53 research outputs found
Hitchin Equation, Singularity, and N=2 Superconformal Field Theories
We argue that Hitchin's equation determines not only the low energy effective
theory but also describes the UV theory of four dimensional N=2 superconformal
field theories when we compactify six dimensional theory on a
punctured Riemann surface. We study the singular solution to Hitchin's equation
and the Higgs field of solutions has a simple pole at the punctures; We show
that the massless theory is associated with Higgs field whose residual is a
nilpotent element; We identify the flavor symmetry associated with the puncture
by studying the singularity of closure of the moduli space of solutions with
the appropriate boundary conditions. For the mass-deformed theory the residual
of the Higgs field is a semi-simple element, we identify the semi-simple
element by arguing that the moduli space of solutions of mass-deformed theory
must be a deformation of the closure of the moduli space of the massless
theory. We also study the Seiberg-Witten curve by identifying it as the
spectral curve of the Hitchin's system. The results are all in agreement with
Gaiotto's results derived from studying the Seiberg-Witten curve of four
dimensional quiver gauge theory.Comment: 42 pages, 20 figures, Hitchin's equation for N=2 theory is derived by
comparing different order of compactification of six dimensional theory on
T^2\times \Sigma. More discussion about flavor symmetries. Typos are
correcte
Realistic Standard Model Fermion Mass Relations in Generalized Minimal Supergravity (GmSUGRA)
Grand Unified Theories (GUTs) usually predict wrong Standard Model (SM)
fermion mass relation m_e/m_{\mu} = m_d/m_s toward low energies. To solve this
problem, we consider the Generalized Minimal Supergravity (GmSUGRA) models,
which are GUTs with gravity mediated supersymmetry breaking and higher
dimensional operators. Introducing non-renormalizable terms in the super- and
K\"ahler potentials, we can obtain the correct SM fermion mass relations in the
SU(5) model with GUT Higgs fields in the {\bf 24} and {\bf 75} representations,
and in the SO(10) model. In the latter case the gauge symmetry is broken down
to SU(3)_C X SU(2)_L X SU(2)_R X U(1)_{B-L}, to flipped SU(5)X U(1)_X, or to
SU(3)_C X SU(2)_L X U(1)_1 X U(1)_2. Especially, for the first time we generate
the realistic SM fermion mass relation in GUTs by considering the
high-dimensional operators in the K\"ahler potential.Comment: JHEP style, 29 pages, no figure,references adde
S-duality and 2d Topological QFT
We study the superconformal index for the class of N=2 4d superconformal
field theories recently introduced by Gaiotto. These theories are defined by
compactifying the (2,0) 6d theory on a Riemann surface with punctures. We
interpret the index of the 4d theory associated to an n-punctured Riemann
surface as the n-point correlation function of a 2d topological QFT living on
the surface. Invariance of the index under generalized S-duality
transformations (the mapping class group of the Riemann surface) translates
into associativity of the operator algebra of the 2d TQFT. In the A_1 case, for
which the 4d SCFTs have a Lagrangian realization, the structure constants and
metric of the 2d TQFT can be calculated explicitly in terms of elliptic gamma
functions. Associativity then holds thanks to a remarkable symmetry of an
elliptic hypergeometric beta integral, proved very recently by van de Bult.Comment: 25 pages, 11 figure
Penner Type Matrix Model and Seiberg-Witten Theory
We discuss the Penner type matrix model recently proposed by Dijkgraaf and
Vafa for a possible explanation of the relation between four-dimensional gauge
theory and Liouville theory by making use of the connection of the matrix model
to two-dimensional CFT. We first consider the relation of gauge couplings
defined in UV and IR regimes of N_f = 4, N = 2 supersymmetric gauge theory
being related as . We then use this relation to discuss the action of modular
transformation on the matrix model and determine its spectral curve.
