1,007 research outputs found
Aspects of Large N Gauge Theory Dynamics as Seen by String Theory
In this paper we explore some of the features of large N supersymmetric and
nonsupersymmetric gauge theories using Maldacena's duality conjectures. We
shall show that the resulting strong coupling behavior of the gauge theories is
consistent with our qualitative expectations of these theories. Some of these
consistency checks are highly nontrivial and give additional evidence for the
validity of the proposed dualities.Comment: 31 pages, LaTeX, 11 eps figures, typos correcte
Extended gaussian ensemble solution and tricritical points of a system with long-range interactions
The gaussian ensemble and its extended version theoretically play the
important role of interpolating ensembles between the microcanonical and the
canonical ensembles. Here, the thermodynamic properties yielded by the extended
gaussian ensemble (EGE) for the Blume-Capel (BC) model with infinite-range
interactions are analyzed. This model presents different predictions for the
first-order phase transition line according to the microcanonical and canonical
ensembles. From the EGE approach, we explicitly work out the analytical
microcanonical solution. Moreover, the general EGE solution allows one to
illustrate in details how the stable microcanonical states are continuously
recovered as the gaussian parameter is increased. We found out that it
is not necessary to take the theoretically expected limit
to recover the microcanonical states in the region between the canonical and
microcanonical tricritical points of the phase diagram. By analyzing the
entropy as a function of the magnetization we realize the existence of
unaccessible magnetic states as the energy is lowered, leading to a treaking of
ergodicity.Comment: 8 pages, 5 eps figures. Title modified, sections rewritten,
tricritical point calculations added. To appear in EPJ
Decay Modes of Unstable Strings in Plane-Wave String Field Theory
The cubic interaction vertex of light-cone string field theory in the
plane-wave background has a simple effective form when considering states with
only bosonic excitations. This simple effective interaction vertex is used in
this paper to calculate the three string interaction matrix elements for states
of arbitrary bosonic excitation and these results are used to examine certain
decay modes on the mass-shell. It is shown that the matrix elements of one
string to two string decays involving only bosonic excitations will vanish to
all orders in 1/mu on the mass-shell when the number of excitations on the
initial string is less than or equal to two, but in general will not vanish
when the number of excitations is greater than two. Also, a truncated
calculation of the mass-shell matrix elements for one string to three string
decays of two excitation states is performed and suggests that these matrix
elements do not vanish on the mass-shell. There is, however, a quantitative
discrepancy between this last result and its (also non-vanishing) gauge theory
prediction from the BMN correspondence.Comment: 11 pages; v2: references added; v3: normalization of interaction
vertex and corresponding amplitudes changed by a factor of mu to reflect SFT
normalization (must now divide by mu to compare with BMN dual gauge theory),
and minor errors correcte
Thermodynamic gauge-theory cascade
It is proposed that the cooling of a thermalized SU() gauge theory can be
formulated in terms of a cascade involving three effective theories with
successively reduced (and spontaneously broken) gauge symmetries, SU()
U(1) Z. The approach is based on the assumption that away
from a phase transition the bulk of the quantum interaction inherent to the
system is implicitly encoded in the (incomplete) classical dynamics of a
collective part made of low-energy condensed degrees of freedom. The properties
of (some of the) statistically fluctuating fields are determined by these
condensate(s). This leads to a quasi-particle description at tree-level. It
appears that radiative corrections, which are sizable at large gauge coupling,
do not change the tree-level picture qualitatively. The thermodynamic
self-consistency of the quasi-particle approach implies nonperturbative
evolution equations for the associated masses. The temperature dependence of
these masses, in turn, determine the evolution of the gauge coupling(s). The
hot gauge system approaches the behavior of an ideal gas of massless gluons at
asymptotically large temperature. A negative equation of state is possible at a
stage where the system is about to settle into the phase of the (spontaneously
broken) Z symmetry.Comment: 25 pages, 6 figures, 1 reference added, minor corrections in text,
