247 research outputs found
The matrix model version of AGT conjecture and CIV-DV prepotential
Recently exact formulas were provided for partition function of conformal
(multi-Penner) beta-ensemble in the Dijkgraaf-Vafa phase, which, if interpreted
as Dotsenko-Fateev correlator of screenings and analytically continued in the
number of screening insertions, represents generic Virasoro conformal blocks.
Actually these formulas describe the lowest terms of the q_a-expansion, where
q_a parameterize the shape of the Penner potential, and are exact in the
filling numbers N_a. At the same time, the older theory of CIV-DV prepotential,
straightforwardly extended to arbitrary beta and to non-polynomial potentials,
provides an alternative expansion: in powers of N_a and exact in q_a. We check
that the two expansions coincide in the overlapping region, i.e. for the lowest
terms of expansions in both q_a and N_a. This coincidence is somewhat
non-trivial, since the two methods use different integration contours:
integrals in one case are of the B-function (Euler-Selberg) type, while in the
other case they are Gaussian integrals.Comment: 27 pages, 1 figur
On the property of Cachazo-Intriligator-Vafa prepotential at the extremum of the superpotential
We consider CIV-DV prepotential F for N=1 SU(n) SYM theory at the extremum of
the effective superpotential and prove the relation Comment: LaTeX, 10 pages; v2: some misprints corrected; v3: submitted to
Phys.Rev.
On Effective Superpotentials and Compactification to Three Dimensions
We study four dimensional N=2 SO/SP supersymmetric gauge theory on R^3\times
S^1 deformed by a tree level superpotential. We will show that the exact
superpotential can be obtained by making use of the Lax matrix of the
corresponding integrable model which is the periodic Toda lattice. The
connection between vacua of SO(2N) and SO(2kN-2k+2) can also be seen in this
framework. Similar analysis can also be applied for SO(2N+1) and SP(2N).Comment: 18 pages, latex file, v2: typos corrected, refs adde
\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
N=1 G_2 SYM theory and Compactification to Three Dimensions
We study four dimensional N=2 G_2 supersymmetric gauge theory on R^3\times
S^1 deformed by a tree level superpotential. We will show that the exact
superpotential can be obtained by making use of the Lax matrix of the
corresponding integrable model which is the periodic Toda lattice based on the
dual of the affine G_2 Lie algebra. At extrema of the superpotential the
Seiberg-Witten curve typically factorizes, and we study the algebraic equations
underlying this factorization. For U(N) theories the factorization was closely
related to the geometrical engineering of such gauge theories and to matrix
model descriptions, but here we will find that the geometrical interpretation
is more mysterious. Along the way we give a method to compute the gauge theory
resolvent and a suitable set of one-forms on the Seiberg-Witten curve. We will
also find evidence that the low-energy dynamics of G_2 gauge theories can
effectively be described in terms of an auxiliary hyperelliptic curve.Comment: 27 pages, late
Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
We give a concise summary of the impressive recent development unifying a
number of different fundamental subjects. The quiver Nekrasov functions
(generalized hypergeometric series) form a full basis for all conformal blocks
of the Virasoro algebra and are sufficient to provide the same for some
(special) conformal blocks of W-algebras. They can be described in terms of
Seiberg-Witten theory, with the SW differential given by the 1-point resolvent
in the DV phase of the quiver (discrete or conformal) matrix model
(\beta-ensemble), dS = ydz + O(\epsilon^2) = \sum_p \epsilon^{2p}
\rho_\beta^{(p|1)}(z), where \epsilon and \beta are related to the LNS
parameters \epsilon_1 and \epsilon_2. This provides explicit formulas for
conformal blocks in terms of analytically continued contour integrals and
resolves the old puzzle of the free-field description of generic conformal
blocks through the Dotsenko-Fateev integrals. Most important, this completes
the GKMMM description of SW theory in terms of integrability theory with the
help of exact BS integrals, and provides an extended manifestation of the basic
principle which states that the effective actions are the tau-functions of
integrable hierarchies.Comment: 14 page
Note on Matrix Model with Massless Flavors
In this note, following the work of Seiberg in hep-th/0211234 for the
conjecture between the field theory and matrix model in the case with massive
fundamental flavors, we generalize it to the case with massless fundamental
flavors. We show that with a little modifications, the analysis given by
Seiberg can be used directly to the case of massless flavors. Furthermore, this
new method explains the insertion of delta functions in the matrix model given
by Demasure and Janik in hep-th/0211082.Comment: 10 pages. Type fixed. Remarks adde
Allogeneic Stem Cell Transplantation in 59 Patients with Adult T-Cell Leukemia/Lymphoma (ATLL) â a Single Center's 13 Years Experience
Conformal SO(2,4) Transformations for the Helical AdS String Solution
By applying the conformal SO(2,4) transformations to the folded rotating
string configuration with two spins given by a certain limit from the helical
string solution in AdS_3 x S^1, we construct new string solutions whose
energy-spin relations are characterized by the boost parameter. When two
SO(2,4) transformations are performed with two boost parameters suitably
chosen, the straight folded rotating string solution with one spin in AdS_3 is
transformed in the long string limit into the long spiky string solution whose
expression is given from the helical string solution in AdS_3 by making a limit
that the modulus parameter becomes unity.Comment: 16 pages, LaTex, no figure
Branched Matrix Models and the Scales of Supersymmetric Gauge Theories
In the framework of the matrix model/gauge theory correspondence, we consider
supersymmetric U(N) gauge theory with symmetry breaking pattern. Due
to the presence of the Veneziano--Yankielowicz effective superpotential, in
order to satisfy the --term condition , we are forced to
introduce additional terms in the free energy of the corresponding matrix model
with respect to the usual formulation. This leads to a matrix model formulation
with a cubic potential which is free of parameters and displays a branched
structure. In this way we naturally solve the usual problem of the
identification between dimensionful and dimensionless quantities. Furthermore,
we need not introduce the scale by hand in the matrix model. These facts
are related to remarkable coincidences which arise at the critical point and
lead to a branched bare coupling constant. The latter plays the role of the
and scale tuning parameter. We then show that a suitable
rescaling leads to the correct identification of the variables. Finally,
by means of the the mentioned coincidences, we provide a direct expression for
the prepotential, including the gravitational corrections, in terms of
the free energy. This suggests that the matrix model provides a triangulation
of the istanton moduli space.Comment: 1+18 pages, harvmac. Added discussion on the CSW relative shifts of
theta vacua and the odd phases at the critical point. References added and
typos correcte
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