905 research outputs found

### Gauge-potential approach to the kinematics of a moving car

A kinematics of the motion of a car is reformulated in terms of the theory of
gauge potentials (connection on principal bundle). E(2)-connection originates
in the no-slipping contact of the car with a road.Comment: 13 pages, AmsTe

### A counterexample to the a-'theorem'

The conclusion of the original paper was wrong, due to the incorrect
assumption that the low-energy limit at the strongly-coupled point consists of
a single, coupled SCFT. By taking into account the fact that the low-energy
limit consists of multiple decoupled parts, it was later shown in
arXiv:1011.4568 that there is no violation of the a-theorem in this system.
Furthermore, the a-theorem itself was convincingly demonstrated in
arXiv:1107.3987, and the argument presented there has been further refined. The
rest of this paper is kept as it was, for some parts of the discussions might
still be of interest.
Original abstract: We exhibit a renormalization group flow for a
four-dimensional gauge theory along which the conformal central charge 'a'
increases. The flow connects the maximally superconformal point of an N=2 gauge
theory with gauge group SU(N+1) and N_f=2N flavors in the ultraviolet, to a
strongly-coupled superconformal point of the SU(N) gauge theory with N_f=2N
massless flavors in the infrared. Our example does not contradict the proof of
the a-theorem via a-maximization, due to the presence of accidental symmetries
in the infrared limit. Nor does it contradict the holographic a-theorem,
because these gauge theories do not possess weakly-curved holographic duals.Comment: 22 pages, 4 figures. v3: The conclusion in the previous version was
superseded. Please refer to the abstract for the detail

### Bounds on Operator Dimensions in 2D Conformal Field Theories

We extend the work of Hellerman (arxiv:0902.2790) to derive an upper bound on
the conformal dimension $\Delta_2$ of the next-to-lowest nontrival primary
operator in unitary two-dimensional conformal field theories without chiral
primary operators. The bound we find is of the same form as found for
$\Delta_1$: $\Delta_2 \leq c_{tot}/12 + O(1)$. We find a similar bound on the
conformal dimension $\Delta_3$, and present a method for deriving bounds on
$\Delta_n$ for any $n$, under slightly modified assumptions. For asymptotically
large $c_{tot}$ and fixed $n$, we show that $\Delta_n \leq
\frac{c_{tot}}{12}+O(1)$. We conclude with a brief discussion of the
gravitational implications of these results.Comment: Corrected typos; revised arguments (adding detail) for clarity,
results unchange

### Axion-Dilaton Black Holes

In this talk some essential features of stringy black holes are described. We
consider charged four-dimensional axion-dilaton black holes. The Hawking
temperature and the entropy of all solutions are shown to be simple functions
of the squares of supercharges, defining the positivity bounds. Spherically
symmetric and multi black hole solutions are presented. The extreme solutions
have some unbroken supersymmetries. Axion-dilaton black holes with zero entropy
and zero area of the horizon form a family of stable particle-like objects,
which we call holons. We discuss the possibility of splitting of nearly extreme
black holes into holons.Comment: 8 pages, LATEX, (Talk presented at the TEXAS/PASCOS conference,
Berkeley, December 1992

### Skyrmions and Hall Transport

We derive a generalized set of Ward identities that captures the effects of
topological charge on Hall transport. The Ward identities follow from the 2+1
dimensional momentum algebra, which includes a central extension proportional
to the topological charge density. In the presence of topological objects like
Skyrmions, we observe that the central term leads to a direct relation between
the thermal Hall conductivity and the topological charge density. We extend
this relation to incorporate the effects of a magnetic field and an electric
current. The topological charge density produces a distinct signature in the
electric Hall conductivity, which is identified in existing experimental data,
and yields further novel predictions. For insulating materials with translation
invariance, the Hall viscosity can be directly determined from the Skyrmion
density and the thermal Hall conductivity to be measured as a function of
momentum.Comment: 6+1 pages including Supplemental Material. Version to appear in
Physical Review Letter

### Structure of Topological Lattice Field Theories in Three Dimensions

We construct and classify topological lattice field theories in three
dimensions. After defining a general class of local lattice field theories, we
impose invariance under arbitrary topology-preserving deformations of the
underlying lattice, which are generated by two new local lattice moves.
Invariant solutions are in one--to--one correspondence with Hopf algebras
satisfying a certain constraint. As an example, we study in detail the
topological lattice field theory corresponding to the Hopf algebra based on the
group ring \C[G], and show that it is equivalent to lattice gauge theory at
zero coupling, and to the Ponzano--Regge theory for $G=$SU(2).Comment: 63 pages, 46 figure

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