We also discuss the decoupling of massive flavors from the N_f = 4 matrix
model and derive matrix models describing asymptotically free N = 2 gauge
theories. We find that the Penner type matrix theory reproduces correctly the
standard results of N = 2 supersymmetric gauge theories.Comment: 22 pages; v2: references added, typos corrected; v3: a version to
appear in JHE
Genus-one correction to asymptotically free Seiberg-Witten prepotential from Dijkgraaf-Vafa matrix model
We find perfect agreements on the genus-one correction to the prepotential of
SU(2) Seiberg-Witten theory with N_f=2, 3 between field theoretical and
Dijkgraaf-Vafa-Penner type matrix model results.Comment: 12 pages; v2: minor revision; v3: more structured, submitted versio
Neutron Electric Dipole Moment Constraint on Scale of Minimal Left-Right Symmetric Model
Using an effective theory approach, we calculate the neutron electric dipole
moment (nEDM) in the minimal left-right symmetric model with both explicit and
spontaneous CP violations. We integrate out heavy particles to obtain
flavor-neutral CP-violating effective Lagrangian. We run the Wilson
coefficients from the electroweak scale to the hadronic scale using one-loop
renormalization group equations. Using the state-of-the-art hadronic matrix
elements, we obtain the nEDM as a function of right-handed W-boson mass and
CP-violating parameters. We use the current limit on nEDM combined with the
kaon-decay parameter to provide the most stringent constraint yet on
the left-right symmetric scale TeV.Comment: 20 pages and 8 figure
Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
In the case of SU(2), associated by the AGT relation to the 2d Liouville
theory, the Seiberg-Witten prepotential is constructed from the Bohr-Sommerfeld
periods of 1d sine-Gordon model. If the same construction is literally applied
to monodromies of exact wave functions, the prepotential turns into the
one-parametric Nekrasov prepotential F(a,\epsilon_1) with the other epsilon
parameter vanishing, \epsilon_2=0, and \epsilon_1 playing the role of the
Planck constant in the sine-Gordon Shroedinger equation, \hbar=\epsilon_1. This
seems to be in accordance with the recent claim in arXiv:0908.4052 and poses a
problem of describing the full Nekrasov function as a seemingly straightforward
double-parametric quantization of sine-Gordon model. This also provides a new
link between the Liouville and sine-Gordon theories.Comment: 10 page
Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
The AGT relation identifies the Nekrasov functions for various N=2 SUSY gauge
theories with the 2d conformal blocks, which possess explicit Dotsenko-Fateev
matrix model (beta-ensemble) representations the latter being polylinear
combinations of Selberg integrals. The "pure gauge" limit of these matrix
models is, however, a non-trivial multiscaling large-N limit, which requires a
separate investigation. We show that in this pure gauge limit the Selberg
integrals turn into averages in a Brezin-Gross-Witten (BGW) model. Thus, the
Nekrasov function for pure SU(2) theory acquires a form very much reminiscent
of the AMM decomposition formula for some model X into a pair of the BGW
models. At the same time, X, which still has to be found, is the pure gauge
limit of the elliptic Selberg integral. Presumably, it is again a BGW model,
only in the Dijkgraaf-Vafa double cut phase.Comment: 21 page
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
Classical conformal blocks from TBA for the elliptic Calogero-Moser system
The so-called Poghossian identities connecting the toric and spherical
blocks, the AGT relation on the torus and the Nekrasov-Shatashvili formula for
the elliptic Calogero-Moser Yang's (eCMY) functional are used to derive certain
expressions for the classical 4-point block on the sphere. The main motivation
for this line of research is the longstanding open problem of uniformization of
the 4-punctured Riemann sphere, where the 4-point classical block plays a
crucial role. It is found that the obtained representation for certain 4-point
classical blocks implies the relation between the accessory parameter of the
Fuchsian uniformization of the 4-punctured sphere and the eCMY functional.
Additionally, a relation between the 4-point classical block and the ,
twisted superpotential is found and further used to re-derive the
instanton sector of the Seiberg-Witten prepotential of the , supersymmetric gauge theory from the classical block.Comment: 25 pages, no figures, latex+JHEP3, published versio
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