3,303 research outputs found
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
Bootstrapping the superconformal index with surface defects
The analytic properties of the N = 2 superconformal index are given a
physical interpretation in terms of certain BPS surface defects, which arise as
the IR limit of supersymmetric vortices. The residue of the index at a pole in
flavor fugacity is interpreted as the index of a superconformal field theory
without this flavor symmetry, but endowed with an additional surface defect.
The residue can be efficiently extracted by acting on the index with a
difference operator of Ruijsenaars-Schneider type. By imposing the
associativity constraints of S-duality, we are then able to evaluate the index
of all generalized quiver theories of type A, for generic values of the three
superconformal fugacities, with or without surface defects.Comment: 60 pages, 7 figure
Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index
We provide the geometrical meaning of the superconformal index.
With this interpretation, the superconformal index can be realized
as the partition function on a Scherk-Schwarz deformed background. We apply the
localization method in TQFT to compute the deformed partition function since
the deformed action can be written as a -exact form. The
critical points of the deformed action turn out to be the space of flat
connections which are, in fact, zero modes of the gauge field. The one-loop
evaluation over the space of flat connections reduces to the matrix integral by
which the superconformal index is expressed.Comment: 42+1 pages, 2 figures, JHEP style: v1.2.3 minor corrections, v4 major
revision, conclusions essentially unchanged, v5 published versio
The Strange Quark Mass From Flavor Breaking in Hadronic Tau Decays
The strange quark mass is extracted from a finite energy sum rule (FESR)
analysis of the flavor-breaking difference of light-light and light-strange
quark vector-plus-axial-vector correlators, using spectral functions determined
from hadronic tau decay data. We point out problems for existing FESR
treatments associated with potentially slow convergence of the perturbative
series for the mass-dependent terms in the OPE over certain parts of the FESR
contour, and show how to construct alternate weight choices which not only cure
this problem, but also (1) considerably improve the convergence of the
integrated perturbative series, (2) strongly suppress contributions from the
region of s values where the errors on the strange current spectral function
are still large and (3) essentially completely remove uncertainties associated
with the subtraction of longitudinal contributions to the experimental decay
distributions. The result is an extraction of m_s with statistical errors
comparable to those associated with the current experimental uncertainties in
the determination of the CKM angle, V_{us}. We find m_s(1 GeV)=158.6\pm 18.7\pm
16.3\pm 13.3 MeV (where the first error is statistical, the second due to that
on V_{us}, and the third theoretical).Comment: 13 pages, 2 figures; final version to appear in Phys. Rev. D;
expanded versions of Figure 2 and Reference 3
Index computation for 3d Chern-Simons matter theory: test of Seiberg-like duality
We work out the superconformal index for N=2 supersymmetric Chern-Simons
matter theories exhibiting Seiberg-like dualities proposed by Giveon and
Kutasov. We consider gauge theories of QCD type and find the
perfect agreements for proposed dual pairs.Comment: References adde
The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields
We consider an "elastic" version of the statistical mechanical monomer-dimer
problem on the n-dimensional integer lattice. Our setting includes the
classical "rigid" formulation as a special case and extends it by allowing each
dimer to consist of particles at arbitrarily distant sites of the lattice, with
the energy of interaction between the particles in a dimer depending on their
relative position. We reduce the free energy of the elastic dimer-monomer (EDM)
system per lattice site in the thermodynamic limit to the moment Lyapunov
exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value
and covariance function are the Boltzmann factors associated with the monomer
energy and dimer potential. In particular, the classical monomer-dimer problem
becomes related to the MLE of a moving average GRF. We outline an approach to
recursive computation of the partition function for "Manhattan" EDM systems
where the dimer potential is a weighted l1-distance and the auxiliary GRF is a
Markov random field of Pickard type which behaves in space like autoregressive
processes do in time. For one-dimensional Manhattan EDM systems, we compute the
MLE of the resulting Gaussian Markov chain as the largest eigenvalue of a
compact transfer operator on a Hilbert space which is related to the
annihilation and creation operators of the quantum harmonic oscillator and also
recast it as the eigenvalue problem for a pantograph functional-differential
equation.Comment: 24 pages, 4 figures, submitted on 14 October 2011 to a special issue
of DCDS-
Parity Violating Bosonic Loops at Finite Temperature
The finite temperature parity-violating contributions to the polarization
tensor are computed at one loop in a system without fermions. The system
studied is a Maxwell-Chern-Simons-Higgs system in the broken phase, for which
the parity-violating terms are well known at zero temperature. At nonzero
temperature the static and long-wavelength limits of the parity violating terms
have very different structure, and involve non-analytic log terms depending on
the various mass scales. At high temperature the boson loop contribution to the
Chern-Simons term goes like T in the static limit and like T log T in the
long-wavelength limit, in contrast to the fermion loop contribution which
behaves like 1/T in the static limit and like log T/T in the long wavelength
limit.Comment: 10 pp, 1 fig, revte
Constraints on chiral operators in N=2 SCFTs
Open Access, © The Authors. Article funded by SCOAP3.
This article is distributed under the terms of the Creative Commons
Attribution License (
CC-BY 4.0
), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited
The Chern-Simons Coefficient in Supersymmetric Non-abelian Chern-Simons Higgs Theories
By taking into account the effect of the would be Chern-Simons term, we
calculate the quantum correction to the Chern-Simons coefficient in
supersymmetric Chern-Simons Higgs theories with matter fields in the
fundamental representation of SU(n). Because of supersymmetry, the corrections
in the symmetric and Higgs phases are identical. In particular, the correction
is vanishing for N=3 supersymmetric Chern-Simons Higgs theories. The result
should be quite general, and have important implication for the more
interesting case when the Higgs is in the adjoint representation.Comment: more references and explanation about rgularization dpendence are
included, 13 pages, 1 figure, latex with revte
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