38 research outputs found
Morse Theory in Field Theory
We describe correlations functions of topological quantum mechanics (TQM) in
terms of Morse theory. We review the basics of topological field theories and
discuss geometric and algebraic interpretations of TQM. We prove that
correlators in TQM can be expressed via intersection numbers of certain
submanifolds of the target space with paths of steepest descent between
critical points of a Morse function. In the end we conjecture another
correspondence between quantum mechanics correlators and integrals of Massey
products of certain cohomology classes.Comment: updated versio
The Confinement Property in SU(3) Gauge Theory
We study confinement property of pure SU(3) gauge theory, combining in this
effort the non-perturbative gluon and ghost propagators obtained as solutions
of Dyson--Schwinger equations with solutions of an integral ladder diagram
summation type equation for the Wilson loop. We obtain the string potential and
effective UV coupling.Comment: 7 pages, 7 figures, v2: references added, discussion reorganize
Anomalous Zero Sound
We show that the anomalous term in the current, recently suggested by Son and
Yamamoto, modifies the structure of the zero sound mode in the Fermi liquid in
a magnetic field.Comment: 14 pages, 2 figure
Analytic Perturbation Theory for Practitioners and Upsilon Decay
Within the ghost-free Analytic Perturbation Theory (APT), devised in the last
decade for low energy QCD, simple approximations are proposed for 3-loop
analytic couplings and their effective powers, in both the space-like
(Euclidean) and time-like (Minkowskian) regions, accurate enough in the large
range (1--100 GeV) of current physical interest.\par Effectiveness of the new
Model is illustrated by the example of decay where the
standard analysis gives value that is
inconsistent with the bulk of data for .
Instead, we obtain that
corresponds to that is close to the world
average.\par The issue of scale uncertainty for decay is also
discussed.Comment: 12 pages, 0 figures. Model slightly modified to increase its
accuracy. Numerical results upgraded, references added. The issue of scale
uncertainty is discusse
Semiclassical Treatment of Induced Schwinger Processes at Finite Temperature
We consider induced pair production in an external field at finite
temperature. One-loop correction to the Green function of a meson is calculated
semiclassically within the framework of saddle-point analysis of Schwinger
proper time integrals. This correction appears to be exponentially small in
terms of inverse temperature dependence. Low-temperature limit is shown to be
in full agreement with previously obtained zero-temperature results. The
corrections in the low-temperature limits are estimated up to the leading
exponential and pre-exponential terms. Comparison is made to earlier
calculations of vacuum decay.Comment: 10 pages, 1 fugur
Lattice QCD Simulations in External Background Fields
We discuss recent results and future prospects regarding the investigation,
by lattice simulations, of the non-perturbative properties of QCD and of its
phase diagram in presence of magnetic or chromomagnetic background fields.
After a brief introduction to the formulation of lattice QCD in presence of
external fields, we focus on studies regarding the effects of external fields
on chiral symmetry breaking, on its restoration at finite temperature and on
deconfinement. We conclude with a few comments regarding the effects of
electromagnetic background fields on gluodynamics.Comment: 31 pages, 10 figures, minor changes and references added. To appear
in Lect. Notes Phys. "Strongly interacting matter in magnetic fields"
(Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye
Matching three-point functions of BMN operators at weak and strong coupling
The agreement between string theory and field theory is demonstrated in the
leading order by providing the first calculation of the correlator of three
two-impurity BMN states with all non-zero momenta. The calculation is performed
in two completely independent ways: in field theory by using the large-
perturbative expansion, up to the terms subleading in finite-size, and in
string theory by using the Dobashi-Yoneya 3-string vertex in the leading order
of the Penrose expansion. The two results come out to be completely identical.Comment: 14 pages, 1 figur
Holographic rho mesons in an external magnetic field
We study the rho meson in a uniform magnetic field eB using a holographic
QCD-model, more specifically a D4/D8/Dbar8 brane setup in the confinement phase
at zero temperature with two quenched flavours. The parameters of the model are
fixed by matching to corresponding dual field theory parameters at zero
magnetic field. We show that the up- and down-flavour branes respond
differently to the presence of the magnetic field in the dual QCD-like theory,
as expected because of the different electromagnetic charge carried by up- and
down-quark. We discuss how to recover the Landau levels, indicating an
instability of the QCD vacuum at eB = m_rho^2 towards a phase where charged rho
mesons are condensed, as predicted by Chernodub using effective QCD-models. We
improve on these existing effective QCD-model analyses by also taking into
account the chiral magnetic catalysis effect, which tells us that the
constituent quark masses rise with eB. This turns out to increase the value of
the critical magnetic field for the onset of rho meson condensation to eB = 1.1
m_rho^2 = 0.67 GeV^2. We briefly discuss the influence of pions, which turn out
to be irrelevant for the condensation in the approximation made.Comment: 26 pages, 10 .pdf figures, v2: version accepted for publication in
JHE
Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz
We compute the first curvature corrections to the spectrum of light-cone
gauge type IIA string theory that arise in the expansion of about a plane-wave limit. The resulting spectrum is shown to
match precisely, both in magnitude and degeneration that of the corresponding
solutions of the all-loop Gromov--Vieira Bethe Ansatz. The one-loop dispersion
relation correction is calculated for all the single oscillator states of the
theory, with the level matching condition lifted. It is shown to have all
logarithmic divergences cancelled and to leave only a finite exponentially
suppressed contribution, as shown earlier for light bosons. We argue that there
is no ambiguity in the choice of the regularization for the self-energy sum,
since the regularization applied is the only one preserving unitarity.
Interaction matrices in the full degenerate two-oscillator sector are
calculated and the spectrum of all two light magnon oscillators is completely
determined. The same finite-size corrections, at the order 1/J, where is
the length of the chain, in the two-magnon sector are calculated from the all
loop Bethe Ansatz. The corrections obtained by the two completely different
methods coincide up to the fourth order in . We
conjecture that the equivalence extends to all orders in and to
higher orders in 1/J.Comment: 32 pages. Published version; journal reference adde
Magnetic Catalysis: A Review
We give an overview of the magnetic catalysis phenomenon. In the framework of
quantum field theory, magnetic catalysis is broadly defined as an enhancement
of dynamical symmetry breaking by an external magnetic field. We start from a
brief discussion of spontaneous symmetry breaking and the role of a magnetic
field in its a dynamics. This is followed by a detailed presentation of the
essential features of the phenomenon. In particular, we emphasize that the
dimensional reduction plays a profound role in the pairing dynamics in a
magnetic field. Using the general nature of underlying physics and its
robustness with respect to interaction types and model content, we argue that
magnetic catalysis is a universal and model-independent phenomenon. In support
of this claim, we show how magnetic catalysis is realized in various models
with short-range and long-range interactions. We argue that the general nature
of the phenomenon implies a wide range of potential applications: from certain
types of solid state systems to models in cosmology, particle and nuclear
physics. We finish the review with general remarks about magnetic catalysis and
an outlook for future research.Comment: 37 pages, to appear in Lect. Notes Phys. "Strongly interacting matter
in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A.
Schmitt, H.-U. Yee. Version 2: references adde