can be generalized to other
gauge groups.Comment: 16 pages, Late
Seiberg-Witten prepotential for E-string theory and random partitions
We find a Nekrasov-type expression for the Seiberg-Witten prepotential for
the six-dimensional non-critical E_8 string theory toroidally compactified down
to four dimensions. The prepotential represents the BPS partition function of
the E_8 strings wound around one of the circles of the toroidal
compactification with general winding numbers and momenta. We show that our
expression exhibits expected modular properties. In particular, we prove that
it obeys the modular anomaly equation known to be satisfied by the
prepotential.Comment: 14 page
Magnon dispersion to four loops in the ABJM and ABJ models
The ABJM model is a superconformal Chern-Simons theory with N=6 supersymmetry
which is believed to be integrable in the planar limit. However, there is a
coupling dependent function that appears in the magnon dispersion relation and
the asymptotic Bethe ansatz that is only known to leading order at strong and
weak coupling. We compute this function to four loops in perturbation theory by
an explicit Feynman diagram calculation for both the ABJM model and the ABJ
extension. We find that all coefficients have maximal transcendentality. We
then compute the four-loop wrapping correction for a scalar operator in the 20
of SU(4) and find that it agrees with a recent prediction from the ABJM
Y-system of Gromov, Kazakov and Vieira. We also propose a limit of the ABJ
model that might be perturbatively integrable at all loop orders but has a
short range Hamiltonian.Comment: LaTeX, feynmp, 17 pages; v2: coupling factor in one Feynman diagram
corrected: modified result in the ABJ case only, formulations improved, typos
fixed, references added; v3: signs of three diagrams corrected, modifying the
final resul
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