382 research outputs found
The absolute position of a resonance peak
It is common practice in scattering theory to correlate between the position
of a resonance peak in the cross section and the real part of a complex energy
of a pole of the scattering amplitude. In this work we show that the resonance
peak position appears at the absolute value of the pole's complex energy rather
than its real part. We further demonstrate that a local theory of resonances
can still be used even in cases previously thought impossible
Response to arXiv:0811.3876 "Comment on a recent conjectured solution of the three dimensional Ising model" by Wu et al
This is a Response to a recent Comment [F.Y. Wu et al., Phil. Mag. 88, 3093
(2008), arXiv:0811.3876] on the conjectured solution of the three-dimensional
(3D) Ising model [Z.D. Zhang, Phil. Mag. 87, 5309 (2007), arXiv:0705.1045].
Several points are made: 1) Conjecture 1, regarding the additional rotation, is
understood as performing a transformation for smoothing all the crossings of
the knots; 2) The weight factors in Conjecture 2 are interpreted as a novel
topologic phase; 3) The conjectured solution and its low- and high-temperature
expansions are supported by the mathematical theorems for the analytical
behavior of the Ising model. The physics behind the extra dimension is also
discussed briefly.Comment: 11 pages, 0 figure
Series Solution and Minimal Surfaces in AdS
According to the Alday-Maldacena program the strong coupling limit of Super
Yang-Mills scattering amplitudes is given by minimal area surfaces in AdS
spacetime with a boundary consisting of a momentum space polygon. The string
equations in AdS systematically reduce to coupled Toda type equations whose
Euclidean classical solutions are then of direct relevance. While in the
simplest case of AdS_3 exact solutions were known from earlier studies of the
sinh-Gordon equation, there exist at present no similar exact forms for the
generalized Toda equations related to AdS_d with d>=4. In this paper we develop
a series method for the solution to those equations and evaluate their
contribution to the finite piece of the worldsheet area. For the known
sinh-Gordon case the method is seen to give results in excellent agreement with
the exact answer.Comment: 19 pages, no figures; references added, one note adde
T-Branes and Monodromy
We introduce T-branes, or "triangular branes," which are novel non-abelian
bound states of branes characterized by the condition that on some loci, their
matrix of normal deformations, or Higgs field, is upper triangular. These
configurations refine the notion of monodromic branes which have recently
played a key role in F-theory phenomenology. We show how localized matter
living on complex codimension one subspaces emerge, and explain how to compute
their Yukawa couplings, which are localized in complex codimension two. Not
only do T-branes clarify what is meant by brane monodromy, they also open up a
vast array of new possibilities both for phenomenological constructions and for
purely theoretical applications. We show that for a general T-brane, the
eigenvalues of the Higgs field can fail to capture the spectrum of localized
modes. In particular, this provides a method for evading some constraints on
F-theory GUTs which have assumed that the spectral equation for the Higgs field
completely determines a local model.Comment: 110 pages, 5 figure
Form factors at strong coupling via a Y-system
We compute form factors in planar N=4 Super Yang-Mills at strong coupling.
Namely we consider the overlap between an operator insertion and 2n gluons.
