4,068 research outputs found

### Noncommutative space-time models

The FRT quantum Euclidean spaces $O_q^N$ are formulated in terms of Cartesian
generators. The quantum analogs of N-dimensional Cayley-Klein spaces are
obtained by contractions and analytical continuations. Noncommutative constant
curvature spaces are introduced as a spheres in the quantum Cayley-Klein
spaces. For N=5 part of them are interpreted as the noncommutative analogs of
(1+3) space-time models. As a result the quantum (anti) de Sitter, Newton,
Galilei kinematics with the fundamental length and the fundamental time are
suggested.Comment: 8 pages; talk given at XIV International Colloquium of Integrable
Systems, Prague, June 16-18, 200

### Weak Chaos from Tsallis Entropy

We present a geometric, model-independent, argument that aims to explain why
the Tsallis entropy describes systems exhibiting "weak chaos", namely systems
whose underlying dynamics has vanishing largest Lyapunov exponent. Our argument
relies on properties of a deformation map of the reals induced by the Tsallis
entropy, and its conclusion agrees with all currently known results.Comment: 19 pages, Standard LaTeX2e, v2: addition of the last paragraph in
Section 4. Three additional refs. To be published in QScience Connec

### Cayley--Klein Contractions of Quantum Orthogonal Groups in Cartesian Basis

Spaces of constant curvature and their motion groups are described most
naturally in Cartesian basis. All these motion groups also known as CK groups
are obtained from orthogonal group by contractions and analytical
continuations. On the other hand quantum deformation of orthogonal group $SO(N)$ is most easily performed in so-called symplectic basis. We reformulate its
standard quantum deformation to Cartesian basis and obtain all possible
contractions of quantum orthogonal group $SO_q(N)$ both for untouched and
transformed deformation parameter. It turned out, that similar to undeformed
case all CK contractions of $SO_q(N)$ are realized. An algorithm for obtaining
nonequivalent (as Hopf algebra) contracted quantum groups is suggested.
Contractions of $SO_q(N), N=3,4,5$ are regarded as an examples.Comment: The statement of the basic theorem have correct. 30 pages, Latex.
Report given at X International Conference on Symmetry Methods in Physics,
August 13-19, 2003, Yerevan, Armenia. Submitted in Journal Physics of Atomic
Nucle

### Quark--anti-quark potential in N=4 SYM

We construct a closed system of equations describing the quark--anti-quark
potential at any coupling in planar N=4 supersymmetric Yang-Mills theory. It is
based on the Quantum Spectral Curve method supplemented with a novel type of
asymptotics. We present a high precision numerical solution reproducing the
classical and one-loop string predictions very accurately. We also analytically
compute the first 7 nontrivial orders of the weak coupling expansion.
Moreover, we study analytically the generalized quark--anti-quark potential
in the limit of large imaginary twist to all orders in perturbation theory. We
demonstrate how the QSC reduces in this case to a one-dimensional Schrodinger
equation. In the process we establish a link between the Q-functions and the
solution of the Bethe-Salpeter equation.Comment: 31 pages, 1 figure; v2: minor correcton

### Numerical results for the exact spectrum of planar AdS4/CFT3

We compute the anomalous dimension for a short single-trace operator in
planar ABJM theory at intermediate coupling. This is done by solving
numerically the set of Thermodynamic Bethe Ansatz equations which are expected
to describe the exact spectrum of the theory. We implement a truncation method
which significantly reduces the number of integral equations to be solved and
improves numerical efficiency. Results are obtained for a range of 't Hooft
coupling lambda corresponding to $0 \leq h(\lambda) \leq 1$, where h(lambda) is
the interpolating function of the AdS4/CFT3 Bethe equations.Comment: v3: corrected Acknowledgements section; v4: minor changes, published
version; v5: fixed typos in Eq. (3.9

### The Isoperimetric Profile of a Noncompact Riemannian Manifold for Small Volumes

In the main theorem of this paper we treat the problem of existence of
minimizers of the isoperimetric problem under the assumption of small volumes.
Applications of the main theorem to asymptotic expansions of the isoperimetric
problem are given.Comment: 33 pages, improved version after the referee comments, (Submitted

### Embedding relatively hyperbolic groups in products of trees

We show that a relatively hyperbolic group quasi-isometrically embeds in a
product of finitely many trees if the peripheral subgroups do, and we provide
an estimate on the minimal number of trees needed. Applying our result to the
case of 3-manifolds, we show that fundamental groups of closed 3-manifolds have
linearly controlled asymptotic dimension at most 8. To complement this result,
we observe that fundamental groups of Haken 3-manifolds with non-empty boundary
have asymptotic dimension 2.Comment: v1: 18 pages; v2: 20 pages, minor change

### On contractions of classical basic superalgebras

We define a class of orthosymplectic $osp(m;j|2n;\omega)$ and unitary
$sl(m;j|n;\epsilon)$ superalgebras which may be obtained from $osp(m|2n)$ and
$sl(m|n)$ by contractions and analytic continuations in a similar way as the
special linear, orthogonal and the symplectic Cayley-Klein algebras are
obtained from the corresponding classical ones. Casimir operators of
Cayley-Klein superalgebras are obtained from the corresponding operators of the
basic superalgebras. Contractions of $sl(2|1)$ and $osp(3|2)$ are regarded as
an examples.Comment: 15 pages, Late

### Analytic Solution of Bremsstrahlung TBA

We consider the quark--anti-quark potential on the three sphere or the
generalized cusp anomalous dimension in planar N=4 SYM. We concentrate on the
vacuum potential in the near BPS limit with $L$ units of R-charge.
Equivalently, we study the anomalous dimension of a super-Wilson loop with L
local fields inserted at a cusp. The system is described by a recently proposed
infinite set of non-linear integral equations of the Thermodynamic Bethe Ansatz
(TBA) type. That system of TBA equations is very similar to the one of the
spectral problem but simplifies a bit in the near BPS limit. Using techniques
based on the Y-system of functional equations we first reduced the infinite
system of TBA equations to a Finite set of Nonlinear Integral Equations
(FiNLIE). Then we solve the FiNLIE system analytically, obtaining a simple
analytic result for the potential! Surprisingly, we find that the system has
equivalent descriptions in terms of an effective Baxter equation and in terms
of a matrix model. At L=0, our result matches the one obtained before using
localization techniques. At all other L's, the result is new. Having a new
parameter, L, allows us to take the large L classical limit. We use the matrix
model description to solve the classical limit and match the result with a
string theory computation. Moreover, we find that the classical string
algebraic curve matches the algebraic curve arising from the matrix model.Comment: 50 pages, 5 figures. v2: references added, JHEP versio

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