111,388 research outputs found
Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua
We study marginal and relevant supersymmetric deformations of the N=4
super-Yang-Mills theory in four dimensions. Our primary innovation is the
interpretation of the moduli spaces of vacua of these theories as
non-commutative spaces. The construction of these spaces relies on the
representation theory of the related quantum algebras, which are obtained from
F-term constraints. These field theories are dual to superstring theories
propagating on deformations of the AdS_5xS^5 geometry. We study D-branes
propagating in these vacua and introduce the appropriate notion of algebraic
geometry for non-commutative spaces. The resulting moduli spaces of D-branes
have several novel features. In particular, they may be interpreted as
symmetric products of non-commutative spaces. We show how mirror symmetry
between these deformed geometries and orbifold theories follows from T-duality.
Many features of the dual closed string theory may be identified within the
non-commutative algebra. In particular, we make progress towards understanding
the K-theory necessary for backgrounds where the Neveu-Schwarz antisymmetric
tensor of the string is turned on, and we shed light on some aspects of
discrete anomalies based on the non-commutative geometry.Comment: 60 pages, 4 figures, JHEP format, amsfonts, amssymb, amsmat
Uniformizing higher-spin equations
Vasiliev's higher-spin theories in various dimensions are uniformly
represented as a simple system of equations. These equations and their gauge
invariances are based on two superalgebras and have a transparent algebraic
meaning. For a given higher-spin theory these algebras can be inferred from the
vacuum higher-spin symmetries. The proposed system of equations admits a
concise AKSZ formulation. We also discuss novel higher-spin systems including
partially-massless and massive fields in AdS, as well as conformal and massless
off-shell fields.Comment: 29 pages, references added, final versio
On generating series of finitely presented operads
Given an operad P with a finite Groebner basis of relations, we study the
generating functions for the dimensions of its graded components P(n). Under
moderate assumptions on the relations we prove that the exponential generating
function for the sequence {dim P(n)} is differential algebraic, and in fact
algebraic if P is a symmetrization of a non-symmetric operad. If, in addition,
the growth of the dimensions of P(n) is bounded by an exponent of n (or a
polynomial of n, in the non-symmetric case) then, moreover, the ordinary
generating function for the above sequence {dim P(n)} is rational. We give a
number of examples of calculations and discuss conjectures about the above
generating functions for more general classes of operads.Comment: Minor changes; references to recent articles by Berele and by Belov,
Bokut, Rowen, and Yu are adde
Global and local properties of AdS(2) higher spin gravity
Two-dimensional BF theory with infinitely many higher spin fields is
proposed. It is interpreted as the AdS(2) higher spin gravity model describing
a consistent interaction between local fields in AdS(2) space including
gravitational field, higher spin partially-massless fields, and dilaton fields.
We carry out analysis of the frame-like and the metric-like formulation of the
theory. Infinite-dimensional higher spin global algebras and their
finite-dimensional truncations are realized in terms of o(2,1) - sp(2) Howe
dual auxiliary variables.Comment: 51 pages; v2: comments and refs added, typos removed, JHEP versio
A statistical mechanics framework for the large-scale structure of turbulent von K{\'a}rm{\'a}n flows
In the present paper, recent experimental results on large scale coherent
steady states observed in experimental von K{\'a}rm{\'a}n flows are revisited
from a statistical mechanics perspective. The latter is rooted on two levels of
description. We first argue that the coherent steady states may be described as
the equilibrium states of well-chosen lattice models, that can be used to
define global properties of von K{\'a}rm{\'a}n flows, such as their
temperatures. The equilibrium description is then enlarged, in order to
reinterpret a series of results about the stability of those steady states,
their susceptibility to symmetry breaking, in the light of a deep analogy with
the statistical theory of Ferromagnetism. We call this analogy
"Ferro-Turbulence
Initial data for fluid bodies in general relativity
We show that there exist asymptotically flat almost-smooth initial data for
Einstein-perfect fluid's equation that represent an isolated liquid-type body.
By liquid-type body we mean that the fluid energy density has compact support
and takes a strictly positive constant value at its boundary. By almost-smooth
we mean that all initial data fields are smooth everywhere on the initial
hypersurface except at the body boundary, where tangential derivatives of any
order are continuous at that boundary.
PACS: 04.20.Ex, 04.40.Nr, 02.30.JrComment: 38 pages, LaTeX 2e, no figures. Accepted for publication in Phys.
Rev.
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