Through the gauge/string duality these are given by minimal surfaces in AdS
space. The surfaces end on an infinite periodic sequence of null segments at
the boundary of AdS. We consider surfaces that can be embedded in AdS_3. We
derive set of functional equations for the cross ratios as functions of the
spectral parameter. These equations are of the form of a Y-system. The integral
form of the Y-system has Thermodynamics Bethe Ansatz form. The area is given by
the free energy of the TBA system or critical value of Yang-Yang functional. We
consider a restricted set of operators which have small conformal dimension
Tailoring Three-Point Functions and Integrability III. Classical Tunneling
We compute three-point functions between one large classical operator and two
large BPS operators at weak coupling. We consider operators made out of the
scalars of N=4 SYM, dual to strings moving in the sphere. The three-point
function exponentiates and can be thought of as a classical tunneling process
in which the classical string-like operator decays into two classical BPS
states. From an Integrability/Condensed Matter point of view, we simplified
inner products of spin chain Bethe states in a classical limit corresponding to
long wavelength excitations above the ferromagnetic vacuum. As a by-product we
solved a new long-range Ising model in the thermodynamic limit.Comment: 37 pages, 10 figure
Quantum Sine(h)-Gordon Model and Classical Integrable Equations
We study a family of classical solutions of modified sinh-Gordon equation,
$\partial_z\partial_{{\bar z}} \eta-\re^{2\eta}+p(z)\,p({\bar z})\
\re^{-2\eta}=0p(z)=z^{2\alpha}-s^{2\alpha}Q(\alpha>0)(\alpha<-1)$ models.Comment: 35 pages, 3 figure
Dynamics and transport near quantum-critical points
The physics of non-zero temperature dynamics and transport near
quantum-critical points is discussed by a detailed study of the O(N)-symmetric,
relativistic, quantum field theory of a N-component scalar field in spatial
dimensions. A great deal of insight is gained from a simple, exact solution of
the long-time dynamics for the N=1 d=1 case: this model describes the critical
point of the Ising chain in a transverse field, and the dynamics in all the
distinct, limiting, physical regions of its finite temperature phase diagram is
obtained. The N=3, d=1 model describes insulating, gapped, spin chain
compounds: the exact, low temperature value of the spin diffusivity is
computed, and compared with NMR experiments. The N=3, d=2,3 models describe
Heisenberg antiferromagnets with collinear N\'{e}el correlations, and
experimental realizations of quantum-critical behavior in these systems are
discussed. Finally, the N=2, d=2 model describes the superfluid-insulator
transition in lattice boson systems: the frequency and temperature dependence
of the the conductivity at the quantum-critical coupling is described and
implications for experiments in two-dimensional thin films and inversion layers
are noted.Comment: Lectures presented at the NATO Advanced Study Institute on "Dynamical
properties of unconventional magnetic systems", Geilo, Norway, April 2-12,
1997, edited by A. Skjeltorp and D. Sherrington, Kluwer Academic, to be
published. 46 page
Correlation function of null polygonal Wilson loops with local operators
We consider the correlator of a light-like polygonal Wilson loop
with n cusps with a local operator (like the dilaton or the chiral primary
scalar) in planar N =4 super Yang-Mills theory. As a consequence of conformal
symmetry, the main part of such correlator is a function F of 3n-11 conformal
ratios. The first non-trivial case is n=4 when F depends on just one conformal
ratio \zeta. This makes the corresponding correlator one of the simplest
non-trivial observables that one would like to compute for generic values of
the `t Hooft coupling \lambda. We compute F(\zeta,\lambda) at leading order in
both the strong coupling regime (using semiclassical AdS5 x S5 string theory)
and the weak coupling regime (using perturbative gauge theory). Some results
are also obtained for polygonal Wilson loops with more than four edges.
Furthermore, we also discuss a connection to the relation between a correlator
of local operators at null-separated positions and cusped Wilson loop suggested
in arXiv:1007.3243.Comment: 36 pages, 2 figure
Yukawa hierarchies at the point of in F-theory
We analyse the structure of Yukawa couplings in local SU(5) F-theory models
with enhancement. In this setting the symmetry is broken down to
SU(5) by a 7-brane configuration described by T-branes, all the Yukawa
couplings are generated in the vicinity of a point and only one family of
quarks and leptons is massive at tree-level. The other two families obtain
their masses when non-perturbative effects are taken into account, being
hierarchically lighter than the third family. However, and contrary to previous
results, we find that this hierarchy of fermion masses is not always
appropriate to reproduce measured data. We find instead that different T-brane
configurations breaking to SU(5) give rise to distinct hierarchical
patterns for the holomorphic Yukawa couplings. Only some of these patterns
allow to fit the observed fermion masses with reasonable local model parameter
values, adding further constraints to the construction of F-theory GUTs. We
consider an model where such appropriate hierarchy is realised and
compute its physical Yukawas, showing that realistic charged fermions masses
can indeed be obtained in this case.Comment: 46 pages + appendices, 5 figures. v2, added references and typos
corrected, version accepted on JHEP. v3, typos correcte
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