665 research outputs found
Chiral perturbation theory in a theta vacuum
We consider chiral perturbation theory (ChPT) with a non-zero theta term. Due
to the CP violating term, the vacuum of chiral fields is shifted to a
non-trivial element on the SU(N_f) group manifold. The CP violation also
provides mixing of different CP eigenstates, between scalar and pseudoscalar,
or vector and axialvector operators. We investigate upto O(theta^2) effects on
the mesonic two point correlators of ChPT to the one-loop order. We also
address the effects of fixing topology, by using saddle point integration in
the Fourier transform with respect to theta.Comment: 31 pages, references added, minor corrections, version published in
PR
The GL_2 main conjecture for elliptic curves without complex multiplication
The main conjectures of Iwasawa theory provide the only general method known
at present for studying the mysterious relationship between purely arithmetic
problems and the special values of complex L-functions, typified by the
conjecture of Birch and Swinnerton-Dyer and its generalizations. Our goal in
the present paper is to develop algebraic techniques which enable us to
formulate a precise version of such a main conjecture for motives over a large
class of p-adic Lie extensions of number fields. The paper ends by formulating
and briefly discussing the main conjecture for an elliptic curve E over the
rationals Q over the field generated by the coordinates of its p-power division
points, where p is a prime greater than 3 of good ordinary reduction for E.Comment: 39 page
Topology conserving gauge action and the overlap-Dirac operator
We apply the topology conserving gauge action proposed by Luescher to the
four-dimensional lattice QCD simulation in the quenched approximation. With
this gauge action the topological charge is stabilized along the hybrid Monte
Carlo updates compared to the standard Wilson gauge action. The quark potential
and renormalized coupling constant are in good agreement with the results
obtained with the Wilson gauge action. We also investigate the low-lying
eigenvalue distribution of the hermitian Wilson-Dirac operator, which is
relevant for the construction of the overlap-Dirac operator.Comment: 27pages, 11figures, accepted versio
Exact Lagrangian submanifolds in simply-connected cotangent bundles
We consider exact Lagrangian submanifolds in cotangent bundles. Under certain
additional restrictions (triviality of the fundamental group of the cotangent
bundle, and of the Maslov class and second Stiefel-Whitney class of the
Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically
indistinguishable from the zero-section. This implies strong restrictions on
their topology. An essentially equivalent result was recently proved
independently by Nadler, using a different approach.Comment: 28 pages, 3 figures. Version 2 -- derivation and discussion of the
spectral sequence considerably expanded. Other minor change
Twisted SUSY Invariant Formulation of Chern-Simons Gauge Theory on a Lattice
We propose a twisted SUSY invariant formulation of Chern-Simons theory on a
Euclidean three dimensional lattice. The SUSY algebra to be realized on the
lattice is the N=4 D=3 twisted algebra that was recently proposed by D'Adda et
al.. In order to keep the manifest anti-hermiticity of the action, we introduce
oppositely oriented supercharges. Accordingly, the naive continuum limit of the
action formally corresponds to the Landau gauge fixed version of Chern-Simons
theory with complex gauge group which was originally proposed by Witten. We
also show that the resulting action consists of parity even and odd parts with
different coefficients.Comment: 22 pages, 5 figures; v2,v3 added references, v4 added two paragraphs
and one figure in the summar
Exploring Topology Conserving Gauge Actions for Lattice QCD
We explore gauge actions for lattice QCD, which are constructed such that the
occurrence of small plaquette values is strongly suppressed. By choosing strong
bare gauge couplings we arrive at values for the physical lattice spacings of
O(0.1 fm). Such gauge actions tend to confine the Monte Carlo history to a
single topological sector. This topological stability facilitates the
collection of a large set of configurations in a specific sector, which is
profitable for numerical studies in the epsilon-regime. The suppression of
small plaquette values is also expected to be favourable for simulations with
dynamical quarks. We use a local Hybrid Monte Carlo algorithm to simulate such
actions, and we present numerical results for the static potential, the
physical scale, the topological stability and the kernel condition number of
the overlap Dirac operator. In addition we discuss the question of reflection
positivity for a class of such gauge actions.Comment: 28 pages, 8 figure
Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds
We investigate the relationship between the Lagrangian Floer superpotentials
for a toric orbifold and its toric crepant resolutions. More specifically, we
study an open string version of the crepant resolution conjecture (CRC) which
states that the Lagrangian Floer superpotential of a Gorenstein toric orbifold
and that of its toric crepant resolution coincide after
analytic continuation of quantum parameters and a change of variables. Relating
this conjecture with the closed CRC, we find that the change of variable
formula which appears in closed CRC can be explained by relations between open
(orbifold) Gromov-Witten invariants. We also discover a geometric explanation
(in terms of virtual counting of stable orbi-discs) for the specialization of
quantum parameters to roots of unity which appears in Y. Ruan's original CRC
["The cohomology ring of crepant resolutions of orbifolds", Gromov-Witten
theory of spin curves and orbifolds, 117-126, Contemp. Math., 403, Amer. Math.
