9,038 research outputs found
U(infinity) Gauge Theory from Higher Dimensions
We show that classical U(infinity) gauge theories can be obtained from the
dimensional reduction of a certain class of higher-derivative theories. In
general, the exact symmetry is attained in the limit of degenerate metric;
otherwise, the infinite-dimensional symmetry can be taken as spontaneously
broken. Monopole solutions are examined in the model for scalar and gauge
fields. An extension to gravity is also discussed.Comment: 13 pages, no figur
Attainability of Carnot Efficiency with Autonomous Engines
The maximum efficiency of autonomous engines with finite chemical potential
difference is investigated. We show that without a particular type of
singularity autonomous engines cannot attain the Carnot efficiency. In
addition, we demonstrate that a special autonomous engine with the singularity
attains the Carnot efficiency even if it is macroscopic. Our results clearly
illustrate that the singularity plays a crucial role for the maximum efficiency
of autonomous engines.Comment: 11 pages, 8 figure
Hausdorff dimension of the scaling limit of loop-erased random walk in three dimensions
Let be the length (number of steps) of the loop-erasure of a simple
random walk up to the first exit from a ball of radius centered at its
starting point. It is shown in [18] that there exists such that is of order in 3 dimensions.
In the present article, we show that the Hausdorff dimension of the scaling
limit of the loop-erased random walk in 3 dimensions is equal to almost
surely.Comment: 39 pages, 1 figur
Anomalous System Size Dependence of Large Deviation Functions for Local Empirical Measure
We study the large deviation function for the empirical measure of diffusing
particles at one fixed position. We find that the large deviation function
exhibits anomalous system size dependence in systems that satisfy the following
conditions: (i) there exists no macroscopic flow, and (ii) their space
dimension is one or two. We investigate this anomaly by using a contraction
principle. We also analyze the relation between this anomaly and the so-called
long-time tail behavior on the basis of phenomenological arguments.Comment: 14 page
Two-sided random walks conditioned to have no intersections
Let be independent simple random walks in
() started at the origin. We construct two-sided random walk paths
conditioned that .Comment: 25 page
Wilson Loops in Open String Theory
Wilson loop elements on torus are introduced into the partition function of
open strings as Polyakov's path integral at one-loop level. Mass spectra from
compactification and expected symmetry breaking are illustrated by choosing the
correct weight for the contributions from annulus and M\"obius strip. We show
that Jacobi's imaginary transformation connects the mass spectra with the
Wilson loops. The application to thermopartition function and cosmological
implications are briefly discussed.Comment: 5 pages, no figur
Growth exponent for loop-erased random walk in three dimensions
We show the existence of the growth exponent for loop-erased random walk in
three dimensions.Comment: 59 pages, 3 figure
Degenerate Fermions and Wilson Loop in Dimensions
We investigate the effect of finite fermion density on symmetry breaking by
Wilson loops in dimensions. We find the breaking and restoration of
symmetry at finite density in the models with and gauge
symmetries, in the presence of the adjoint fermions. The transition can occur
at a finite density of fermions, regardless of the periodic or antiperiodic
boundary condition of the fermion field; this is in contrast to the
finite-temperature ease examined by Ho and Hosotani (Nucl. Phys. B345 (1990)
445) where the boundary condition of fractional twist is essential to the
occurrence of the phase transition.Comment: 8 pages, 4 figure
Finite-time thermodynamic uncertainty relation do not hold for discrete-time Markov process
Discrete-time counterpart of thermodynamic uncertainty relation (conjectured
in P. Pietzonka, et.al., arXiv:1702.07699 (2017)) with finite time interval is
considered. We show that this relation do not hold by constructing a concrete
counterexample to this. Our finding suggests that the proof of thermodynamic
uncertainty relation with finite time interval, if true, should strongly rely
on the fact that the time is continuous.Comment: 3 page
Hosotani model in closed-string theory
The Hosotani mechanism in the closed-string theory with current algebra
symmetry is described by the (old covariant) operator method. We compare the
gauge symmetry breaking mechanism in a string theory which contains SU(2)
symmetry originated from current algebra with the one in an equivalent
compactified closed-string theory. We also investigate the difference between
the Hosotani mechanism and the Higgs mechanism in closed-string theories by
calculation of a four-point amplitude of `Higgs' bosons at tree level.Comment: 16 pages, no figur
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