69 research outputs found
Low Energy Processes Associated with Spontaneously Broken N=2 Supersymmetry
We consider low energy processes described by the N=2 supercurrent on its
partially (to N=1) and spontaneously broken vacuum and the attendant
Nambu-Goldstone fermion (NGF), which the presence of the electric and magnetic
Fayet-Iliopoulos (FI) terms is responsible for. We show suppressions of
amplitudes decaying into the NGF as its momentum becomes small. In the
lagrangian realization (namely, the model of arXiv:hep-th/0409060) of the
conserved supercurrent, the NGF resides in the overall U(1), which is
nonetheless not decoupled, and interacts with the SU(N) sector through
nonderivative as well as derivative couplings. The low energy suppression is
instead accomplished by a cancellation between the annihilation diagram from
the Yukawa couplings and the contact four-Fermi terms. We give a complete form
of the supercurrent and the model is recast in more transparent notation.Comment: 20 pages, 6 figure
Instantons on ALE spaces and Super Liouville Conformal Field Theories
We provide evidence that the conformal blocks of N=1 super Liouville
conformal field theory are described in terms of the SU(2) Nekrasov partition
function on the ALE space O_{P^1}(-2).Comment: 10 page
\beta-deformed matrix model and Nekrasov partition function
We study Penner type matrix models in relation with the Nekrasov partition
function of four dimensional \mathcal{N}=2, SU(2) supersymmetric gauge theories
with N_F=2,3 and 4. By evaluating the resolvent using the loop equation for
general \beta, we explicitly construct the first half-genus correction to the
free energy and demonstrate the result coincides with the corresponding
Nekrasov partition function with general \Omega-background, including higher
instanton contributions after modifying the relation of the Coulomb branch
parameter with the filling fraction. Our approach complements the proof using
the Selberg integrals directly which is useful to find the contribution in the
series of instanton numbers for a given deformation parameter.Comment: 25 page
Quiver Gauge Theory and Extended Electric-magnetic Duality
We construct N=1 A-D-E quiver gauge theory with the gauge kinetic term which
depends on the adjoint chiral superfields, as a low energy effective theory on
D5-branes wrapped on 2-cycles of Calabi-Yau 3-fold in IIB string theory. The
field-dependent gauge kinetic term can be engineered by introducing B-field
which holomorphically varies on the base space (complex plane) of Calabi-Yau.
We consider Weyl reflection on A-D-E node, which acts non-trivially on the
gauge kinetic term. It is known that Weyl reflection is related to N=1
electric-magnetic duality. Therefore, the non-trivial action implies an
extension of the electric-magnetic duality to the case with the field-dependent
gauge kinetic term. We show that this extended duality is consistent from the
field theoretical point of view. We also consider the duality map of the
operators.Comment: 24 pages; v2: references added, typos correcte
On "Dotsenko-Fateev" representation of the toric conformal blocks
We demonstrate that the recent ansatz of arXiv:1009.5553, inspired by the
original remark due to R.Dijkgraaf and C.Vafa, reproduces the toric conformal
blocks in the same sense that the spherical blocks are given by the integral
representation of arXiv:1001.0563 with a peculiar choice of open integration
contours for screening insertions. In other words, we provide some evidence
that the toric conformal blocks are reproduced by appropriate beta-ensembles
not only in the large-N limit, but also at finite N. The check is explicitly
performed at the first two levels for the 1-point toric functions.
Generalizations to higher genera are briefly discussed.Comment: 10 page
Uniformization, Calogero-Moser/Heun duality and Sutherland/bubbling pants
Inspired by the work of Alday, Gaiotto and Tachikawa (AGT), we saw the
revival of Poincar{\'{e}}'s uniformization problem and Fuchsian equations
obtained thereof.
Three distinguished aspects are possessed by Fuchsian equations. First, they
are available via imposing a classical Liouville limit on level-two null-vector
conditions. Second, they fall into some A_1-type integrable systems. Third, the
stress-tensor present there (in terms of the Q-form) manifests itself as a kind
of one-dimensional "curve".
Thereby, a contact with the recently proposed Nekrasov-Shatashvili limit was
soon made on the one hand, whilst the seemingly mysterious derivation of
Seiberg-Witten prepotentials from integrable models become resolved on the
other hand. Moreover, AGT conjecture can just be regarded as a quantum version
of the previous Poincar{\'{e}}'s approach.
Equipped with these observations, we examined relations between spheric and
toric (classical) conformal blocks via Calogero-Moser/Heun duality. Besides, as
Sutherland model is also obtainable from Calogero-Moser by pinching tori at one
point, we tried to understand its eigenstates from the viewpoint of toric
diagrams with possibly many surface operators (toric branes) inserted. A
picture called "bubbling pants" then emerged and reproduced well-known results
of the non-critical self-dual c=1 string theory under a "blown-down" limit.Comment: 17 pages, 4 figures; v2: corrections and references added; v3:
Section 2.4.1 newly added thanks to JHEP referee advice. That classical
four-point spheric conformal blocks reproducing known SW prepotentials is
demonstrated via more examples, to appear in JHEP; v4: TexStyle changed onl
BPS Monopole Equation in Omega-background
We study deformed supersymmetries in N=2 super Yang-Mills theory in the
Omega-backgrounds characterized by two complex parameters . When one of the -parameters vanishes, the theory has
extended supersymmetries. We compute the central charge of the algebra and
obtain the deformed BPS monopole equation. We examine supersymmetries preserved
by the equation.Comment: 14 pages, typos corrected, published version in JHE
Four-Dimensional SCFTs from M5-Branes
We engineer a large new set of four-dimensional N=1 superconformal field
theories by wrapping M5-branes on complex curves. We present new supersymmetric
AdS_5 M-theory backgrounds which describe these fixed points at large N, and
then directly construct the dual four-dimensional CFTs for a certain subset of
these solutions. Additionally, we provide a direct check of the central charges
of these theories by using the M5-brane anomaly polynomial. This is a companion
paper which elaborates upon results reported in arXiv:1112:5487.Comment: 45 pages, 11 figure
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