Soc., Providence, RI, 2006]. We prove the open CRC for the weighted projective
spaces using an equality between open
and closed orbifold Gromov-Witten invariants. Along the way, we also prove an
open mirror theorem for these toric orbifolds.Comment: 48 pages, 1 figure; v2: references added and updated, final version,
to appear in CM
SYZ mirror symmetry for hypertoric varieties
We construct a Lagrangian torus fibration on a smooth hypertoric variety and
a corresponding SYZ mirror variety using -duality and generating functions
of open Gromov-Witten invariants. The variety is singular in general. We
construct a resolution using the wall and chamber structure of the SYZ base.Comment: v_2: 31 pages, 5 figures, minor revision. To appear in Communications
in Mathematical Physic
semileptonic form factors from lattice QCD with M\"obius domain-wall quarks
We calculate the form factors for the decay in 2+1
flavor lattice QCD. For all quark flavors, we employ the M\"obius domain-wall
action, which preserves chiral symmetry to a good precision. Our gauge
ensembles are generated at three lattice cutoffs , 3.6 and 4.5
GeV with pion masses as low as MeV. The physical lattice size
satisfies the condition to control finite volume effects
(FVEs), while we simulate a smaller size at the smallest to directly
examine FVEs. The bottom quark masses are chosen in a range from the physical
charm quark mass to to control discretization effects. We
extrapolate the form factors to the continuum limit and physical quark masses
based on heavy meson chiral perturbation theory at next-to-leading order. Then
the recoil parameter dependence is parametrized using a model independent form
leading to our estimate of the decay rate ratio between the tau ()
and light lepton () channels in the Standard
Model. A simultaneous fit with recent data from the Belle experiment yields
, which is consistent with previous
exclusive determinations, and shows good consistency in the kinematical
distribution of the differential decay rate between the lattice and
experimental data.Comment: 37 pages, 13 figure
Yukawa couplings in intersecting D-brane models
We compute the Yukawa couplings among chiral fields in toroidal Type II
compactifications with wrapping D6-branes intersecting at angles. Those models
can yield realistic standard model spectrum living at the intersections. The
Yukawa couplings depend both on the Kahler and open string moduli but not on
the complex structure. They arise from worldsheet instanton corrections and are
found to be given by products of complex Jacobi theta functions with
characteristics. The Yukawa couplings for a particular intersecting brane
configuration yielding the chiral spectrum of the MSSM are computed as an
example. We also show how our methods can be extended to compute Yukawa
couplings on certain classes of elliptically fibered CY manifolds which are
mirror to complex cones over del Pezzo surfaces. We find that the Yukawa
couplings in intersecting D6-brane models have a mathematical interpretation in
the context of homological mirror symmetry. In particular, the computation of
such Yukawa couplings is related to the construction of Fukaya's category in a
generic symplectic manifold.Comment: 47 pages, using JHEP3.cls, 11 figures. Typos and other minor
corrections. References adde
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