389 research outputs found
Pure Gauge SU(2) Seiberg-Witten Theory and Modular Forms
We identify the spectral curve of pure gauge SU(2) Seiberg-Witten theory with
the Weierstrass curve \mathbbm{C}/L \ni z \mapsto (1,\wp(z),\wp(z)') and
thereby obtain explicitely a modular form from which the moduli space parameter
and lattice parameters , can be derived in terms of modular
respectively theta functions. We further discuss its relationship with the
triplet model conformal field theory.Comment: 11 + 2 pages, no figures, shortened, to be published in jm
Nonrelativistic Chern-Simons Vortices on the Torus
A classification of all periodic self-dual static vortex solutions of the
Jackiw-Pi model is given. Physically acceptable solutions of the Liouville
equation are related to a class of functions which we term
Omega-quasi-elliptic. This class includes, in particular, the elliptic
functions and also contains a function previously investigated by Olesen. Some
examples of solutions are studied numerically and we point out a peculiar
phenomenon of lost vortex charge in the limit where the period lengths tend to
infinity, that is, in the planar limit.Comment: 25 pages, 2+3 figures; improved exposition, corrected typos, added
one referenc
Quantum N=3, d=3 Chern-Simons Matter Theories in Harmonic Superspace
We develop the background field method for studying classical and quantum
aspects of N=3, d=3 Chern-Simons and matter theories in N=3 harmonic
superspace. As one of the immediate consequences, we prove a nonrenormalization
theorem implying the ultra-violet finiteness of the corresponding supergraph
perturbation theory. We also derive the general hypermultiplet and gauge
superfield propagators in a Chern-Simons background. The leading supergraphs
with two and four external lines are evaluated. In contrast to the
non-supersymmetric theory, the leading quantum correction to the massive
charged hypermultiplet proves to be the super Yang-Mills action rather than the
Chern-Simons one. The hypermultiplet mass is induced by a constant triplet of
central charges in the N=3, d=3 Poincare superalgebra.Comment: 1+37 pages, 3 figures; v2: a reference added, to appear in JHE
Non-Critical String Duals of N=1 Quiver Theories
We construct N=1 non-critical strings in four dimensions dual to strongly
coupled N=1 quiver gauge theories in the Coulomb phase, generalizing the string
duals of Argyres-Douglas points in N=2 gauge theories. They are the first
examples of superstrings vacua with an exact worldsheet description dual to
chiral N=1 theories. We identify the dual of the non-critical superstring using
a brane setup describing the field theory in the classical limit. We analyze
the spectrum of chiral operators in the strongly coupled regime and show how
worldsheet instanton effects give non-perturbative information about the gauge
theory. We also consider aspects of D-branes relevant for the holographic
duality.Comment: JHEP style; 40 pages, 3 figures; v2: minor corrections, refs added,
version to appear in JHE
Infrared stability of ABJ-like theories
We consider marginal deformations of the superconformal ABJM/ABJ models which
preserve N=2 supersymmetry. We determine perturbatively the spectrum of fixed
points and study their infrared stability. We find a closed line of fixed
points which is IR stable. The fixed point corresponding to the ABJM/ABJ models
is stable under marginal deformations which respect the original SU(2)xSU(2)
invariance, while deformations which break this group destabilize the theory
which then flows to a less symmetric fixed point. We discuss the addition of
flavor degrees of freedom. We prove that in general a flavor marginal
superpotential does not destabilize the system in the IR. An exception is
represented by a marginal coupling which mixes matter charged under different
gauge sectors. Finally, we consider the case of relevant deformations which
should drive the system to a strongly coupled IR fixed point recently
investigated in arXiv:0909.2036 [hep-th].Comment: 1+11 pages, 4 figures; v2: minor correction
Argyres-Douglas Loci, Singularity Structures and Wall-Crossings in Pure N=2 Gauge Theories with Classical Gauge Groups
N=2 Seiberg-Witten theories allow an interesting interplay between the
Argyres-Douglas loci, singularity structures and wall-crossing formulae. In
this paper we investigate this connection by first studying the singularity
structures of hyper-elliptic Seiberg-Witten curves for pure N=2 gauge theories
with SU(r+1) and Sp(2r) gauge groups, and propose new methods to locate the
Argyres-Douglas loci in the moduli space, where multiple mutually non-local BPS
states become massless. In a region of the moduli space, we compute dyon
charges for all 2r+2 and 2r+1 massless dyons for SU(r+1) and Sp(2r) gauge
groups respectively for rank r>1. From here we elucidate the connection to the
wall-crossing phenomena for pure Sp(4) Seiberg-Witten theory near the
Argyres-Douglas loci, despite our emphasis being only at the massless sector of
the BPS spectra. We also present 2r-1 candidates for the maximal
Argyres-Douglas points for pure SO(2r+1) Seiberg-Witten theory.Comment: 81 pages, 41 figures, LaTeX; v2: Minor cosmetic changes and
correction of a typographical error in acknowledgement. Final version to
appear in JHE
On the infrared behaviour of 3d Chern-Simons theories in N=2 superspace
We discuss the problem of infrared divergences in the N=2 superspace approach
to classically marginal three-dimensional Chern-Simons-matter theories.
Considering the specific case of ABJM theory, we describe the origin of such
divergences and offer a prescription to eliminate them by introducing
non-trivial gauge-fixing terms in the action. We also comment on the extension
of our procedure to higher loop order and to general three-dimensional
Chern-Simons-matter models.Comment: 26 pages, 6 figures, JHEP3; v2: minor corrections and references
added; v3: introduction expanded, presentation of section 3.3.1 improved,
references added, version to appear in JHE
Moduli Redefinitions and Moduli Stabilisation
Field redefinitions occur in string compactifications at the one loop level.
We review arguments for why such redefinitions occur and study their effect on
moduli stabilisation and supersymmetry breaking in the LARGE volume scenario.
For small moduli, although the effect of such redefinitions can be larger than
that of the corrections in both the K\"ahler and scalar potentials,
they do not alter the structure of the scalar potential. For the less well
motivated case of large moduli, the redefinitions can dominate all other terms
in the scalar potential. We also study the effect of redefinitions on the
structure of supersymmetry breaking and soft terms.Comment: 21 pages, 3 figures; v2. references adde
Moduli Stabilisation and de Sitter String Vacua from Magnetised D7 Branes
Anomalous U(1)'s are ubiquitous in 4D chiral string models. Their presence
crucially affects the process of moduli stabilisation and cannot be neglected
in realistic set-ups. Their net effect in the 4D effective action is to induce
a matter field dependence in the non-perturbative superpotential and a
Fayet-Iliopoulos D-term. We study flux compactifications of IIB string theory
in the presence of magnetised D7 branes. These give rise to anomalous U(1)'s
that modify the standard moduli stabilisation procedure. We consider simple
orientifold models to determine the matter field spectrum and the form of the
effective field theory. We apply our results to one-modulus KKLT and
multi-moduli large volume scenarios, in particular to the Calabi-Yau
P^4_{[1,1,1,6,9]}. After stabilising the matter fields, the effective action
for the Kahler moduli can acquire an extra positive term that can be used for
de Sitter lifting with non-vanishing F- and D-terms. This provides an explicit
realization of the D-term lifting proposal of hep-th/0309187.Comment: 35 pages, 1 figure. v2: Minor changes, references adde
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