905 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
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
Investigating the BPS Spectrum of Non-Critical E_n Strings
We use the effective action of the non-critical strings to study its
BPS spectrum for . We show how to introduce mass parameters, or
Wilson lines, into the effective action, and then perform the appropriate
asymptotic expansions that yield the BPS spectrum. The result is the
character expansion of the spectrum, and is equivalent to performing the mirror
map on a Calabi-Yau with up to nine K\"ahler moduli. This enables a much more
detailed examination of the structure of the theory, and provides
extensive checks on the effective action description of the non-critical
string. We extract some universal ( independent) information concerning
the degeneracies of BPS excitations.Comment: 50 pages, harvmac (b
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