errors in Sec. 3.2 corrected, PRD versio
Adler Function, DIS sum rules and Crewther Relations
The current status of the Adler function and two closely related Deep
Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for
polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A
new result is presented: an analytical calculation of the coefficient function
of the latter sum rule in a generic gauge theory in order O(alpha_s^4). It is
demonstrated that the corresponding Crewther relation allows to fix two of
three colour structures in the O(alpha_s^4) contribution to the singlet part of
the Adler function.Comment: Talk presented at 10-th DESY Workshop on Elementary Particle Theory:
Loops and Legs in Quantum Field Theory, W\"orlitz, Germany, 25-30 April 201
Cyclotomic integers, fusion categories, and subfactors
Dimensions of objects in fusion categories are cyclotomic integers, hence
number theoretic results have implications in the study of fusion categories
and finite depth subfactors. We give two such applications. The first
application is determining a complete list of numbers in the interval (2,
76/33) which can occur as the Frobenius-Perron dimension of an object in a
fusion category. The smallest number on this list is realized in a new fusion
category which is constructed in the appendix written by V. Ostrik, while the
others are all realized by known examples. The second application proves that
in any family of graphs obtained by adding a 2-valent tree to a fixed graph,
either only finitely many graphs are principal graphs of subfactors or the
family consists of the A_n or D_n Dynkin diagrams. This result is effective,
and we apply it to several families arising in the classification of subfactors
of index less then 5.Comment: 47 pages, with an appendix by Victor Ostri
Strong Evidence In Favor OF The Existence Of S-Matrix For Strings In Plane Waves
Field theories on the plane wave background are considered. We discuss that
for such field theories one can only form 1+1 dimensional freely propagating
wave packets. We analyze tree level four point functions of scalar field theory
as well as scalars coupled to gauge fields in detail and show that these four
point functions are well-behaved so that they can be interpreted as S-matrix
elements for 2 particle 2 particle scattering amplitudes. Therefore, at
least classically, field theories on the plane wave background have S-matrix
formulation.Comment: Latex file, 26 pages, 4 eps figures. v3: In the end of paper there is
a "Note Added" as an update of the result
The M Theory Five-Brane and the Heterotic String
Brane actions with chiral bosons present special challenges. Recent progress
in the description of the two main examples -- the M theory five-brane and the
heterotic string -- is described. Also, double dimensional reduction of the M
theory five-brane on K3 is shown to give the heterotic string.Comment: 13 pages, latex, no figures; ICTP Conference Proceeding
Shimura curve computations via K3 surfaces of Neron-Severi rank at least 19
It is known that K3 surfaces S whose Picard number rho (= rank of the
Neron-Severi group of S) is at least 19 are parametrized by modular curves X,
and these modular curves X include various Shimura modular curves associated
with congruence subgroups of quaternion algebras over Q. In a family of such K3
surfaces, a surface has rho=20 if and only if it corresponds to a CM point on
X. We use this to compute equations for Shimura curves, natural maps between
them, and CM coordinates well beyond what could be done by working with the
curves directly as we did in ``Shimura Curve Computations'' (1998) =
Comment: 16 pages (1 figure drawn with the LaTeX picture environment); To
appear in the proceedings of ANTS-VIII, Banff, May 200
Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case
The analytic result for the singlet part of the Adler function of the vector
current in a general gauge theory is presented in five-loop approximation.
Comparing this result with the corresponding singlet part of the
Gross-Llewellyn Smith sum rule [1], we successfully demonstrate the validity of
the generalized Crewther relation for the singlet part. This provides a
non-trivial test of both our calculations and the generalized Crewther
relation. Combining the result with the already available non-singlet part of
the Adler function [2,3] we arrive at the complete
expression for the Adler function and, as a direct consequence, at the complete
correction to the annihilation into hadrons in
a general gauge theory.Comment: 4 pages, 1 figure. Final published versio
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